characterization of creping marks in paper1219118/...master of science thesis in electrical...

Master of Science Thesis in Electrical EngineeringDepartment of Electrical Engineering, Linköping University, 2018

Characterization of crepingmarks in paper

Isak Strömberg

Master of Science Thesis in Electrical Engineering

Characterization of creping marks in paper

Isak Strömberg

LiTH-ISY-EX--18/5151--SE

Supervisor: Gustav Hägerisy, Linköpings universitet

Niklas ElvinBillerudKorsnäs

Examiner: Klas Nordbergisy, Linköpings universitet

Computer Vision LaboratoryDepartment of Electrical Engineering

Linköping UniversitySE-581 83 Linköping, Sweden

Copyright © 2018 Isak Strömberg

Abstract

The cost and environmental damage of reclaims is a large problem within thepaper industry. With certain types of paper, so called crepe marks on the pa-per’s surface is a common issue, leading to printing defects and consequentlyreclaims. This thesis compares four different image analysis methods for evalu-ating crepe marks and predicting printing results. The methods evaluated con-sists of one established methods, two adaptations of established methods andone novel method. All methods were evaluated on the same data, topographicheight images of paper samples from 4 paper rolls of similar type but differingin roughness. The method based on 1D Fourier analysis and the method basedon fully convolutional networks performs best, depending on if speed or detailedcharacteristics is a priority.

iii

Contents

Notation ix

1 Introduction 11.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

1.1.1 Creping mark definition . . . . . . . . . . . . . . . . . . . . 11.2 Problem Formulation . . . . . . . . . . . . . . . . . . . . . . . . . . 31.3 Thesis Process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

1.3.1 Pilot Study . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31.3.2 Samples and Measurements . . . . . . . . . . . . . . . . . . 41.3.3 Analysis Methods . . . . . . . . . . . . . . . . . . . . . . . . 4

1.4 Limitations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

2 Theory 52.1 Papermaking . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

2.1.1 Flexographic Printing . . . . . . . . . . . . . . . . . . . . . . 62.2 Photometric Stereo . . . . . . . . . . . . . . . . . . . . . . . . . . . 62.3 Wavelet Transform . . . . . . . . . . . . . . . . . . . . . . . . . . . 82.4 Artificial Neural Networks . . . . . . . . . . . . . . . . . . . . . . . 9

2.4.1 Training . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102.5 Convolutional Neural Networks . . . . . . . . . . . . . . . . . . . . 11

2.5.1 Training . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

3 Related Research 153.1 Fourier Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153.2 Multiresolution Analysis . . . . . . . . . . . . . . . . . . . . . . . . 173.3 Neural Networks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

4 Method 214.1 Paper samples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

4.1.1 Trial printing . . . . . . . . . . . . . . . . . . . . . . . . . . 224.2 Measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

4.2.1 Data set . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 224.2.2 Verification . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

v

vi Contents

4.3 Fourier Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 244.3.1 2D Fourier Analysis . . . . . . . . . . . . . . . . . . . . . . . 244.3.2 1D Fourier Analysis . . . . . . . . . . . . . . . . . . . . . . . 24

4.4 Multiresolution Analysis . . . . . . . . . . . . . . . . . . . . . . . . 254.4.1 Detection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 264.4.2 Segmentation . . . . . . . . . . . . . . . . . . . . . . . . . . 274.4.3 Characterization . . . . . . . . . . . . . . . . . . . . . . . . . 29

4.5 Neural Net Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . 294.5.1 Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 294.5.2 Training Data . . . . . . . . . . . . . . . . . . . . . . . . . . 304.5.3 Hyperparameters . . . . . . . . . . . . . . . . . . . . . . . . 304.5.4 Training . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 314.5.5 Implementation . . . . . . . . . . . . . . . . . . . . . . . . . 31

5 Results 335.1 Trial Printing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 335.2 Measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34

5.2.1 Verification . . . . . . . . . . . . . . . . . . . . . . . . . . . . 345.3 Fourier Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36

5.3.1 2D Fourier Analysis . . . . . . . . . . . . . . . . . . . . . . . 365.3.2 1D Fourier Analysis . . . . . . . . . . . . . . . . . . . . . . . 37

5.4 Multiresolution Analysis . . . . . . . . . . . . . . . . . . . . . . . . 385.5 Neural Net Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . 40

5.5.1 Network Selection and Training . . . . . . . . . . . . . . . . 405.5.2 Data Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . 40

6 Discussion 436.1 Printing and Measurements . . . . . . . . . . . . . . . . . . . . . . 436.2 Fourier Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44

6.2.1 2D Fourier Analysis . . . . . . . . . . . . . . . . . . . . . . . 446.2.2 1D Fourier Analysis . . . . . . . . . . . . . . . . . . . . . . . 44

6.3 Multiresolution Analysis . . . . . . . . . . . . . . . . . . . . . . . . 446.4 Neural Net Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . 45

7 Conclusion 477.1 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 477.2 Project Work in a Wider Context . . . . . . . . . . . . . . . . . . . . 487.3 Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48

A Neural Network Structures 51

B 1D Fourier Analysis 57

C Multiresolution Analysis 61

D Neural Net Analysis 69

Contents vii

Bibliography 75

Notation

Some sets

Notation Meaning

R Set of real numbers

Abbreviations

Abbreviation Meaning

md Machine directioncd Cross directionuca Uncovered areasem Scanning electron microscopefft Fast Fourier transformmra Multiresolution analysiscd Artificial neural networkcd Back propagationcnn Convolutional neural networkfcn Fully convolutional network

ix

1Introduction

1.1 Background

Reclaims of printed paper is a large problem within the paper industry. It leadsto increased costs in the form of transport, printing and waste costs, as well asincreased environmental damage. When producing certain types of paper irreg-ularities in the paper surface might occur, so called creping marks. These marksresult in a poor and uneven printing quality, which in turn leads to costly re-claims of printed paper. If these creping marks could be characterized beforeprinting, their characteristics could be used to predict the printing result, whichmeans that poor quality paper rolls could be discarded before printing.

Currently there are no methods for predicting printing quality from these cre-ping marks with sufficient accuracy. If the poor quality paper resulting in print-ing defects could be detected before printing, large gains would be achieved bothfinancially and environmentally. Furthermore the iteration time when develop-ing new types of paper and tuning the production process would be drasticallydecreased. The purpose of this thesis is to examine different analysis methods todetermine if such a prediction of printing quality from creping marks is possible.

1.1.1 Creping mark definition

The irregularities mentioned in the previous section appear as small bumps ordents in the surface due to unwanted folds in the paper. In the context of thisreport, these will be referred to as creping marks. Creping marks appear as dentsor pits on one side of the paper, henceforth called the front side, and as bumps orhills on the other side, henceforth called the back side.

These marks are characterized by their height and shape. The height is greaterthan that of the normal variations in the paper’s surface, generally around 2-10 µm

1

2 1 Introduction

compared to <1 µm. The shape is generally a long, thin and fairly straight line.A typical crepe mark is shown in figure 1.1.

Furthermore creping marks generally appear periodically, either in local clus-ters or evenly distributed over an entire sheet of paper. Another prominent fea-ture is that these marks generally are oriented so that they form wave fronts in themachine direction (MD). The machine direction is the paper’s direction of travelthrough the paper machine and the perpendicular direction the cross direction.These properties are shown in figure 1.2.

Figure 1.1: 3D image of a single crepe mark showing typical size, shape andorientation

5 10 15 20 25 30

CD [mm]

5

10

15

20

25

30

MD

[m

m]

Figure 1.2: Orientation of creping marks relative MD and apperance eitherin clusters (left) or evenly throughout the entire sample (right)

1.2 Problem Formulation 3

1.2 Problem Formulation

The task of predicting printing results due to creping marks can be divided intothree subtask: producing good enough raw data from paper samples, producinggood enough characteristics from raw data and predicting printing results fromthese characteristics. This process flow is illustrated in figure 1.3.

Methods used to produce raw data from paper samples are henceforth calledmeasurement methods. This could for instance be image capture of the sampleilluminated with raking light. Methods used to produce crepe mark characteris-tics (i.e. information about the crepe marks) will be referred to as analysis meth-ods. This could for instance be counting the number of marks in a given area.Methods used to predict printing results from these characteristics will be calledprediction methods.

Figure 1.3: Prediction flowchart for the paper analysis process, showing dif-ferent methods and data types.

This thesis aims to determine if this is possible by answering the followingquestions:

• How well suited is photometric stereo for producing raw data for analysisof crepe marks?

• Which analysis method produces the most accurate crepe mark characteris-tics?

• How can these characteristics be used to predict printing results?

1.3 Thesis Process

The thesis work process is divided into three main parts: pilot study, samplecollection and measurements, and evaluation of analysis methods. Predictionmethods will not be examined in detailed, which is described further in section1.4.

1.3.1 Pilot Study

A pilot study was made, with the goal of finding suitable measurement and anal-ysis methods. In the pilot study, both analysis methods developed specificallyfor paper evalutation and more general surface characterization methods wereconsidered.

4 1 Introduction

1.3.2 Samples and Measurements

A set of physical samples from paper rolls of varying quality (ranging from verypoor to very good) were collected. These were then evaluated using a measure-ment method. The purpose of the evaluation is to find the best conditions forfurther analysis. This is done by comparing the data from the different methodswith established methods, e.g. scanning electron microscope as well as visualinspection.

The pilot study found that photometric stereo is a good candidate measure-ment method and the L&W OptiTopo will be used to produce raw data frompaper samples. The OptiTopo is a commercially available system for measuringsurface topology on a small scale (1 - 100 µm). The device uses photometricstereo, which is explained further in section 2.2. More details on the OptiTopo’sproperties are presented in section 4.2.

1.3.3 Analysis Methods

Evaluation of the proposed analysis methods was made on data from the bestmeasurement method. The purpose of the evaluation is to find the method whichproduces the most accurate characteristics. Using some or all of these character-istics, the printing result will then be predicted, and the predictions will thenbe compared to the actual printing results. Printing results are measured usinguncovered area. Uncovered area (uca) is a measurement commonly used to quan-tify printing results. As the name suggests it’s a measure of the amount of printedarea which is not covered in ink after printing, meaning a lower value is better.

The following analysis methods were proposed by the pilot study:

• Fourier Transform Analysis

• Multiresolution Analysis

• Neural Networks

1.4 Limitations

For logistical reasons it is not possible verify the measurement method by mea-suring the exact same area with different methods. Instead validation will belimited to comparing paper samples from the same roll, and therefore with thesame general characteristics, with different methods.

The prediction of printing results will be done at a very simple level, i.e. a sim-ple classification (good or bad) from a given set of characteristics. No predictionof exact printing defects will be done, since it is a significantly harder problemand not commersially relevant.

2Theory

This chapter contains the theoretical concepts used in this thesis. It contains thebasis needed for understanding the following chapters. Each subsection, how-ever, is independent and can be read in any order.

2.1 Papermaking

Papermaking is the process of producing different types of paper from woodenfibres. Most paper machines in use today are based on the principles of the Four-drinier paper machine. The main feature of this design is that it uses a wovenmesh conveyor belt to produce a continious paper web [4]. As mentioned previ-ously the paper’s direction of travel through the machine is called the machinedirection and the perpendicular direction is called the cross direction. These aregenerally distinguished between, since the paper’s properties (strength, extensi-bility etc.) in each direction may differ.

The paper machine is fed with pulp, either from mechanical or chemical pulp-ing or return fibres, and can be divided into four main sections (see figure 2.1 fora schematic image):

1. Forming section - pulp containing a mix of fibre and water (at around0.1-1 % fibre concentration) is fed through the headbox onto the wire form-ing a wet web of fibre. Using air suction the dry content (dryness) of theweb is increased to around 20 %.

2. Press section - the web is pressed with felt covered rollers further increasingthe dryness to around 40 %.

3. Drying section - the paper web is dried between a large number of steamheated rolls on the inside and felt on the outside.

5

6 2 Theory

4. Finishing section - lastly the paper may be coated to achieve specific prop-erties and is pressed once more (so called calendering) to achieve a smoothsurface.

Figure 2.1: Schematic image of a Fourdrinier paper machine showing itsmain components.

2.1.1 Flexographic Printing

Flexography is a popular printing technique used for industrial scale printing. Ituses one or several flexible relief plates to apply ink to the printing surface, inprinciple working as a modern equivalent of a letter press. Flexography’s mainadvantages is that it works with a wide range of inks and adapts well to differentmaterials, which allows printing on almost any type of substrate.

In short, flexographic printing works using four cylinders, as seen in figure2.2. The Fountain cylinder picks up ink from a tray and applies it to the Aniloxcylinder, which has microscopic pores all over its surface to ensure the rightamount of ink is tranfered Plate cylinder. The Plate cylinder, which holds theflexible printing plate, then prints on to the substrate using the impression cylin-der to create pressure on to the substrate.

2.2 Photometric Stereo

Traditional stereo image capture techniques determine the distance to an objectby comparing images captured from different angles, finding matching featuresin all images and using triangulation to estimate the range. Determining thesurface structure (its surface normals) of an object is done in the same way, bylocating a number of matching features along the objects surface. However, find-ing these corresponding features is sometimes difficult, especially when dealingwith uniformly textured surfaces.

In 1980 Woodham [12] introduced photometric stereo as a solution to thisproblem. Photometric stereo is a technique for estimating surface normals usinga stationary image capture point and instead varying the lighting conditions. The

2.2 Photometric Stereo 7

Figure 2.2: Schematic image of a flexographic printing press

technique is based on the fact that the amount of light reflected off a surfacedepends on the surface’s orientation with respect to the observer as well as to thelight source.

Given a camera positioned along the z-axis above a surface f (x, y), assumingLambertian (diffuse) reflectance and 3 known point-like light sources positionedfar away from f (x, y) (as shown in figure 2.3), f (x, y) can be determined throughthe following equations.

Let ik(x, y) be the k:th image intensity at the point (x, y),

N = (p, q,−1)T /√p2 + q2 + 1

the normal unit vector to the surface f (x, y) at the point (x, y), Lk the unit illu-mination vector from the surface towards the k:th light source and ρ the surfacereflectance at the given point (x, y). Then the following equation holds

I = ρ ·LN, I = [i1, i2, i3]T , L = [l1, l2, l3]T .

Provided that the three illumination vectors L1, L2 and L3 are non-coplanar (notlocated in the same plane) the matrix L is invertible and

M = L−1I = ρ ·N,

where M = [m1, m2, m3]T . Then the surface gradient components and surfacereflectance are given by

p = −m1

m3, q = −m2

m3, ρ =

√m2

1 + m22 + m2

3.

The surface function f (x, y) can be determined by integrating over the normalunit vectors N for each point (x, y).

8 2 Theory

Worth noting is that it is possible to estimate the surface topography usingonly two light sources. This requires the surface reflectance to be known. How-ever, there are ways to overcome this problem, which is described further in sec-tion 4.2.

Figure 2.3: Photometric stereo setup using three light sources

2.3 Wavelet Transform

The wavelet transform is a signal transform which is localized both in time andfrequency, unlike for instance the Fourier transform which is only localized in fre-quency. Instead of the basis functions being sines and cosines (as with the Fouriertransform), the bases in wavelet transform are decompositions and translationsof a function called the mother wavelet [11]. The basis decomposition is done bypowers of 2 and the translation with fixed values (which are also decomposed bythe same powers of 2). The signal f (t) is then transformed by projecting it ontothe wavelet bases.

As with many other transforms there exists both a continous and a discretewavelet transform (CWT and DWT respectively). For most real-world applica-tions only the DWT is useful.

Let L2(R) be the space of square integrable functions on real number andψ ∈ L2(R) some mother wavelet. Then the DWT bases are given by

ψm,n(t) =1√

2mψ

(t − n2m

2m

), m, n ∈ Z,

2.4 Artificial Neural Networks 9

and the DWT Wf (m, n) of f (t) ∈ L2(R) by

Wf (m, n) = 〈f (t)|ψm,n〉 =1√

2m

∞∫−∞

f (t)ψ∗(t − n2m

2m

)dt.

It is possible to choose ψ such that the set of wavelets is orthonormal and com-plete, and the signal f (t) can then be perfectly reconstructed as

f (t) =∑m,n

Wf (m, n)ψm,n.

Such a orthonormal and complete set of wavelets it is possible to form a fil-terbank, that is a set of filters that decomposes a signal f (t) into a number ofbandpass filtered components. This decomposition is done by projecting f (t)onto a set of nested subspaces V0 ⊂ V1 ⊂ V2 ⊂ ... ⊂ L2(R), where V0 contains theroughest approximation of f (t), V1 the second roughest, and so on.

Wavelet transforms allows a signal to be decomposed into different frequencyband with good accuracy (meaning a very small reconstruction error). This prop-erty is exploited in multiresolution analysis (described further in section 3.2)which is commonly used to examine surface profiles.

2.4 Artificial Neural Networks

Artificial Neural Networks (ann:s) is a machine learning approach inspired bynature. The general design is inspired by the human brain and its network ofnerve cells (neurons) [5]. Due to recent advances in computational power, ann:sand similar machine learning techniques, such as convolutional neural networks(described in section 2.5), have made great advances within the field of imageclassification. This can be used to characterize surfacess, which is described fur-ther in section 3.3.

