automatic contextual pattern modeling

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Automatic Contextual Pattern Automatic Contextual Pattern ModelingModeling

Pengyu HongPengyu HongBeckman Institute for Advanced Science and TechnologyBeckman Institute for Advanced Science and Technology

University of Illinois at Urbana ChampaignUniversity of Illinois at Urbana Champaign

[email protected]@ifp.uiuc.edu

http://www.ifp.uiuc.edu/~honghttp://www.ifp.uiuc.edu/~hong

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OverviewOverview

MotivationsMotivations

Define the problemDefine the problem

Formulation the problemFormulation the problem

Experimental resultsExperimental results

Conclusions and discussionsConclusions and discussions

Design the algorithmDesign the algorithm

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The global featuresThe global features

EdgeEdge

++

Color histogramColor histogram

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The color histograms of six imagesThe color histograms of six images

A simple example. A simple example. What kind of visual pattern shared by the following histograms?What kind of visual pattern shared by the following histograms?

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The normalized wavelet texture histograms of those six imagesThe normalized wavelet texture histograms of those six images

The global texture information is also given …The global texture information is also given …

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The imagesThe images

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The global features of an object are the The global features of an object are the mixtures of the local features of the mixtures of the local features of the primitives. primitives.

! The global features alone are not The global features alone are not enough for distinguishing different enough for distinguishing different objects/scenes in many cases.objects/scenes in many cases.

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!! It is very important to model both It is very important to model both the primitives and the relations. the primitives and the relations.

An object consists of several primitives among An object consists of several primitives among which various contextual relations are defined.which various contextual relations are defined.

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In terms of imagesIn terms of images Examples of primitivesExamples of primitives

RegionsRegions EdgesEdges ……

Examples of relationsExamples of relations Relative distance between two primitivesRelative distance between two primitives Relative orientation between two primitivesRelative orientation between two primitives The size ratio between two primitivesThe size ratio between two primitives ……

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The representationThe representation

Attributed relational graph (ARG) [Tsai1979] has been Attributed relational graph (ARG) [Tsai1979] has been extensively used to represent objects/scenes. extensively used to represent objects/scenes.

An example of ARGAn example of ARG

First, we need to choose an representation for the First, we need to choose an representation for the information in order to calculate it.information in order to calculate it.

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The representation – ARGThe representation – ARG

The lines represent the relations between the The lines represent the relations between the object primitives. object primitives.

The nodes of an ARG represent the object The nodes of an ARG represent the object primitives. The attributes (color histogram, primitives. The attributes (color histogram, shapes, texture, etc.) of the nodes represent the shapes, texture, etc.) of the nodes represent the appearance features of the object primitives. appearance features of the object primitives.

ARGARG

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The representation – ARGThe representation – ARGAn example: The image is segmented and represented as an ARG.An example: The image is segmented and represented as an ARG.

The nodes represents the regions. The color of the nodes The nodes represents the regions. The color of the nodes denotes the mean color of the regionsdenotes the mean color of the regions

The lines represent the adjacent relations among the regions.The lines represent the adjacent relations among the regions.

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Separate the local features and allow the user to Separate the local features and allow the user to examine the objects/scenes on a finer scale.examine the objects/scenes on a finer scale.

The advantage of the ARG representation.The advantage of the ARG representation.

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Scene 2Scene 2Scene 1Scene 1


Separate the local spatial transformations and the Separate the local spatial transformations and the global spatial transformations of the object.global spatial transformations of the object.

The advantage of the ARG representation.The advantage of the ARG representation. Separate the local features and allow the user to examine the objects Separate the local features and allow the user to examine the objects

on a finer scale.on a finer scale.

Scene 2Scene 2

Global translation and rotationGlobal translation and rotation

+ Local deformation+ Local deformation

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Problem definitionProblem definition

A set of A set of sample sample ARGsARGs

SummarizeSummarize

Pattern modelPattern model

DetectionDetection RecognitionRecognition SynthesisSynthesis

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Problem definitionProblem definition

Pattern modelPattern modelHow to build this How to build this

Manually designManually design

Learn from multiple observationsLearn from multiple observations

??

