Associative Hierarchical CRFs for Object Class Image Segmentation L’ubor Ladick’y and Chris Russell Oxford Brookes University Pushmeet Kohli Microsoft.

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Associative Hierarchical CRFs for Object Class Image Segmentation

L’ubor Ladick’y and Chris RussellOxford Brookes University

Pushmeet KohliMicrosoft Research Cambridge

International Conference on Computer Vision (ICCV) 2009

Philip H.S. TorrOxford Brookes University

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Outline• Introduction

• Random Fields for Labelling Problems

• Hierarchical CRF for Object Segmentation

• Experiments and Results

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Structure

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Introduction

Distribution of identical billiard balls

Region ofinterest

Center ofmass

Mean Shiftvector

Objective : Find the densest region

Mean Shift

Distribution of identical billiard balls

Region ofinterest

Center ofmass

Mean Shiftvector

Objective : Find the densest region

Mean Shift

Distribution of identical billiard balls

Region ofinterest

Center ofmass

Mean Shiftvector

Objective : Find the densest region

Mean Shift

Distribution of identical billiard balls

Region ofinterest

Center ofmass

Mean Shiftvector

Objective : Find the densest region

Mean Shift

Distribution of identical billiard balls

Region ofinterest

Center ofmass

Mean Shiftvector

Objective : Find the densest region

Mean Shift

Distribution of identical billiard balls

Region ofinterest

Center ofmass

Mean Shiftvector

Objective : Find the densest region

Mean Shift

Distribution of identical billiard balls

Region ofinterest

Center ofmass

Objective : Find the densest region

Mean Shift

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Pixel V.S. Segment The difference of pair CRFs between based on pixels and segments

a) Based on pixels:a) No quantization errors

b) Lack of long range interactions

c) Results oversmoothed

b) Based on segmentsa) Allows long range interactions

b) Can not recover from incorrect segmentation

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Introduction Propose a novel hierarchical CRF

Integration of features derived for different quantisation levels

Propose new sophisticated potentials defined over the different levels of the quantisation hierarchy

Use a novel formulation that allows context to be incorporate at multiple levels of multiple quantisation

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Random Fields for Labelling Problems Introduce the pixel-based CRF used for formulation the

object class segmentation problem

One discrete R.V. per image pixel, each of which may take a value from the set of labels

Symbols:

Label:

R.V. :

Pixel

The set of all neighbours of the variable :

A clique c is a set of random variables

Labelling: denoted by take the value from

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CRFs

D: the set of the data, Z: the partition function, C: the set of all cliques

: the potential function of the clique ,

The energy form:

The most probable or MAP labeling :

Wrote as the sum of unary and pairwise potentials

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The Robust Model Extended by the robust potentials [KohLi et al., 2008 ]

S: the set of the segments

The pixels within the same segment are more like likely to take the same label

the form of the robust potentials:

;

The weighted version:

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-Based Hierarchical CRFs

The single auxiliary variable where c is a segment or a clique

Take the value from an extended label set

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-Based Hierarchical CRFs New cost function over

The unary potential over Y,

The pairwise potential

over Y and X

Goal:

The new energy function:

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Recursive Form

The auxiliary variables in the last layer are the input variable

The new energy function:

The recursive form:

Initial form:

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Hierarchical CRF for Object Segmentation

Describe the set of potentials in the object-class segmentation problem

Include unary potentials for both pixels and segments, pairwise potentials between pixels and segments and connective potentials between pixels and their containing segments

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Robustness to misleading segmentations

Using unsupervised segmentation algorithm may be misleading – segment may contain multiple object classed

Assigning the same label to all pixels will result in an incorrect labeling

Overcome it by using the segment quality measures [Rabinovich et at., 2009] and [Ren and Malik, 2003]

By modifying the potentials according to a quality sensitive measure for all segment c

Writing weight features based potential over c

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Potentials for object class segmentation Refer to elements of each layer as pixels, segments, and super-

segments

At the pixel level:

The unary potentials are computed using a boosted dense feature classifier [Shotton et al., 2006]

The pairwise potentials [Boykov and Jolly, 2001] , [Rother at al., 2004]:

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Potentials for object class segmentation

At the segment level:

Initially found using a fine scale mean-shift algorithm [Comaniciu and Meer, 2002]

Contain little novel local information, but strong predictors of consistency

The potentials learning at this level are uniform, due to the lack of unique features, however as they are strongly indicative of local consistency, the penalty associated with breaking them is high

To encourage neighbouring segments with similar texture to take the same label, used pairwise potentials based on the Euclidean distance if normalized histograms of colour

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Potentials for object class segmentation

At the super-segment level:

Based upon a coarse mean-shift segmentation, performed over the result of the previous segmentations

Contain significantly more internal information than their smaller children

Propose unary segment potential based on the histograms of features

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Unary Potentials From Dense Feature

Perform texture based segmentation at pixel level

Derived from TextonBoost [Shotton et al., 2006]

The features are computed on every pixel

Extend the TextonBoost by boosting classifiers defined on multiple dense feature together

Dense–feature shape filters defined by triplets: [f, t, r] where f is a feature type, t is a feature cluster, and r is a rectangular region

Feature response : Given a point i, the number of features of type f belong to the cluster t in the region r relative to the point i

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Histogram-Based Segment Unary Potentials

Defined over segments and super-segments

The distribution of dense features responses are more discriminative than any feature along

The unary potential of an auxiliary variable representing a segment is learnt by (using the normalized histograms of multiple clustered dense features) using multi-class Gentle Ada-boost[Torralba et al., 2004]

Weak classifiers: f: the normalized histogram of the feature set t: the cluster index a: threshold

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Histogram-Based Segment Unary Potentials

The segment potential: a : the response given by the Ada-boost classifier to clique c taking label l a : the truncation threshold a , and a normalizing constant

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Learning Weights for Hierarchical CRFs

Uses a coarse to fine, layer-based, local search scheme over a validation set

Introduce additional notation:

a) : the variable contained in the layer

b) : the labelling of associated with a MAP estimate

c) Determine a dominant label for each segment c, such that when , if there is no such dominant label, set a

d) The label of a clique : correspond to the dominant label of this clique(segment) in the ground truth (or ) for its containing ot be correctly labelled

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Learning Weights for Hierarchical CRFs

At each layer, seek to minimize the discrepancy between the dominant ground truth of a clique(segment), and the value of the MAP estimate

Choose parameters λ to minimize

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Algorithm

: the weighting of unary terms in the layer a : the weighting of pairwise terms in the layer a : a scalar modifier of all terms in the layer a : an arbitrary constant that controls the precision of the final assignment of

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Experiments Two data sets

1. MSRC-21 [Shotton et al., 2006]

Resolution: pixels

21 object classes

2. PASCAL VOC 2008 [Everingham et al., 2008, website]

511 training, 512 validation and 512 segmented test images

20 foreground and 1 background classes

10, 057 images for which only the bounding boxes of the objects present in the image are marked

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Results on The MSRC-21

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Results on The MSRC-21

[25]: J. Shotton et al., CVPR, 2008

[26]: J. Shotton et al., ECCV, 2006

[1]: D. Batra et al., CVPR, 2008

[25]: L. Yang et al., CVPR, 2007

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Results on The MSRC-21

[25]: J. Shotton et al., CVPR, 2008

[26]: J. Shotton et al., ECCV, 2006

[1]: D. Batra et al., CVPR, 2008

[25]: L. Yang et al., CVPR, 2007

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Results on The VOC-2008

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Results on The VOC-2008