An ann consists of an input layer, an arbitrary number of hidden layers andan output layer. This is referred to as the ann’s network structure. The networkstructure describes the network’s layers and the connections between each layer.Each layer consists of a number of nodes, as seen in figure 2.4. The nodes of alayer are connected both to the previous and the next layer (if such a layer exists).Two layers can be either fully connected, meaning that every node in the firstlayer is connected to every layer of the second (as with the hidden and outputlayer in figure 2.4), or partially connected (as with the input and hidden layer infigure 2.4).

Every node in an ann consists of an artificial neuron, which is made fromtwo parts: a weighted summation and an activation function. A schematic imageof an artifical neuron is presented in figure 2.5. For a given node i let xi be thevector containing the input, wi the input weights and yi the scalar output of thenode. Then their relation is given by

zi = wiT xi (2.1)

yi = f (zi) (2.2)

10 2 Theory

Figure 2.4: An artificial neural network with an input layer, locally con-nected to a hidden layer, fully connected to an output layers

where f ( · ) is some non-linear activation function. The main purpose of the acti-vation function is to introduce non-linearity into the network and to confine theneuron output to a given interval. Common activation functions are the sigmoidfunction, the hyperbolic tangent function and the rectifier

f (z) =1

1 + exp(z),

f (z) = tanh(z) =1 − exp(−2z)1 + exp(−2z)

,

f (z) = max(0, z).

Depending on if the output should be on the interval (0, 1), (−1, 1) or (0,∞).

2.4.1 Training

When a network structure has been selected, the ann must be trained to fit theproblem at hand. This is generally done by defining a cost function and opti-mizing the neuron input weights to minimize that cost function. This is doneby using training data. Training data is a set of input data for which the outputis known. Evaluating the training data using the network a network output isobtained, which can then be compared to the ground truth output of the trainingdata. For this type of data a suitable cost function could be the distance betweenthe correct output and the network output. The weights could then be optimizedby calculating the gradient descent of the cost function, which means changingthe weights to minimize the cost function.

2.5 Convolutional Neural Networks 11

Figure 2.5: An artificial neuron with N inputs and M output, illustratingequation 2.1

This process can be split in to two parts: a forward pass and a backward pass.During the forward pass the network is used to calculate output values basedon the training data input. During the backwards pass the network output iscompared to the true output and the network weights are updated using somelearning algorithm like gradient descent. One forward and backward pass on allthe training data is refered to as an epoch.

However, a problem with this approach is that calculating the gradient for thehidden layers is very difficult, since desired results generally only are availablefor the output layer. In 1986 Rumelhart et al. [10] proposed the back propaga-tion (bp) algorithm as a solution to this problem. The bp algorithm is a rigorousmethod for setting the weights of the hidden layers of an ann.

2.5 Convolutional Neural Networks

Convolutional Neural Networks (cnn) are a type of ann often used in imageanalysis. In 1968 Hubel and Wiesel [6] found that the visual cortex of monkeyscontains cells, where each cell is sensitive to a sub-region of the monkey’s visualfield, called a receptive field. This knowledge inspired the design of cnn:s whereadjacent layers are only locally connected (explained shortly). Typically cnn:sconsists of one or more convolutional and pooling layers followed by one or amore fully connected layers (as shown in figure 2.6).

The main features of cnn:s are their convolutional and pooling layers whichallows for strong feature extraction and shift invariance [3]. Generally, each con-volutional level of a cnn consists of a convolutional layer, a pooling layer, and anon-linearity of some sort.

Convolving an image with different filters (kernels) is an established methodfor feature extraction. The principle of a convolutional layer is the same as withmanual feature extraction through convolution. The image is convolved with N

12 2 Theory

Figure 2.6: cnn with two convolution + pooling layers and two fully con-nected layers

kernels, producing N images. An example of such a convolution, along with itsresponse, is shown in figure 2.7. Worth noting is that the convolution kernelsused in cnn:s are trained by the network, rather than handmade like the filter inthe figure. Through pooling (described below) the strongest features from eachimage are extracted and passed on through the network to the next convolutionallevel or the fully connected layers.

Figure 2.7: Example of one convolutional filter and its response when con-volved with an image

Pooling layers help reduce the dimensionality of the network, as well as pro-viding some shift invariance. The most common type of pooling is a max pool-ing, where only the maximum value within the pooling window is passed on asoutput. Pooling layers properties are controlled by two parameters: stride andsize. The stride specifies the distance between two adjacent pools within thesame layer, while pooling size specifies the size of the pool.

Each convolutional level of the network also contains some kind of nonlinearactivation function. These serve the same purpose as the activation functionsdescribed in section 2.4, namely introducing non-linearities to the network andconfining the layer output to a given interval.

2.5 Convolutional Neural Networks 13

2.5.1 Training

Due to the size of most cnn:s and consequently the size of their training dataset, training can become slow and computationally demanding. A popular strat-egy when training cnn:s is training using mini-batch gradient descent. This isa version of the gradient descent method described in section 2.4.1 were only asubset of the training data (a mini-batch) is used to calculate the gradient descentand update the layer weights. This means that each epoch consists of several it-erations were one forward and one backward pass is performed on a mini-batchof data. This method of training is often better in terms of avoiding local min-ima, increasing convergence speed and limiting the amount of memory neededto train (since only the mini-batch needs to be kept in memory).

Another important part of training cnn:s is validation. This is done by split-ting the available data set into two parts: training data and validation data. Thetraining data is, as mentioned earlier, used to train the network by minimizingthe training error. The validation data is used to prevent over-fitting, that is fit-ting the neural network to the specific data in the training data, rather than theunderlying process. This is done by comparing the training and validation errorand their change during training.

3Related Research

From the pilot study three candidate analysis methods were found. The firsttwo methods: Fourier transform analysis and multiresolution analysis, are bothcommonly used when characterizing paper surfaces and were therefore deemedsuitable. The last method: neural network analysis, is based on a state-of-the-arttechnique in image processing and has been used to characterize other types ofsurfaces with good results. This chapter contains a more detailed description ofthe research related to these three methods.

Unlike the previous chapter, which contains general theory, this chapter de-scribes specific implementations similar to the ones used in this thesis.

3.1 Fourier Analysis

In [9] Raunio and Ritala propose an analysis method for characterizing crepingpatterns (similar to the creping marks examined in this report), by looking at thepower spectrum of a surface depth image. The surface images used as input wereproduced using photometric stereo, with a setup similar to the one described insection 2.2. Ideally, the creping patterns should be a sinusoidal wave front withno variation regarding amplitude, phase or frequency. Such a pattern would pro-duce a infinately narrow peak pair in the power spectrum. The authors proposethat, by examining how much the actual spectrum deviates from the ideal, it ispossible to quantify the creping pattern variations.

Let x be the point (x, y) in spatial space, k the point in frequency space, andF(k) the Fourier transform of f (x), then the power spectrum S(k) is

S(k) = |F(k)|2. (3.1)

In order to reduce uncertainty, the spectrum estimate was computed using Welch’s[1] method with 15 subimages (1/2 height, 1/3 width and 50 % overlap), and to

15

16 3 Related Research

reduce edge effects, a Hamming window [7] was applied to each subimage. Thespectrum S(i, j) is then calculated as

S(i, j) =1

15

15∑k=1

Sk(i, j), (3.2)

which produces a spectrum, for instance looking like the one shown in figure 3.1.

32 24 16 8 0 8 16 24 32

CD [mm-1

]

32

24

16

8

0

MD

[m

m-1

]

Figure 3.1: 2D power spectrum of the height image shown in figure 4.1.Calculated as described by equations 3.1 and 3.2.

This Welch spectrum estimate was then transformed to polar coordinates pro-ducing a spectrum, for instance looking like the one shown in figure 3.2. Themain lobe of this polar power spectrum is then approximated with a 2D Gaus-sian function, giving the intensity function

I(si) = exp(−1

2(si − s0)TΣ−1(si − s0)

), Σ =

(W 2 00 Q2

)(3.3)

where si is a point (k, φ) in polar frequency space and s0 is a parameter determin-ing the location of the Gaussian function in the same space. The parameters Wand Q determine the standard deviation of the intensity function in the k and φ,meaning the frequency and angle variations of the creping pattern respectively.

3.2 Multiresolution Analysis 17

0 45 90 135 180

Angle [deg]

32

24

16

8

0

Fre

quency [m

m-1

]

Figure 3.2: 2D spectrum shown in figure 3.1 converted to polar coordinates.

3.2 Multiresolution Analysis

In [8] Raja et al. describe how the height of most manufactured surfaces consistsof a number of spatial frequencies, and the common need of separating these fre-quency ranges. High frequency variations are refered to as roughness, mediumfrequency variations as waviness and low frequency variations as form. An exam-ple of this partitioning is shown in figure 3.5. The authors also examine a numberof commonly used methods in surface metrology. Multiresolution Analysis (mra)is presented as one of the most powerful methods for separating frequency bandswhile minimizing distortion.

