Matching of shapes bound by freeform curves
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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
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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.
CAD’11, Taipei
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Department of Engineering Design, IIT Madras
Approaches used
Global properties Manifold learning Local properties such as shape
diameter For silhouettes - skeletal context,
contour-based descriptor, region-based, graph-based.
CAD’11, Taipei
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Department of Engineering Design, IIT Madras
Skeletal-based approaches
Graph-based Part-based Skeletal graph, shock graph, Reeb
graph
CAD’11, Taipei
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Department of Engineering Design, IIT Madras
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.
CAD’11, Taipei
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Department of Engineering Design, IIT Madras
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.
CAD’11, Taipei
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Department of Engineering Design, IIT Madras
Examples of MA
CAD’11, Taipei
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Department of Engineering Design, IIT Madras
Properties of MA
Symmetry information One to one correspondence Rigid-body transformation Homotopy Deriving Shape functions
CAD’11, Taipei
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Department of Engineering Design, IIT Madras
Algorithm for shape matching
CAD’11, Taipei
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Department of Engineering Design, IIT Madras
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.
CAD’11, Taipei
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Department of Engineering Design, IIT Madras
Distance function (DF)
CAD’11, