Shape Matching with Occlusion in Image Databases

Aristeidis DiplarosEuripides G.M. Petrakis

Evangelos Milios

Technical University of Crete

Given a shape database, retrieve shapes which are similar to an example shape.

Shape matching is the central problem of shape retrieval.

How similar?

Problem description

Methodology

Main idea: Merging of a "noisy" sequence of segments and matching with one or more segments of the other shape.

Merging of 3 segments of the upper curve And matching with one segment of the lower curve

B-spline approximation.

Curvature:

Inflections points are given by k(u)=0.

Segments with k>0

are convex (C).

Segments with k<0

are concave (V).

The shape is transformed

to a sequence of segments VCVC.

k u x yy x

x2 y

2 3 2

Shape A Dynamic Programming Table

i

2

1

1 2 3 Shape B j

transitions = matching of segments.

simple or compound transitions.

Shape Á

i

2

1

1 2 3 Shape  j

No matching of C with V.

CVC...C -> C and VCV...V-> V.

Only half of the cells are filled with values.

Matching cases

???????? ????????

????? ???????? ? ????? ????????

? ???????? ???????

? ???????? ???????

? ???????? ???????

? ???????? ???????

? ???????? ???????

Shape MatchingShape Matching

Global Matching Local Matching

A openB open

A openB closed

A closedB closed

A openB open

A openB closed

The DP table consists of three distinct areas:

Initialization area (the first row) -

filled with :

Termination area (the last row) – all complete paths end at cells in this area.

Computation area (the remaining rows)

1 2 3 4 5 6 7

5

4

3

2

1 S S S S

X X X

X X X

X X X

T T T

X

T

i

j

1

2

g 1 ,j0 ,u0 ,v0 ,m0 ,n00 ,M ,N ,0 ,0

For each "accessible" cell we calculate the matching cost as:

Where:

Constant ë: small ë favours merging. large ë prevents merging.

a i w1i w ,b jw1 jw MergingCost a i w1i w

MergingCost b jw1 jw DissimilarityCost a i t1i t ,b jt1 j t

g iw , jw mini w1 ,jw1

g iw1 ,jw1 aiw1iw ,b jw1 jw

Three features are calculated for each segment:

l = arc length. S = area between the chord and the arc. ₩ = the angle traversed by the tangent to the segment.

Experimental results

Two datasets: 1000 closed shaped 1500 open shapes

20 queries. Precision / recall diagrams. Human relevance judgments. Demonstrate the superiority of our method over traditional

shape matching method based on Fourier and Moments

Example

Closed dataset

Open dataset

Conclusions

Our approach handles occluded, noisy or deformed shapes and is independent of translation, scale, rotation, starting point selection and symmetric transformations of shapes.

Our evaluation indicates that our approach is well suited to shape matching and retrieval.