In [13] Liu and Raja describe an application of mra for surface profile anal-ysis and evaluates suitable wavelet bases based on different mother wavelets, asdescribed in section 2.3. Four filter banks were examined by the authors: twobased on Daubechies bases (shown in figure 3.3) and two based on biorthogonalspline wavelets (shown in figure 3.4). The main differences between the two typesare a much flatter passband for the Daubechies filter but also a non-linear phasefrequency response, whereas the spline filters have large ripples in the passbandmagnitude but linear phase frequency response.

The four different filter banks were used to deconstruct different 1D surfaceprofiles, from typical industrial applications. For surface analysis purposes itwas concluded that both filter types performed very well compared to a moretraditional Gaussian filter, with a slight edge to the Daubechies filters, due tosmaller signal reconstruction error.

18 3 Related Research

0 2 4 6

0

0.5

1Daubechies8 Scaling Functions

0 2 4 6

-1

-0.5

0

0.5

Daubechies8 Wavelets

0 2 4 6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

Daubechies16 Scaling Functions

0 2 4 6

-0.5

0

0.5

Daubechies16 Wavelets

Figure 3.3: Scaling and wavelet functions of Daubechies wavelets

0 2 4 6

-2

0

2

4

Biorthogonal m3n3 Scaling Functions

De

Re

0 2 4 6

-5

0

5

Biorthogonal m3n3 Wavelets

De

Re

0 2 4 6

0

0.5

1

1.5

Biorthogonal m5n5 Scaling Functions

De

Re

0 2 4 6

-1

-0.5

0

0.5

1

1.5

Biorthogonal m5n5 Wavelets

De

Re

Figure 3.4: Scaling and wavelet functions of biorthogonal spline waveletsfor both deconstruction (De) and reconstruction (Re)

3.3 Neural Networks 19

0 500 1000 1500 2000 2500 3000 3500 40000

0.2

0.4H

eig

ht

Raw profile

0 500 1000 1500 2000 2500 3000 3500 4000-0.05

0

0.05

Heig

ht

Roughness

0 500 1000 1500 2000 2500 3000 3500 4000-0.1

0

0.1

Heig

ht

Waviness

0 500 1000 1500 2000 2500 3000 3500 40000.05

0.1

0.15

Heig

ht

Form

Figure 3.5: Example of paper surface profile divided into roughness, wavi-ness and form

3.3 Neural Networks

In [2] Yang et al. propose a method for classifying and locating (detecting) defectsin a steel surface using an ann trained using the bp algorithm (as described insections 2.4 and 2.4.1 respectively) and basic morphology on binary images. Theann used by the authors was a 3-layer fully connected network, using the RGB-data of each pixel in an image as input. This meant that the network was verysimple and had to be evaluated on each pixel of an image separately.

The authors used images of industrial steel surfaces with defects, which hadbeen manually labelled, as training and validation data for the network. Eachimage was preprocessed by median filtering and some brightness and contrastenhancements. Then, the ann was trained using the bp algorithm.

The trained annwas then used to detect pixels showing defects in the surface.Following some morphological operations, to reduce the number of misclassifiedpixles due to noise, this produced very good results, by far outperforming tradi-tional segmentation methods.

4Method

This chapter contains a detailed description of the implementation of the dif-ferent analysis methods evaluated in this thesis, as well as a description of theprocess of collecting the data used to evaluate all methods.

Three different analysis methods are described: Fourier analysis, multiresolu-tion analysis and neural net analysis. Furthermore the Fourier analysis is dividedin to a 1-dimensional and a 2-dimensional version. All methods are based on theresearch described in the previous chapter. Either as a direct adaptation, in thecase of the 2D Fourier analysis, as an extension, in the case of the multiresolutionanalysis, or new adaptation inspired by the same principles, as in the case of the1D Fourier analysis and neural net analysis.

All methods use the same height images, obtained by measuring the papersamples with the OptiTopo, as their input data. The data collection is describedin detail below.

4.1 Paper samples

Four paper rolls of the same paper type (i.e. same weight and from the same ma-chine), produced with slightly different settings (machine speed, pulp type etc.),were selected to create the sample set for all experiments. Due to the differencesin production, these rolls had varying surface roughness. As a baseline, each rollwas measured using the standardized Bendtsen air leakage technique on bothsides. In short, Bendtsen technique measures surface roughness by measuring airleakage from a pressurized measuring head traversing the surface.

From these four rolls a number of samples were cut, approximately 20×30 cmin size. 16 unprinted samples and 32 printed samples (16 front side + 16 backside) were produced from each roll, producing a total of 192 physical samplesthat form the sample set. The printing process is described further in section

21

22 4 Method

4.1.1.

4.1.1 Trial printing

After unprinted samples had been collected, all four rolls went through trialprinting using a full-scale flexographic printing press. This was done in orderto determine the uca of each material after full-tone printing. Printing was doneon both front and back side of all four rolls, using optimized printing settings.

The uca of each roll was also compared to the values of previously printedmaterial of similar type, which had been approved either by customers or qualitycontrol panels.

4.2 Measurements

The topography of all unprinted paper sample surfaces were measured usingthe L&W OptiTopo Expert. It uses photometric stereo (described in section 2.2)to determine surface topography, using two opposite facing light sources. Asdescribed in section 2.2 this requires the surface reflectance to be known. TheOptiTopo overcomes this problem by capturing an additional image, illuminatedby both light sources simultaneously, to determine surface reflectance.

The measured area of the OptiTopo is 32 × 32 mm and the resolution 2048 ×2048 pixels, which gives a pixel size of approximately 16 × 16 µm. Furthermorethe light source inclination angle of 15° gives a height resolution of around 0.2µm.

From the OptiTopo’s built-in software a bandpass filtered 2D height map wasaquired. The bandpass filtering is automatic and is used to avoid any large scaleheight variations due to the sample not lying entirely flat.

Both the front and back side of all unprinted samples were measured. In the-ory, the height image produced from photometric stereo should be orientationindependent, as long as the requirements mentioned in section 2.2 are met. How-ever, in practice, with limited spatial and dynamic resolution of the image sensor,this is not the case. Consequently, all samples were also measured in two differentorientations: 0° and 90°. This resulted in four measurements of the same surface.However, when conducting the analyses only one of these four measurementswas used, namely the one producing the best images in terms of representabilityand separability over the entire sample set. A typical height image is shown infigure 4.1.

Lastly, all measurements were done on three different spots on the paper sam-ple, in order to get a larger data set.

4.2.1 Data set

To summarize the data set used for all experiments can be divided in to fourlevels: roll, orientation, sample and image, as shown in table 4.1. This gives atotal of 768 image files in the data set.

4.2 Measurements 23

4 8 12 16 20 24 28 32

CD [mm]

4

8

12

16

20

24

28

32

MD

[m

m]

Figure 4.1: Typical height image of a paper sample with crepe marks mea-sured using the OptiTopo.

Roll Orientation Sample ImageO1 Front 1 1O2 Front (rotated 90°) 2 2

O3 Back... 3

O4 Back (rotated 90°) 16Table 4.1: Four different levels of the data set

24 4 Method

4.2.2 Verification

A small subset of the paper samples were measured using two other measure-ment methods: the Keyence VR-3200 3D macroscope and a cross section mea-surement using a scanning electron microscope (sem). This was done in order toverify the accuracy of the OptiTopo. The macroscope produces the same heightimage as the OptiTopo, while the sem produces a 1D profile of a surface crosssection. These methods will be presented in further detail along with the verifi-cation results in section 5.2.1.

However, due to limitations in resources and logistical reasons these verifi-cations could not be made on the exact same area of the paper samples as theOptiTopo measurements.


Fourier analysis of the paper samples was conducted in two ways: based on the2D Fourier transform as described in section 3.1 and based on the 1D Fouriertransform in the MD.

4.3.1 2D Fourier Analysis

As described in section 3.1 this analysis is based on calculating the 2D FourierTransform of the height image, converting the spectrum into polar coordinatesand fitting a 2D Gaussian to the spectrum’s main lobe. The width of the fittedGaussian should then, according to [9], correspond to the roughness of the pa-per’s surface which in turn depends on the density of crepe marks.

The analysis described above was performed on 1 image from each of the16 sets from each of the 4 rolls to yield a large enough result while minimizingcomputational time.


Since the crepe marks mainly are oriented as wave fronts in the machine direc-tion, looking at the 1D power spectrum in themd was proposed as an alternativeto the 2D Fourier analysis by the author. Given that the crepe marks appear ina different frequency range than the normal variations in the paper surface, theamount of marks could be detected by looking at the 1D power spectrum.