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Related workRelated work Maron and Lozano-Pérez 1998Maron and Lozano-Pérez 1998

Develop a Develop a BayesBayes learning framework to learn visual learning framework to learn visual patterns from multiple labeled images.patterns from multiple labeled images.

Frey and Jojic 1999Frey and Jojic 1999Use generative model to jointly estimate the transformations Use generative model to jointly estimate the transformations and the appearance of the image pattern.and the appearance of the image pattern.

Guo, Zhu, & Wu. 2001Guo, Zhu, & Wu. 2001

Integrate descriptive model and generative model to learn Integrate descriptive model and generative model to learn visual pattern from multiple labeled images.visual pattern from multiple labeled images.

Hong & Huang 2000, Hong , Wang & Huang 2000Hong & Huang 2000, Hong , Wang & Huang 2000

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The contributionThe contribution

Develop the methodology and theory for Develop the methodology and theory for automatically learning a probability automatically learning a probability parametric pattern model to summarize a set parametric pattern model to summarize a set of observed samples.of observed samples.

The probability parametric pattern model is The probability parametric pattern model is called the pattern ARG model. It models called the pattern ARG model. It models both the appearance and the structure of the both the appearance and the structure of the objects/scenes.objects/scenes.

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Formulate the problemFormulate the problem

Assume the observations sample ARGs {Assume the observations sample ARGs {GGii} are the } are the

realizations of some underlying stochastic process realizations of some underlying stochastic process governed by a probability distribution governed by a probability distribution ff((GG).).

The objective of learning is to estimate a model The objective of learning is to estimate a model pp((GG) to approximate ) to approximate ff((GG) by minimizing the ) by minimizing the Kullback-Leibler divergence Kullback-Leibler divergence KLKL((f f || || pp). ). [Cover & [Cover & Thomas 1991]:Thomas 1991]:

)]([log)]([log)(

)(log)()||( GpEGfEdG

Gp

GfGfpfKL ff

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Formulate the problemFormulate the problem

Therefore, we have a maximum likelihood estimator Therefore, we have a maximum likelihood estimator (MLE).(MLE).

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ff((GG))

How to calculate How to calculate pp(o) ?(o) ?

Simplicity:Simplicity: The model uses a set of parameters The model uses a set of parameters to represent to represent ff((GG).).

Generality:Generality: Use a set of components (mixtures) to Use a set of components (mixtures) to approximate the true distribution.approximate the true distribution.

In practice, it is often necessary to In practice, it is often necessary to impose structures on the distribution.impose structures on the distribution.

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For example, linear familyFor example, linear family

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Illustration of modelingIllustration of modeling

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A set of sample ARGs {A set of sample ARGs {GGii}, }, ii = 1, … = 1, … SS..

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Illustration of modelingIllustration of modeling

MM << << SS

A set of sample ARGs {A set of sample ARGs {GGii}, }, ii = 1, … = 1, … SS..

SummarizeSummarize

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A pattern ARG model A pattern ARG model of of MM components components {{ii}, }, ii = 1, …, = 1, …, MM 1414

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MM3434

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Hierarchically linear modelingHierarchically linear modeling

A pattern ARG A pattern ARG with with MM

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On macro scaleOn macro scale

A sample ARG = A sample ARG = hhhh

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Hierarchically linear modelingHierarchically linear modeling

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componentscomponents

oo1212A sample node = A sample node = hh((hhhh))

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On micro scaleOn micro scale

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The underlying distributionsThe underlying distributions

1414

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1111 1313112112 113113

134134

Attributed distributionsAttributed distributions

Relational distributionsRelational distributions

Each component of the pattern ARG model is a Each component of the pattern ARG model is a parametric model.parametric model.

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The task is to…The task is to…

The parameters of the distribution functionsThe parameters of the distribution functions

Learn the parameters of the pattern ARG Learn the parameters of the pattern ARG model given the sample ARGs.model given the sample ARGs.

The parameters ({The parameters ({hh}, {}, {hh}) that describe the }) that describe the contribution of the model components.contribution of the model components.

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Sometimes …Sometimes …The instances of the pattern are in various backgrounds.The instances of the pattern are in various backgrounds.

