matching of shapes bound by freeform curves

Department of Engineering Design, IIT Madras CAD’11, Taipei

MATCHING OF SHAPES BOUND BY FREEFORM CURVES

M. RamanathanDepartment of Engineering DesignIndian Institute of Technology Madras

Department of Engineering Design, IIT Madras

Shape Matching A problem that finds similar shape to

the query one. Prominent inputs include 3D models,

images, curves.

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Approaches used

Global properties Manifold learning Local properties such as shape

diameter For silhouettes - skeletal context,

contour-based descriptor, region-based, graph-based.

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Skeletal-based approaches

Graph-based Part-based Skeletal graph, shock graph, Reeb

graph

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Main Contribution Alternate scheme to component-based or part-

based approach typically used in skeleton-based shape matching which calls for identification of correspondences between shapes – a complex task by itself.

Statistical-based skeleton property matching has been proposed and demonstrated.

Footpoints, the corresponding points for a point on MA, appear to have been a neglected entity so far in matching, have been employed to define one of the shape functions.

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Definition of Medial Axis (MA) MA is the locus of points inside domain D

which lie at the centers of all closed discs (or balls in three dimensions) which are maximal (contained in D but is not a proper subset of any other disc (or ball)) in D, together with the limit points of this locus.

The radius function of the MA of D is a continuous, real-valued function defined on M(D) whose value at each point on the MA is equal to the radius of the associated maximal disc or ball.

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Examples of MA

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Properties of MA

Symmetry information One to one correspondence Rigid-body transformation Homotopy Deriving Shape functions

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Algorithm for shape matching

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Shape functions and signature Shape function derived from MA are

Distance between footpoints (DF) Radius function at a point on MA (RF) Curvature at a point on MA (CF)

Shape signature – normalized value of the shape functions, 64-bin histogram

Broad idea is to replace the graph-based approach with statistics-based one.

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Distance function (DF)

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Radius function (RF)

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Curvature function (CF)

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RF and CF

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Similarity Measurement

Given two shape signatures, its similarity can be computed using distance measures such as χ2, Minkowski’s LN, Mahalanobis.

For its simplicity, L2 has been employed.

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Database details

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Models in the database

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Partially similar

MA is vastly different for similar shape


Retrieval results for DF

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All airplanes are retrieved in the firstRow.


Retrieval results for RF

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Gear is retrieved at least in the secondRow.


Retrieval results for CF

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All brackets are retrieved in the firstRow.


First ten results for DF

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First ten results for RF

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First ten results for CF

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First and second tier

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DF

RF


First and second tier

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CF


Interpretation

The classes ‘airplane’, and ‘bracket’ have performed really well.

L-shaped (ell) – it suffers in DF and RF. With CF, it showed good improvements (‘ell’ contains shapes that are of non-uniformly scaled ones, which affect DF and RF, but not CF that much.)

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Interpretation (contd.)

The class ‘rect’ suffered in CF since it zero curvature. The class ‘bird’ also suffers because

it contains a shape with hole and also a shape that is only partially similar. However, the good point here is that, when the shape with hole is given as query, similar non-holed shape is also retrieved

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Robustness

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Retrieval results for 0.02 sample size


Computation Time

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Comparsion Princeton Shape

Benchmark, Engineering shape Benchmark

No freeform dataset available . Closest one Kimia dataset, silhouette in the form of images

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T. Sebastian, P. Klein, and B. Kimia. Recognition of shapes by editing their shock graphs. Pattern Analysis and Machine Intelligence, IEEE Transactions on, 26(5):550–571, May 2004.


Comparsion (contd.) Inner-distance

method Retrieval results

are comparable ID requires

alignment Shapes need to be

articulated variants.

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Shape geodesics method Uses Bull’s eye test Top 40 most similar

shapes are retrieved.

Second tier results are comparable to our method.


Strengths and Limitations The strength of this method is, though

at times the MA structure can vary significantly, similarities are captured.

The method is very fast. Signatures are global in nature – partial

shape matching not possible. Accuracy relies on the computation of

MA Spatial distribution is not considered.

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Future work

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Suitable weighting scheme. Visual saliency and other measures. Creation of freeform database. Homotopy property of MA has to be

explored.


Conclusions

A statistical-based skeleton property matching has been proposed and demonstrated.

Shape functions have been derived from the MA of curved boundaries.

This has the potential to replace component-based or part-based approach typically used in skeleton-based shape matching method.

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matching of shapes bound by freeform curves

Documents

iit madras8algorithm

iit madrasmatching of

ma of d

skeletonbased shape

graphbased approach

shape functionscad11

shape matchingcad11

similar shape