As with the 2D Fourier analysis, the spectrum estimate is computed usingWelch’s method in order to reduce noise. Let f (x, y) be a height image from thedata set, with (x, y) being the coordinates in cd and md respectively. 15 subim-ages fk(x, y) is then extracted from f (x, y) in 3 × 5 grid with 50 % overlap. Thepower spectrum of each subimage is calculated as

Sk(x, j) = |Fk(x, j)|2, (4.1)

where Fk(x, j) is the 1D Fourier transform (in the y-direction) of subimage fk(x, y),which is also Hanning windowed to avoid edge effects. The spectrum S(x, j) is


then calculated as

S(x, j) =1

15

15∑k=1

Sk(x, j), (4.2)

which produces a spectrum, for instance looking like the one shown in figure 4.2.

4 8 12 16 20 24 28 32

CD [mm]

32

24

16

8

0

Fre

quency [m

m-1

]

Figure 4.2: Power spectrum calculated column-wise in md, as described byequations 4.1 and 4.2.

Since the expected value of each column x in S(x, j) should be the same, the1D spectrum is calculated as

S(j) =1N

N∑x=1

S(x, j), (4.3)

where N is the number of columns in S(x, j). This produced a 1D spectrum likethe one shown in figure 4.3.

The analysis described above was performed on 1 image from each of the16 sets from each of the 4 rolls to yield a large enough result while minimizingcomputational time.


The mra based analysis was done in three steps: crepe mark candidate detectionusing mra (described in section 3.2), crepe mark segmentation through binaryoperations and crepe mark characterization.

26 4 Method

0 5 10 15 20 25 30

Frequency [mm-1

]

5

10

15

20

25E

nerg

y

Figure 4.3: Average power spectrum calculated from the spectrum shown infigure 4.2 as described by equation 4.3.

4.4.1 Detection

Let f (x, y) be a height image from the data set, with (x, y) being the coordinatesin cd and md respectively, and g(y) = f (a, y) a column of the image for somea ∈ [1, 2048]. Let Vk ∈ L2(R), k ∈ K = {0, ..., 11} be the set of nested subspaces ofan 11-level filter bank, using Daubechies16-wavelets.

Assuming g(y) ∈ L2(R) the signal can be decomposed by its projections Pkg(y)on Vk such that

g(y) =∑k∈K

Pkg(y),

and by recreating h(y) from only a subset of Pkg(y), the signal g(y) is bandpassfiltered with very small distortion. Recreating h(y) as

h(y) =6∑k=3

Pkg(y)

corresponds in this application to bandpass filtering the signal g(y) between1 mm−1 and 8 mm−1. Through some early testing this was concluded to be asuitable frequency range for detecting crepe marks.

Every 10 columns of the image f (x, y) were retrieved and filtered as describedabove, since it was quite computationally demanding. After filtering each col-umn, peaks with a certain height and prominence (height compared to neighbour-ing area) were retrieved. Since the crepe marks appear as bumps in the paper’s


surface with a certain size and height, each peak should correspond to a possiblecrepe mark.

Doing this for every filtered column generated a binary image h(x, y) contain-ing crepe mark candidates. An example of such an image is shown in figure 4.4.

1 2 3 4

CD [mm]

1

2

3

4

MD

[m

m]

Figure 4.4: Binary image of crepe mark candidates. Each point correspondsto a peak found in the mra.

4.4.2 Segmentation

The line-like shape and orientation (wide in cd and narrow inmd) of crepe markswas exploited to connect the crepe mark candidates above to form crepe marks,as well as to remove any false positives among the mark candidates. The binaryimage h(x, y) was then dilated with a 11 × 21 pixel rectangular structuring ele-ment, which means that mark candidates 0 or 1 steps away in the y-direction and0, 1 or 2 steps away in the x-direct was connected. These were then thinned to askeleton, producing a binary image i(x, y) like the one shown in figure 4.5.

Lastly the skeletal objects in i(x, y) were dilated using a structuring disk sdiskof radius 30 pixels and combined with the original image f (x, y) (above a certainthreshold)

j(x, y) =(i(x, y) ⊕ sdisk

)×(f (x, y) > 3µm

)(4.4)

generating a crepe mark area image. From this area image crepe marks smallerthan a certain area were removed, resulting in an image like the one shown infigure 4.6. All these binary operations combine to produce a very precise crepemark detector.

28 4 Method

1 2 3 4

CD [mm]

1

2

3

4

MD

[m

m]

Figure 4.5: Binary image of connected crepe mark candidates. Note howpoints isolated in md have been removed compared to figure 4.4.

1 2 3 4

CD [mm]

1

2

3

4

MD

[m

m]

Figure 4.6: Binary image of detected crepe marks. Same area as in figure 4.5but morphed according to equation 4.4 and with small marks removed.

4.5 Neural Net Analysis 29

4.4.3 Characterization

Using the crepe mark area image j(x, y) and the original height image f (x, y) thecrepe mark’s characteristics were determined. The examined characteristics are:

• Length (cd)

• Maximum width (md)

• Average width (md)

• Area

• Maximum height

• Average height

The three step analysis described above was performed on 1 image from eachof the 16 sets from each of the 4 rolls to yield a large enough result while mini-mizing computational time. The distributions of each of the crepe mark charac-teristics was then compared to determine which properties were most suited totell the different paper rolls apart.

4.5 Neural Net Analysis

Four different cnn:s (described in 2.5) were evaluated to find the one most suit-able for this analysis. The four networks evaluated were: three networks withfully connected layers at the end of increasing depth and one fully convolutionalnetwork (fcn). All networks were implemented using matconvnet in matlab.

4.5.1 Structure

Three cnn:s were constructed for a gray scale input image of 32× 32 pixels. Thiswas deemed a large enough input size to separate crepe marks from non-marks,while maintaining good computational speed. The networks had one, two andthree convolutional layers respectively. Each convolutional layer was followed bya max pooling layer (of different stride depending on network depth) and a rec-tified linear unit. Each cnn had two fully connected layers at the end. Detailedschematics of each network can be found in appendix A.

The fcn was constructed with one convolutional layer like the 1-level cnnfollowed by another two convolutional layers, replacing the fully connected lay-ers of the cnn:s. This allowed the fcn to be trained on the same 32 × 32 patchesas the other networks. A detailed schematic of the network can be found in ap-pendix A.

In summary four different network structures were compared:

• One leveled cnn (1 convolutional layer)

• Two leveled cnn (2 convolutional layers)

30 4 Method

• Three leveled cnn (3 convolutional layers)

• One leveled fcn (1 + 2 convolutional layers)

4.5.2 Training Data

The results from the mra was used in order to automatically generate trainingand validation data. All the crepe marks found with themra were used to createa binary image of mark and non-mark areas. From each crepe mark one posi-tive patch was selected, using the marks centroid as center. An equal amount ofnegative patches were randomly sampled from the non-mark areas. Figure 4.7shows an example of this training data selction with positive and negative patchcenters in cyan and red respectively. Each patch was 64 × 64 pixels in size, down-sampled to 32 × 32 and normalized by substracting the patch mean and dividingby its standard deviation. This type of normalization (called standardization)is a commonly used normalization for cnn:s, and prevents single features fromsaturating the output.

0 2 4 6 8 10 12 14 16

CD [mm]

0

2

4

6

8

10

12

14

16

MD

[m

m]

Figure 4.7: Training data selectio using mra results. Crepe mark patches incyan and non-mark negative patches in red.

This resulted in a data set of roughly 22 000 labeled patches which was di-vided into 70 % training and 30 % validation data.

4.5.3 Hyperparameters

In order to select suitable hyperparameters, a few different learning rates andbatch sizes were tried. Due to the computational cost of training cnn:s each


parameter was evaluated individually on the 1-layer cnn.First, some different constant learning rates were tried ranging from 0.01 to

0.15 in order to determine a suitable range for the learning rate. During thesetests a suitable number of training epochs was also determined.

Following this, the learning rate decay was determined by trying five different:constant, step-wise decreasing, linearly decreasing, exponentially decreasing andlogarithmicly decreasing. All these were used within the suitable learning raterange determined earlier.

Thirdly, a few different batch sizes were selected and tried. For computationalefficiency these were selected as powers of 2, ranging from 24 = 16 to 28 = 256.

4.5.4 Training

After suitable training hyperparameters had been selected, all four networks de-scribed in 4.5.1 were trained on the entire data set using mini-batch gradientdescent. This was done until convergence, that is, until the network showed nosignificant decrease in training or validation error.

4.5.5 Implementation

The trained networks were then used as part of a crepe mark classifierm, but inslightly different ways, since they produce different outputs.

The cnn:s were used for detection similarily to the mra described in section4.4.1. Patches, 32 × 32 pixels in size, were extracted from the 2048 × 2048 heightimage and classified as a mark or non-mark by the cnn, creating a binary imageof possible mark candidates. These were then segmented into marks or rejectedas described in section 4.4.2, and lastly the characteristics of each crepe mark wasretrieved as described in section 4.4.3.