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Sometimes …Sometimes …

It is labor intensive to manually extract each instance It is labor intensive to manually extract each instance out of its background.out of its background.

The learning procedure should automatically extract the The learning procedure should automatically extract the instances of the pattern ARG out of the sample ARGs.instances of the pattern ARG out of the sample ARGs.

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Modified version of modelingModified version of modeling

MM << << SS SummarizeSummarize

A pattern ARG model A pattern ARG model with with MM components components {{ii}, }, ii = 1, …, = 1, …, MM 1414

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Learning via the EM algorithmLearning via the EM algorithm

]},{|);},({[log);( )()( tf

t GYGpEQ

The EM The EM [[Dempster1977]Dempster1977] algorithm is a technique of finding algorithm is a technique of finding the maximum likelihood estimate of the parameters of the the maximum likelihood estimate of the parameters of the underlying distributions from a training set.underlying distributions from a training set.

The EM algorithm defines a likelihood function, which in The EM algorithm defines a likelihood function, which in this case is:this case is:

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]},{|);},({[log);( )()( tf

t GYGpEQ

The sample The sample ARG set.ARG set.

The correspondences The correspondences between the sample ARGs between the sample ARGs

and the pattern ARG model.and the pattern ARG model.

The parameters to The parameters to be estimated.be estimated.

);( )(tQ is a function of is a function of under the assumption that under the assumption that = = ((tt))

Underlying distributionUnderlying distribution

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AnalogyAnalogy

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Expectation stepExpectation step

The EM algorithm works iteratively in two steps: The EM algorithm works iteratively in two steps: ExpectationExpectation & & MaximizationMaximization

);( )(tQ is calculated, where is calculated, where tt is the number of is the number of iterations.iterations.

Maximization stepMaximization step

is updated byis updated by ),(maxarg )()1( tt Q

Modify the structure of the pattern ARG modelModify the structure of the pattern ARG model

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Initialize the pattern ARG modelInitialize the pattern ARG model

A sample ARGA sample ARG

For example if the pattern ARG For example if the pattern ARG model has 3 components.model has 3 components.

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The Expectation stepThe Expectation step

Please refer to the paper for the details.Please refer to the paper for the details.

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Calculate the likelihood of the dataCalculate the likelihood of the data

It is not so complicated as it appears!It is not so complicated as it appears!

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The Maximization stepThe Maximization step

The expressions for the parameters ({The expressions for the parameters ({hh}, {}, {hh}), which }), which

describe the contribution of model components, can be describe the contribution of model components, can be derived without knowing the forms of the attributed derived without knowing the forms of the attributed distributions and those of the relational distributions.distributions and those of the relational distributions.

For Gaussian attributed distributions and Gaussian For Gaussian attributed distributions and Gaussian relational distributions, we can obtain analytical relational distributions, we can obtain analytical expressions to estimate the distribution parameters.expressions to estimate the distribution parameters.

Please refer to the paper for the details.Please refer to the paper for the details.

Update Update

Derive the expressions for Derive the expressions for ((tt+1)+1)..

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The parameters of the Gaussian attributed distributionsThe parameters of the Gaussian attributed distributions

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The parameters of the Gaussian relational distributionsThe parameters of the Gaussian relational distributions

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Modify the structureModify the structure

Null nodeNull node

Initialize the components of Initialize the components of the pattern ARG modelthe pattern ARG model

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Modify the structure of the pattern ARG model.Modify the structure of the pattern ARG model.

It is very possible that the model components are initialized It is very possible that the model components are initialized so that they contain some nodes representing backgrounds.so that they contain some nodes representing backgrounds.

During the iterations of the algorithm, we examine the During the iterations of the algorithm, we examine the parameters parameters ({({hh}, {}, {hh}}) and decide which model nodes ) and decide which model nodes

should be marked as background nodes.should be marked as background nodes.

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During the iterations of the algorithm, we During the iterations of the algorithm, we examine the parameters ({examine the parameters ({hh}, {}, {hh}) and }) and

decide which model nodes should be marked decide which model nodes should be marked as background nodes.as background nodes.

