Download ppt - Shape context

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Shape Context

Rocío Cabrera u1908272

Vanya Valindria u1908259

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Introduction

Can you guess what number it is?

Objectives

“Have descriptors that can be computed in one image and used to find corresponding points, if visible, in another image.”

“Given a query model image, to develop an algorithm capable of retrieving similar-shaped images from an extensive database”

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Process Stages

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Solve the correspondence problem between

the two shapes

Use the correspondences to estimate an

aligning transform

Compute the distance between

the two shapes

Evaluate the distance and classify the

shape

. .... ??

SHAPE CONTEXT“A novel approach to measuring similarities between shapes and exploit it for object classification/recognition”

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Shape Context Computation

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Step 1. Obtain from ShapeP and ShapeQ n-samples uniformly spaced taken from their edge elements


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Step 2. Compute the Euclidean distance (r) and the angle (θ) from each point in the set to all the other n-1 points. Normalize r by the median distance (λ) and measure the angle relative to the positive x-axis.


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Step 3. Compute the log of the r vector.Discretize the distance and angle measurements


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Step 4. For each origin point, capture number of points that lie a given θ,R bin.

Each shape context is a log-polar histogram of the coordinates of the n-1 points measured from the origin reference point.


Shape context of the sample points in ShapeP and ShapeQ.

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Matching Shape Contexts

How can we assign the sample points of ShapeP to correspond to those of ShapeQ?

Determining shape correspondences such that:

1. Corresponding points have very similar descriptors

2. The correspondences are unique

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Define matching cost function

Shape context Distance between the two normalized histograms

Local appearance Dissimilarity of the tangent angles

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Modeling Transformation

Given a set of correspondences, estimate a transformation that maps the model into the target

Euclidean transformation

Affine model

Thin Plate Spline (TPS)

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Classification/Recognition

This enables a measure of shape similarity The dissimilarity between two shapes can be computed

as the sum of matching errors between corresponding points, together with a term measuring the magnitude of the aligning transform

Given a dissimilarity measure, a k-NN technique can be used for object classification/recognition

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Method Evaluation

Advantages Incorporates invariance to:

Translation

Scale

Rotation

Occlusions

Drawbacks Sensitive local distortion or

blurred edges

Problems in cluttered background

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Applications

Digit recognition

Silhouette similarity-based retrieval

3 D object recognition

Trademark retrieval

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Database for Digit Recognition

MNIST datasets of handwritten digits:

60,000 training and 10,000 test digits

Links:

http://yann.lecun.com/exdb/mnist/

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Database for Silhouette

MPEG-7 shape silhouette database (Core Experiment CE-Shape-1 part B)

1400 images: 70 shapes categories and 20 images per category

Links:

http://mpeg.chiariglione.org/standards/mpeg-7/mpeg-7.htm

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Database for 3-D object recognition

COIL-20 database

20 common household objects; turned every 5˚ for a total of 72 views per object

Links:

http://www1.cs.columbia.edu/CAVE/software/softlib/coil-20.php

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Database for Trademark retrieval

300 different real-world trademark

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MATLAB DEMO

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Conclusions

The shape context method is simple to implement yet it is a rich shape descriptor

The methodology makes it invariant to translation, scale and rotation

Useful tool for shape matching and recognition

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