The main advantage of the fcn is that both detection and segmentation can bedone by the network, since the fcn handles input of variable size. Consequentlythe entire 2048 × 2048 pixels height image was used as input to the network,outputting 505 × 505 pixels mark image. The mark image was then padded to512×512 pixels and upsampled to 2048×2048 creating a segmented mark imageof correct size. Each mark in this image was then characterized as described insection 4.4.3.

When analysing the full data set only the best performing network structurewas used. The analysis described above was performed on 1 image from each ofthe 16 sets from each of the 4 rolls to yield a large enough result while minimizingcomputational time. The distributions of each of the crepe mark characteristicswas then compared to determine which properties were most suited to tell thedifferent paper rolls apart.

5Results

This chapter contains the results produced by the analysis methods described inthe previous chapter. Furthermore, it contains the results from printing, mea-surements and validation of the measurement method.

5.1 Trial Printing

Table 5.1 shows the measured surface roughness (described in 4.1) and uca (de-scribed in 4.1.1) of all four rolls in the sample set. Worth noting is that the frontside is the normal printing side, which is why very poor uca for O3 and O4 whenprinting on the back side is to be expected. This is because the surface roughnesslies outside the tolarable range of a regular printing press, like the one used toprint these samples, which leads to abnormal printing defects and very poor uca.

Roll #Roughness [ml/min] uca [%]

Front side Back side Front side Back sideO1 1750 3000 0.00038 0.0011O2 2000 3500 0.0099 0.085O3 2500 5000 0.024 4.03O4 3000 6000 0.381 3.75

Table 5.1: Roughness and uca of the sample set

When comparing the uca of these samples to previously printed samples,which have been deemed high enough quality, it was found that O1 was of goodenough quality, O2 slightly below adequate quality while O3 and O4 were farbelow adequate.

33

34 5 Results

5.2 Measurements

From both visual inspection of the height images and some early testing it wasconcluded that the best sample orientation is with the back side up and rotated90°. This means measuring the crepe mark bumps (rather than pits) with theOptiTopo’s light falling in the machine direction, i.e. perpendicular to the crepemarks’ orientation.

The 90° rotation produced the most accurate representation of each crepemark (as determined by visual inspection of the images) and the back side pro-duced the best separability between each roll (as determined by early testing).Consequently this was the subset of data which was used for all analysis.

5.2.1 Verification

From verifications using the 3D macroscope (described in 4.2.2) it was concludedthat the OptiTopo’s representation of the paper surface structure was accurate.Figures 5.1 and 5.2 show parts of a height image of a sample from the roughestroll using the macroscope and OptiTopo respectively. Note that since it is not theexact same area being measured, the surfaces do not look exactly the same, butrather share the same general structure.

Figure 5.1: Height image from Keyence VR-3200. Note how the topologyresembles the one shown in figure 5.2.

5.2 Measurements 35

-15

1500

1000

MD [ m]

1500500

1000

CD [ m]

0

500

z [

m]

0 0

15

Figure 5.2: Height image from OptiTopo. Note how the topology resemblesthe one shown in figure 5.1.

The images from the scanning electron microscope (sem) show the same re-sults as the verification using 3D macroscope. Figure 5.3 shows the same generalappearance in the sem cross section as a cross section from an OptiTopo imagefrom the same roll. The red line in the sem profile (top) should resemble the Op-tiTopo profile (bottom) regarding height and size of the peaks. Figure 5.4 showsthat the surface has the same general structure as both the OptiTopo and 3Dmacroscope surfaces.

SEM

0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

Sample cross section [mm]

20

40

60

80

100

120

[m

]

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

Cross section [mm]

-15

-10

-5

0

5

10

15

[m

]

OptiTopo Profile

Figure 5.3: Cross section profile from sem and OptiTopo measurement. Notethe resemblance in roughness between the two red lines.

36 5 Results

Figure 5.4: Surface image from sem measurement. Note how the topologyresembles the one shown in figures 5.1 and 5.2.


This section contains the results of both the 2D and the 1D Fourier analysis meth-ods, described in sections 4.3.1 and 4.3.2 respectively.


Performing the 2D Fourier analysis yielded the result shown below. Each anal-ysed image produced a 2D Gaussian with a mean si and standard deviation Σ, asdescribed by equation 3.3 in section 3.1. The mean si of each analysed samplecan be seen in figure 5.5, where each dot corresponds to one set and all sets fromone roll are marked with the same color. As seen in the figure, the mean does notappear to differ significantly between the different paper rolls.

Figure 5.6 shows the standard deviation Σ of the 2D Gaussians. The frequencystandard deviation and the angle standard deviation correspond to W and Q re-spectively (as described by equation 3.3 in section 3.1). Each dot correspondsto one set and all sets from one roll are marked with the same color. From fig-ure 5.6 it is evident that the different paper rolls: O1, O2 and O3/O4 can beseparated using the standard deviation, since they form separable clusters. Thisvalue could therefore be used to distinguish between different paper qualities.However forming a decision boundary poses some problems, which is discussedfurther in section 6.2.1.

5.3 Fourier Analysis 37

84 86 88 90 92 94 96 98

Angle mean [deg]

2.5

3

3.5

Fre

quency m

ean [m

m-1

]

O1

O2

O3

O4

Figure 5.5: Mean of the 2D Gaussian fitted by the 2D FFT analysis. Each dotrepresents one set. Note how the different rolls (colors) are mixed together.

35 40 45 50 55 60 65 70 75

Angle standard deviation [deg]

7

8

9

Fre

quency s

tandard

devia

tion [m

m-1

]

O1

O2

O3

O4

Figure 5.6: Standard deviation of the 2D Gaussian fitted by the 2D FFT anal-ysis. Each dot represents one set. Note how O1, O2 and O3/O4 form sepa-rable clusters (marked with ellipses).


Performing the 1D Fourier analysis yielded the result shown below. Each anal-ysed image produced a 1D spectrum, consisting of the average of all spectras inthe y-direction. Figure 5.7 shows the average spectrum of all the images from

38 5 Results

each roll. The spectra for each set are shown in appendix B.

As seen in the figure the samples with poorer printing results have a largeramount of their energy concentrated in the 2 mm−1 to 8 mm−1 frequency range.Therefore this could be used to separate the different paper qualities, which isdiscussed further in section 6.2.2.

0 8 16 24 32

Frequency [mm-1

]

2

4

6

8

10

12

14

16

Energ

y

O1

O2

O3

O4

Figure 5.7: Average 1D spectra of all sets from each roll. Note the differencesin energy in the 2 mm−1 to 8 mm−1 frequency range


The mra analysis produced height images with a detected crepe mark overlay,as well as statistics for the different types of crepe mark characteristics. Imagesshowing the detected crepe marks (in red) can be found in appendix C. Fromvisual inspection of the overlay images it was concluded that approximately 10-30 % of all crepe marks were found using the mra method, depending on thesample roughness.

The characteristics of the crepe marks from each roll can be viewed in sum-mary in table 5.2. The table displays the mean and standard deviation of thedistribution of the characteristics. A more detailed display of each characteris-tic’s distribution can be found in appendix C.

As seen in the table the average and maximum height appears to be the bestcharacteristics in terms of separability between the different rolls.


Property O1 O2 O3 O4

Number of marksMean 37 120 260 290

Std 23 54 39 37

Length [µm]Mean 1160 1280 1540 1600

Std 360 470 650 720

Average height [µm]Mean 2.9 3.4 4.0 4.2

Std 0.4 0.5 0.5 0.6

Max height [µm]Mean 6.2 7.0 8.4 9.9

Std 0.8 1.0 1.0 1.0

Average width [µm]Mean 160 190 200 200

Std 40 45 36 36

Max width [µm]Mean 270 320 330 330

Std 83 94 82 85

Area [µm2]Mean 1.5e5 2.0e5 3.1e5 3.2e5

Std 6.9e4 8.7e4 1.3e5 1.3e5Table 5.2: Crepe mark characteristics obtained using mramethod

40 5 Results


This section contains the results from neural net training and the best suitednetwork and parameters, as well as the results from analyzing the data set usingthe best net.

5.5.1 Network Selection and Training

When comparing the different networks structures very small differences werefound. All networks had a misclassification rate of <10 %. Furthermore, the bestnet (the three level cnn) only outperformed the worst net (the one level cnn)by roughly 3 %. A detailed comparison of each network’s training and validationerror is shown in appendix D. Due to this small difference in performance and thelarge gains in computational speed, the fcn was deemed the best suited networkstructure and was therefore used for testing on the full data set.