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Detect the patternDetect the pattern

Use the learned pattern ARG model to detect the pattern.Use the learned pattern ARG model to detect the pattern.

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Given an new graph Given an new graph GGnewnew, we calculate the following , we calculate the following

likelihood likelihood

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Experimental results IExperimental results I

In this experiment, the images are segmented. The In this experiment, the images are segmented. The color feature (RGB and its variances) of a segment color feature (RGB and its variances) of a segment is used. However, our theory can be applied is used. However, our theory can be applied directly on image pixels (see Discussions) or other directly on image pixels (see Discussions) or other image primitives (e.g. edges). Segmentation is just image primitives (e.g. edges). Segmentation is just used to reduce the computational complexity.used to reduce the computational complexity.

Automatic image pattern extractionAutomatic image pattern extraction

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The imagesThe images


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The segmentation resultsThe segmentation results

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The ARGsThe ARGs

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Experimental Results IExperimental Results I

The learning results as subgraph in the sample ARGsThe learning results as subgraph in the sample ARGs

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The corresponding image segmentsThe corresponding image segments

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DetectionDetection

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Experimental Results IIExperimental Results II

Improve pattern detectionImprove pattern detection

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Experimental results IIExperimental results II

Lighting 1Lighting 1

Lighting 2Lighting 2

(208, 150, 69)(208, 150, 69) (202, 138, 60)(202, 138, 60) (206, 144, 71)(206, 144, 71)The ‘m’The ‘m’

(240, 173, 116)(240, 173, 116) (240, 180, 109)(240, 180, 109) (241, 192, 120)(241, 192, 120)The ‘m’The ‘m’

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Bad guessBad guessgood guessgood guessbetter guessbetter guessand better guessand better guess

Experimental results IIExperimental results IIWe implemented the probability relaxation graph matching We implemented the probability relaxation graph matching algorithm [algorithm [Christmas, Kittler & Petrou 1995].Christmas, Kittler & Petrou 1995].

The matching results depend on the values of the parametersThe matching results depend on the values of the parameters

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Our approachOur approach

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Compare the results shown in the previous two slides. It will Compare the results shown in the previous two slides. It will not be difficult to see the followings. not be difficult to see the followings.

The learning procedure automatically adjusts the parameters The learning procedure automatically adjusts the parameters for graph matching. The learning results include the for graph matching. The learning results include the correspondences between the pattern ARG model and the correspondences between the pattern ARG model and the sample ARGs. sample ARGs.

The learning procedure utilizes the evidence provided by The learning procedure utilizes the evidence provided by multiple samples to get rid of backgrounds.multiple samples to get rid of backgrounds.

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Experimental results IIIExperimental results III Structural texture modeling and synthesisStructural texture modeling and synthesis

Model the structureModel the structure Model the Model the appearanceappearance

Normalize the Normalize the texture elements texture elements to the same sizeto the same size

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Experimental results IIIExperimental results III

Synthesize new texture …Synthesize new texture …

First, synthesize the structure.First, synthesize the structure.

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Then, synthesize the appearance.Then, synthesize the appearance.

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Experimental Results IIIExperimental Results III


Borrow the structure and synthesize new texture …Borrow the structure and synthesize new texture …

Modify the appearance Modify the appearance node of the learned model.node of the learned model.

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samplesample synthesizedsynthesized

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Experimental Results IVExperimental Results IV

Automatic FAQ detectionAutomatic FAQ detection

Student Jack: “What are Java applets?”Student Jack: “What are Java applets?”

Student Tom: “Would you please define Java programs?”Student Tom: “Would you please define Java programs?”

Student Jenny: “Could you tell me the definitions of Java Student Jenny: “Could you tell me the definitions of Java applet and Java application?”applet and Java application?”

For example ….For example ….

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Using the Word Concept Model [Li & Levinson 2001]. Using the Word Concept Model [Li & Levinson 2001]. We can parse the questions into graphs.We can parse the questions into graphs.

Student Jack: “What are Java applets?”Student Jack: “What are Java applets?”

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Student Tom: “Would you please define Java programs?”Student Tom: “Would you please define Java programs?”

