Object RecognitionBy

A.Sravya

Given some knowledge of how certain objects may appear and an image of a scene possibly containing those objects, report which objects are present in the scene and where.

Object recognition problem

Image panoramas Image watermarking Global robot localization Face Detection Optical Character Recognition Manufacturing Quality Control Content-Based Image Indexing Object Counting and Monitoring Automated vehicle parking systems Visual Positioning and tracking Video Stabilization

Applications

Pattern or Object: Arrangement of descriptors(features)

Pattern class: Family of patterns that share some common properties

Pattern Recognition: Techniques for assigning patterns to their respective classes

Common pattern arrangements: 1. vectors – ( for quantitative descriptors) 2. strings 3. trees – (for structural descriptors) Approaches to pattern recognition Decision – theoretic quantitative descriptors Structural qualitative descriptors

Introduction

where xi represents the ith descriptor

n is no: of descriptors associated with the pattern

Example : Consider 3 types of iris flowers- setosa,virginica and versicolor Each flower is described by petal length and width . Therefore the pattern vector is given by:

Patterns and pattern classes vector example

Here is another example of pattern vector generation.

In this case, we are interested in different types of noisy shapes.

Patterns and pattern classesanother vector example

Recognition problems in which not only quantitative measures about each feature but also the spatial relationships between them determine class membership, are solved by structural approach

Example: Fingerprint recognition

Strings

String descriptions generate patterns of objects whose structure is based on relatively simple connectivity of primitives usually associated with boundary shape

Strings and trees

String of symbols w =……..abababab……….

String example

Tree descriptors more powerful than strings Most hierarchical ordering schemes lead to tree

structures Example:

Trees

Recognition based on Decision-Theoritic MethodsBased on the use of decision functions ( d(x) )Here we find W decision functions d1(x), d2(x),....... dW(x) with the property that, if a pattern x belongs to class ωi , then

ijWjdd ji ;,...,2,1 )()( xx

The decision boundary separating class and is given by

0)()(or )()( xxxx jiji dddd

Now the objective is to develop various approaches for finding decision functions that satisfy Eq(1)

1

Here we represent each class by a prototype pattern vector

An unknown pattern is assigned to the class to which it is closest in terms of a predefined approach

The two approaches are:

Minimum distance classifier – calculate the Euclidean distance

correlation

Decision theoritic methods- matching

Minimum distance classifier

Prototype pattern vector

Calculate the Euclidean distance between the unknown vector and the prototype vector

Distance measure is the decision function

…….large numerical value

Contd..

Decision boundary b/w classes and is

….perpendicular bisector

If dIj(x) > 0, then x belongs to

If dIj(x) < 0, then x belongs to

i

j

example

Correlation is used for finding matches of a sub image w(x,y) of size J X K within an image f(x,y) of size M X N

Correlation between w(x,y) and f(x,y) is given by

Matching by correlation

1,...,2,1,0

,1,...,2,1,0for

),(),(),(

Ny

Mx

tysxwtsfyxcs t

The maximum values of c indicates the positions where w best matches f

Contd..

This is a probabilistic approach to pattern recognition

Average loss

Optimum statistical classifiers

The classifier that minimizes the total average loss is called the Bayes classifier

Optimum statistical classifiers

Bayes classifier assigns an unknown pattern x to class if i

Loss for a correct decision is assigned ‘0’ and for incorrect decision ‘1’

Optimum statistical classifiers

Further simplified to

Finally

….Bayes Decision Function

BDF depends on the pdfs of the patterns in each class and the probability of occurrence of each class

Sample patterns are assigned to each class and then necessary parameters are estimated

Most commonly used form for is the Gaussian pdf

Bayesian classifier for guassian pattern classesBayes decision function for Gaussian pattern classes is

)(2

1 )()|()(

2

2

2

)(

j

mx

j

jjj pepxpxd j

j

here n = 1 & W = 2

Bayesian classifier for guassian pattern classes In n-dimensional case

Bayesian decision function for gaussian pattern classes under 0-1 loss function

Bayesian classifier for guassian pattern classes•BDF reduces to minimum distance classifier if:1. Pattern classes are Gaussian2. All covariance matrices are equal to the identity matrix3. All classes are equally likely to occur

• Therefore minimum distance classifier is optimum in Bayes sense if the above conditions are satisfied

Neural Networks

Neural network: information processing paradigm inspired by biological nervous systems, such as our brain

Structure: large number of highly interconnected processing elements (neurons) working together

Neurons are arranged in layers

Neural Networks

Each neuron within the network is usually a simple processing unit which takes one or more inputs and produces an output. At each neuron, every input has an associated weight which modifies the strength of each input. The neuron simply adds together all the inputs and calculates output.

Neurons: Elemental nonlinear computing elements

We use these networks for adaptively developing the coefficients of decision functions via successive presentations of training set of patterns

Training patterns: Sample patterns used to estimate desired parameters

Training set: Set of such patterns from each class Learning or Training: Process by which a training

set is used to obtain decision functions Perceptron model basic model of a neuron Perceptrons are learning machines

NN contd..

Perceptron for two pattern classes

Another way :

Training algorithms-linearly seperable classes

then

If ω2 and

This algorithm makes a change in w only if the pattern being considered at the kth step in the training sequence is misclassified

This method minimizes the error between the actual and the desired response

Training algorithms-Nonseperable classes

From gradient descent algorithm

Training algorithms-Nonseperable classes

Changing weights reduces the error by a factor

Multilayer feedforward neural networks We focus on decision functions of multiclass pattern recognition

problems, independent of whether the classes are separable or not

Activation element is a sigmoid function

Multilayer feedforward neural networks

Input to the activation element of each node in layer J

The outputs of layer K are

The final sigmoid function is

We begin by concentrating on the output layer The process starts with an arbitrary set of weights through out

the network Generalized delta rule has two basic phases: Phase 1 A training vector is propagated through the layers to compute

the output Oj for each node The outputs Oq of the nodes in the output layer are then

compared against their desired responses rp, to generate the error terms δq

Phase 2 A backward pass through the network during which the

appropriate error signal is passed to each node and the corresponding weight changes are made

Training by back propagation

example

Performance of a neural network as a function of noise level

Improvement in peformance by increasing no.of training patterns

Face recognition

Thank you