When comparing different learning rate decays and batch sizes, the differ-ences were also very small between the different types. The learning rate de-cays performed almost identically and therefore the constant learning rate wasselected, because of its simplicity. When comparing batch sizes, a small advan-tage was found in using the smallest size (16 patches per batch) so this was usedto train the final net. A detailed comparison of learning rate decays and batchsizes, regarding training and validation error, is shown in appendix D.

To summarize, the network used in the final testing on the full data set wasthe one-level fcn, trained for 50 epochs with a constant learning rate of 0.07 anda batch size of 16.

5.5.2 Data Analysis

This analysis produced height images with a detected crepe mark overlay, as wellas statistics for the different types of crepe mark characteristics. Images showingthe detected crepe marks (in green) can be found in appendix C. From visualinspection of the overlay images it was concluded that approximately 70-80 % ofall crepe marks were found using the neural net method, independent of sampleroughness.

The characteristics of the crepe marks from each roll can be viewed in sum-mary in table 5.3. The table displays then mean and standard deviation of thedistribution of the characteristics. A more detailed display of each characteris-tic’s distribution can be found in appendix D.

Similar to the results from themra, the average and maximum height appearto be the best characteristics in terms of separability between the different rolls.


Property O1 O2 O3 O4

Number of marksMean 1100 1100 1200 1300

Std 100 120 50 20

Length [µm]Mean 860 910 1100 1200

Std 420 500 740 780

Average height [µm]Mean 1.9 2.4 3.2 3.4

Std 0.5 0.8 0.8 0.9

Max height [µm]Mean 5.2 7.0 8.4 8.9

Std 0.8 1.2 1.4 1.5

Average width [µm]Mean 110 130 130 130

Std 15 90 19 19

Max width [µm]Mean 160 210 190 190

Std 28 260 38 37

Area [µm2]Mean 1.0e5 1.3e5 1.5e5 1.6e5

Std 5.3e4 2.2e5 1.1e5 1.2e5Table 5.3: Crepe mark characteristics obtained using neural net method

6Discussion

In this chapter the results presented in the previous chapter will be discussed andinterpreted to provide a basis for the finishing conclusions in the next chapter.Furthermore, possible improvements to the method will be discussed.

6.1 Printing and Measurements

From the printed samples it was concluded that the printing on the first roll (O1)was of good enough quality, while all other samples were either slightly belowor far below adequate printing quality. From this we can conclude that, in orderto be relevant, the analysis methods must be able to differentiate between thefirst two rolls: O1 and O2. This also means that the set of all paper samplesis extensive enough to include commercially relevant samples, that is sampleswhich yield good enough uca and bad enough uca.

However, there are some improvements that could be made to the sample set.For all samples the following relationship holds

Bendtsen ∝ UCA (6.1)

where ∝ denotes proportionality. This means that the Bendtsen value could sim-ply be used to predict printing quality, using a threshold as the decision criterion.However, from experience this is not always the case. Especially when comparingmaterials produced using different paper machines, the Bendtsen value does notalways correlate with the printing quality. Therefore, it would have been prefer-able to have a larger sample set, including paper samples where equation 6.1 didnot hold.

The strength of the data set could have been further improved by verifyingthat different samples from the same subset share the same characteristics, usingsome quantitative method, since this was assumed when evaluating the analysis

43

44 6 Discussion

methods. This was only done in a qualitative way through visual inspection ofthe samples.

Verifications of the measurement method showed that OptiTopo’s represen-tation of the paper sample surface is accurate. However, since no two measure-ments could be done on exactly the same sample there is some uncertainty in thisverification. It would have been preferable to perform measurements using twodifferent methods on the exact same sample surface.



The results of the 2D Fourier Analysis were good enough to separate the differentrolls, but quite hard to interpret. Figure 5.5 show that the different rolls can’t bedifferentiated using the mean si of the fitted 2D Gaussian. However, figure 5.6shows that rolls O1, O2 and O3/O4 can be separated by looking at the standarddeviation Σ.

However, the results are not easily interpreted since there is no clear patternof how the standard deviation changes with poorer material quality. Going fromO1 to O2 (slightly worse quality) the standard deviation in frequency decreases,but increases in angle. Whereas from O1 to O3/O4 (much worse quality) thestandard deviation in both frequency and angle decreases. This also means thatgood and poor quality can’t be separated by a single linear decision boundary,limiting the practical use of this method.

The reason for this insufficient performance might be due to incorrect assump-tions about the power spectrum resembling a 2D Gaussian distribution, whichwas shown by the 1D Fourier Analysis. The 1D spectra (shown in figure 5.7),which in essence is the same as the 2D spectra along coordinates (f , 90◦), showsthat a Gaussian distribution clearly is a poor fit, especially for the rougher sam-ples O3 and O4. Changing this might have improved the results.


The 1D Fourier Analysis allowed for clear differentiation between the differentrolls, which is seen when comparing the average spectra as shown in figure 5.7.By comparing the energy in the 4 mm−1 frequency range to the energy in the14 mm−1 range we get a ratio discriminative enough to separate all four rolls.Even when comparing single samples, all rolls could be differentiated, which isseen when comparing the spectra in figures B.1 through B.4.


The multiresolution analysis performed fairly well for discovering crepe marks.Although only 20-40 % of all marks were detected there were very few false pos-itives and from visual inspection it appears to find different variations of marks,


rather than just one kind of marks. The main issue with this method is thatthe number of detected marks is quite dependent on surface roughness, whichmeans that a larger subset is needed to get a statistically significant result fromthe smoother paper rolls.

From the characteristics presented in table 5.2 we find that the maximum andaverage height appear to be suitable characteristics for differentiating the differ-ent subsets. Compared to their standard deviation this characteristic is fairly wellseparated between the different subsets, being at least 1σ apart.

Since this is a handcrafted mark detector, there is of course room for improve-ment. As mentioned earlier the main problem with this method is the varyingnumber of marks detected. The fact that much fewer marks are detected in thesmoother samples suggests that some sort normalization of the input image oradaptive thresholding could be useful to improve performance.


The neural net analysis outperformed themramethod by a large margin. Firstly,the number of detected marks was up to 25 times higher and independent ofsample roughness. Secondly the neural network method was significantly fasterthan the mra method, regardless of network structure. The cnn:s were at leasttwice as fast, due to faster mark candidate detection. But the largest time benefitcame from using the fcn, since the morphological operations of the mra weredone directly by the network. This decreased the processing time of a single2048×2048 height image from 1-2 minutes with themramethod to 5-10 secondsusing the fcn method, while maintaining the improved accuracy share by allneural networks.

Because of this large gain in both accuracy and speed the main improvementsto neural network method is regarding scope. Since the method performs sowell it would have been interesting to extend the number of different networkstructures and parameters tried, mainly by trying fcn:s of different sizes. Thiscould however be seen as a purely theoretical problem, since the method alreadyperforms good enough for most practical applications. However, even better net-works could allow for classification between different types of marks, the use ofwhich is discussed further in section 7.3.

Furthermore, the training process could have been improved by trying com-binations of hyperparameters together, rather than trying each parameter sepa-rately.

Lastly, the training data could be improved by using the network to gener-ate and train on data iteratively. Instead of using the mra method to generatetraining data, described in section 4.5.2, the 1st iteration of the network would beused to classify crepe mark and non-crepe-mark patches. These patches wouldthen be used to train the 2nd iteration of the same network. Since the networkoutperformed the mra this might yield better training results.

7Conclusion

This chapter contains a summary of the discussion and conclusions drawn fromit, as well as a recommendation for future work.

7.1 Summary

It was concluded that all four analysis methods are able to separate the differentpaper rolls. However, the 2D Fourier analysis posed problems in generating asingle linear decision boundary and themramethod is outperformed by the neu-ral network based method both in regard to speed and accuracy. Consequentlytwo of the methods must be seen as most suitable to solving this problem: the 1DFourier analyis and the neural net analysis.

These two methods differ somewhat in terms of applicability. If ease of use,speed and simplicity are a priority then the 1D Fourier analysis is best suited.This is because it provides a simple 1D spectrum, which could even be reduced toa simple ratio between frequency ranges as discussed earlier, and its calculationsare performed very quickly. If, on the other hand, detailed and nuanced informa-tion is of high priority then the neural net analysis is best suited. It provides arange of characteristics from the sample as well as information about statisticalproperties.

In conclusion the purpose of this thesis is fulfilled and two candidate solu-tions to the problem has been provided. Regarding the questions set out to beanswered we find the following answers:

• How well suited is photometric stereo for producing raw data for analysis ofcrepe marks?The photometric stereo based OptiTopo managed to produce height imagesof good enough quality for further analysis, while giving an accurate repre-sentation of the sample surface.

47

48 7 Conclusion

• Which analysis method produces the most accurate crepe mark characteristics?The most accurate crepe mark statistics were provided by the 1D Fourieranalysis and the neural net analysis.