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Student Jenny: “Could you tell me the definitions of a Student Jenny: “Could you tell me the definitions of a Java applet and a Java application?”Java applet and a Java application?”

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The summarized FAQThe summarized FAQ

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Experimental Results VExperimental Results V

Original videoOriginal video SegmentedSegmented ARG sequenceARG sequence

Foreground subgraphForeground subgraph ForegroundForegroundSummarizationSummarization

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Experimental Results VExperimental Results V

…………

Retrieve resultsRetrieve results

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ConclusionsConclusions

Develop the methodology and theory for evidence Develop the methodology and theory for evidence combining that fuses the appearance information combining that fuses the appearance information and structure information of the observed samples.and structure information of the observed samples.

Choose representationChoose representation

Define and formulate the problemDefine and formulate the problem

Design the algorithm to solve the problemDesign the algorithm to solve the problem

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ConclusionsConclusions

Automatically learns a compact parametric Automatically learns a compact parametric model to represent a pattern that is observed model to represent a pattern that is observed under various conditions. under various conditions.

Automatically eliminates the backgrounds Automatically eliminates the backgrounds by using multiple samples.by using multiple samples.

The mathematical frameworkThe mathematical framework

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Discussions IDiscussions I

The learning results depend on the quality of the The learning results depend on the quality of the results of low-level image processing.results of low-level image processing.

Low-level image processingLow-level image processing

LearningLearning

Sample imagesSample images

Learned high-level Learned high-level knowledgeknowledge

Human Human interaction or interaction or some super some super

modelsmodels

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Low-level image processingLow-level image processing

LearningLearning


Corrected high-level Corrected high-level knowledgeknowledge

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Knowledge based Low-level Knowledge based Low-level image processingimage processing

LearningLearning


Corrected high-level Corrected high-level knowledgeknowledge

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Discussions IIDiscussions II

If enough computational power is available, we can If enough computational power is available, we can work directly on pixel-level.work directly on pixel-level.

Each pixel is a node.Each pixel is a node.

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Discussions IIDiscussions II If enough computational power is available (e.g. If enough computational power is available (e.g.

parallel/distributed computing), we can work parallel/distributed computing), we can work directly on pixel-level.directly on pixel-level.

Or even more complicated relationsOr even more complicated relations

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Discussions IIIDiscussions III Multiple resolutions/layers for complex phenomenaMultiple resolutions/layers for complex phenomena

11

MM

The pattern ARG modelThe pattern ARG model

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Discussions IIIDiscussions III

Recognizer networksRecognizer networks

Each node can represent a primitive recognizer.Each node can represent a primitive recognizer.

Face detection and recognitionFace detection and recognition

Face and facial motion trackingFace and facial motion tracking

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Discussions IVDiscussions IV

Automatic FAQ DetectionAutomatic FAQ Detection

Reconfigurable HardwareReconfigurable Hardware

It is more than softwareIt is more than software

Computer programsComputer programs

Diagram (or Graph)Diagram (or Graph)

Frequently executed codesFrequently executed codes

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Discussions VDiscussions V

Higher dimensional dataHigher dimensional data

For example, molecular modeling …For example, molecular modeling …

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Discussions VDiscussions V

Higher dimensional dataHigher dimensional data

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Discussion VIDiscussion VI

Why?Why?

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Discussions VIDiscussions VI

Microarray data of genesMicroarray data of genes

Source: Dr. Robin E. Everts, 210 ERML, UIUC.Source: Dr. Robin E. Everts, 210 ERML, UIUC.

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AcknowledgeAcknowledge

Supported by USA ARL under Cooperative Supported by USA ARL under Cooperative Agreement No. DAAL01-96-2-0003. Agreement No. DAAL01-96-2-0003.

Felzenszwalb & Huttenlocher for image Felzenszwalb & Huttenlocher for image segmentation program.segmentation program.

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http://www.ifp.uiuc.edu/~honghttp://www.ifp.uiuc.edu/~hong

[email protected]@ifp.uiuc.edu

automatic contextual pattern modeling

Documents

pattern arg model

arg representation

object primitives

local features

image pattern

representation argseparate

appearance features

descriptive model