S hape Matching and Classification Using Height Functions

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# S hape Matching and Classification Using Height Functions - PowerPoint PPT Presentation

S hape Matching and Classification Using Height Functions. Xide Xia ENGN 2560 Advisor: Prof. Kimia Project Initial Presentation. S hape Matching:. object recognition, character recognition, medical image and protein analysis …

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### Shape Matching and Classification Using Height Functions

Xide Xia

ENGN 2560

Project Initial Presentation

Shape Matching:

object recognition, character recognition, medical image and protein analysis …

• Geometric Transformations (translation, rotation, scaling, etc.)
• Nonlinear Deformations (noise, articulation and occlusion)
Steps:
• 1) Shape descriptor with height functions
• 2) Similarity measure using the height descriptor
Shape descriptor with height functions:
• A sequence of equidistant sample points X:

X={Xi} , i=1,2,….,N

• Tangent line Li:

its direction is always starting from Xi-1 to Xi+1

• Height value Hi:

the symboled distance between the jth (j = 1,. . . ,N) sample point Xj and the tangent line Li is defined as a height value hi,j.

(the height value of the jth sample point Xj according to the reference axis Li of the point Xi)

Descriptor Hi：
• the direction of the reference axis Li
• the location of the sample point Xi on the shape contour X.

Smoothed height values:

F is an M *N matrix with column i being the shape descriptor Fi of the sample point Xi.

Local nomalization:

Consequently, the value of each entry in the matrix F after normalization is in the interval [-1, 1].

Similarity measure using the height descriptor:

In shape recognition, we usually compute a shape similarity or dissimilarity (distance) to find the optimal correspondence of contour points.

Dynamic Programming (DP) algorithm to find the correspondence

The shape dissimilarity: the sum of the distances of the corresponding points.

The cost (distance) of matching p and q:

• Weight coefficient
• Dissimilarity between the two shapes:

Given two shapes X and Y. With DP we compute an optimal correspondence x to y that the is minimal.

Humans are generally more sensitive to contour deformations when the complexity of the contour is lower!

• Shape complexity:

where std denotes the standard deviation.

The dissimilarity or distance between two shapes X, Y normalized by their shape complexity values:

where the factor is used to avoid divide-by-zero.

Shape descriptor with height functions:
• A sequence of equidistant sample points X
• Tangent line Li
• Height value Hi
• Smoothed height values
• Local nomalization

Similarity measure using the height descriptor:

• The cost (distance) of matching p and q
• Weight coefficient
• Dissimilarity between the two shapes
• Shape complexity
• Dissimilarity normalized by complexity values
Schedule:
• 1st week: Learn the algorithm well
• 2nd ~3th week: Write up the codes of the shape descriptor part
• 4th ~5th week: Write up the codes of the matching part
• 6th~7th week: Debug and Test in different datasets, Make Comparison with other shape matching algorithm (Shock Graphs)
• 8th week: Make conclusion, Prepare for the final presentation