• How can these characteristics be used to predict printing results?Both these analysis methods provided characteristics of sufficient quality,enabling a accurate prediction of printing results on the given set of papersamples. Either by looking at the energy in a certain frequency range (de-scribed in section 6.2.2) or by looking at the average or maximum height(described in section 6.4).

7.2 Project Work in a Wider Context

By integrating these analysis methods into production, companies could decreasethe costs and environmental effects of their returned products significantly. Fur-thermore, using these methods in product development would allow for a sub-stantial decrease in iteration time, from weeks or months using trial printing tohours or even minutes using these evaluation methods internally in a lab setting.

7.3 Future Work

There are mainly two interesting fields for future work within the scope of thisthesis: further examination of the link between specific characteristics and print-ing defects and online analysis of paper.

By developing the analysis methods further it might be possible to determineif there are different types of crepe marks, and if so exactly which marks gener-ate printing defects. This detailed information about crepe marks and printingdefects might provide valuable insight into the production process, eventuallyfinding and eliminate the source of these marks.

Online measurements and analysis is another interesting topic for future work.As with many other modern producing industries, the paper industry is undergo-ing a large automation revolution. This makes the need for machine integrated(online) quality evaluation systems greater than ever. Measuring the paper qual-ity in regard to crepe marks could help identifying the relationship between dif-ferent production variables and these crepe marks, eventually allowing produc-tion to be tuned to prevent problematic marks.

Appendix

ANeural Network Structures

This section contains figures showing a schematic image of each neural networkstructure (described in section 4.5.1) used in the neural net analysis. The beigeboxes represent data, showing its name and size, the blue boxes represent filtercoefficients, showing its name and size, and the red boxes represent differentfilter types, showing its name and its corresponding matconvnet function.

51

52 A Neural Network Structures

Figure A.1: One leveled cnn structure showing the type, input and filtersize of each layer.

53

Figure A.2: Two leveled cnn structure showing the type, input and filtersize of each layer.

54 A Neural Network Structures

Figure A.3: Three leveled cnn structure showing the type, input and filtersize of each layer.

55

Figure A.4: One leveled fcn structure showing the type, input and filter sizeof each layer.

B1D Fourier Analysis

This section contains figures showing the results of the 1D Fourier analysis (de-scribed in section 5.3.2) of each set. Worth noting is the low variance between thedifferent spectra in each figure. This means that samples from different paperrolls can be separated using only one measurement.

0 8 16 24 32

Frequency [mm-1

]

2

4

6

8

10

12

14

16

18

Energ

y

Figure B.1: 1D spectrum of each set from O1. Note the low variance betweensets.

57

58 B 1D Fourier Analysis

0 8 16 24 32

Frequency [mm-1

]

2

4

6

8

10

12

14

16

18

Energ

y


0 8 16 24 32

Frequency [mm-1

]

2

4

6

8

10

12

14

16

Energ

y


59

0 8 16 24 32

Frequency [mm-1

]

2

4

6

8

10

12

14

16

18

Energ

y


CMultiresolution Analysis

This section contains figures showing results from the mra (described in section5.4. Figures C.1 through C.4 show a comparison of the number detected crepemarks using the mra and cnn analysis methods. Since both of these methodsare designed to detect the same type of details in a height image the number ofdetected marks should be the same. Howevere, in these figures is the significantdifferent in the number of detected marks, as well as how the number of detectedmarks increases with rougher paper for themramethod but stays fairly constantwith the cnnmethod.

Furthermore figure C.5 shows the number of marks detect when analysingsets from each roll. Note how the number of detected marks increase with in-crease paper roll roughness.

Lastly figures C.6 through C.11 show the distribution of different characteris-tics in the detected marks. Worth noting is the low variance and roughly Normaldistribution of both the average and maximum height characteristics.

61

62 C Multiresolution Analysis

Figure C.1: Height image from O1 with crepe mark overlay withmra in redand neural net in green. Note the difference in the number of marks.


63




1 2 3 4

Roll number

0

50

100

150

200

250

300

350

# o

f m

ark

s

O1, mean = 36.3, std = 22.5 / O2, mean = 121.7, std = 54.3


Figure C.5: Number of detected marks from each roll using mra analysis.Note how the number of marks increase with paper roll roughness.

Figure C.6: Histogram of detected mark lengths using mra analysis. Notehow the distributions are fairly overlapping.

65

Figure C.7: Histogram of detected mark average heights usingmra analysis.Note how the distributions are separable compared to other characteristics.

Figure C.8: Histogram of detected mark max heights using mra analysis.Note how the distributions are separable compared to other characteristics.


Figure C.9: Histogram of detected mark average width using mra analysis.Note how the distributions are fairly overlapping.

Figure C.10: Histogram of detected mark max width using mra analysis.Note how the distributions are fairly overlapping.

67

Figure C.11: Histogram of detected mark areas using mra analysis. Notehow the distributions are fairly overlapping.

DNeural Net Analysis

This section contains figures showing the training and validation error from train-ing using different parameters. Figure D.1 compares different network depth.Worth noting is that even though there is a significant difference between the net-works regarding network depth and consequently number of nodes, all networksperform very well with a misclassification rate of <10 %. Figure D.2 shows a com-parison of different learning rates and figure D.3 a comparison of different batchsizes. Note how there is very little difference between the compared learningrates and batch sizes.

Furthermore, figure D.4 shows the number of detected marks when analysingsets from each roll. Note how the number of detected marks is fairly constant forall paper rolls.

Lastly, figures D.5 through D.10 show the distribution of different characteris-tics in the detected marks. Worth noting is the low variance and roughly normaldistribution of both the average and maximum height characteristics.

69

70 D Neural Net Analysis

0 5 10 15 20 25 30 35 40 45 50

Epoch

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35Training error

oneLayerNet, emin

= 0.092 @ 45

twoLayerNet, emin

= 0.071 @ 42

threeLayerNet, emin

= 0.063 @ 47

oneLayerSlideNet, emin

= 0.078 @ 42

0 5 10 15 20 25 30 35 40 45 50

Epoch

0.06

0.08

0.1

0.12

0.14

0.16Validation error

oneLayerNet, emin

= 0.092 @ 45

twoLayerNet, emin

= 0.071 @ 42

threeLayerNet, emin

= 0.063 @ 47

oneLayerSlideNet, emin

= 0.078 @ 42

Figure D.1: Training and validation error of different networks. All net-works perform very well (<10 % misclassification).

0 5 10 15 20 25 30 35 40 45 50

Epoch

0.05

0.1

0.15

0.2

0.25

0.3Training error

Constant, emin

= 0.105 @ 44

Step-wise, emin

= 0.106 @ 38

Linear, emin

= 0.108 @ 42

Exponential, emin

= 0.108 @ 48

Logarithmic, emin

= 0.106 @ 34

0 5 10 15 20 25 30 35 40 45 50

Epoch

0.1

0.11

0.12

0.13

0.14

0.15

0.16

0.17

0.18Validation error

Constant, emin

= 0.105 @ 44

Step-wise, emin

= 0.106 @ 38

Linear, emin

= 0.108 @ 42

Exponential, emin

= 0.108 @ 48

Logarithmic, emin

= 0.106 @ 34

Figure D.2: Training and validation error of different learning rates. Notethat there’s no significant difference in the final error.

71

0 5 10 15 20 25 30 35 40 45 50

Epoch

0

0.1

0.2

0.3

0.4

0.5Training error

Batch size = 16, emin

= 0.090 @ 49


= 0.104 @ 46


= 0.113 @ 49


= 0.124 @ 47


= 0.129 @ 43

0 5 10 15 20 25 30 35 40 45 50

Epoch

0

0.1

0.2

0.3

0.4

0.5Validation error


= 0.090 @ 49


= 0.104 @ 46


= 0.113 @ 49


= 0.124 @ 47


= 0.129 @ 43

Figure D.3: Training and validation error of different batch sizes. Note thatthere’s no significant difference in the final error.

1 2 3 4

Roll number

800

900

1000

1100

1200

1300

# o

f m

ark

s



Figure D.4: Number of detected marks from each roll using neural net anal-ysis. Note how the number of detected marks is fairly independent of paperroll roughness.


Figure D.5: Histogram of detected mark lengths using neural net analysis.Note how the distributions are fairly overlapping.

Figure D.6: Histogram of detected mark average heights using neural netanalysis. Note how the distributions are separable compared to other char-acteristics.

73

Figure D.7: Histogram of detected mark max heights using neural net anal-ysis. Note how the distributions are separable compared to other character-istics.

Figure D.8: Histogram of detected mark average width using neural netanalysis. Note how the distributions are fairly overlapping.


Figure D.9: Histogram of detected mark max width using neural net analy-sis. Note how the distributions are fairly overlapping.

Figure D.10: Histogram of detected mark areas using neural net analysis.Note how the distributions are fairly overlapping.

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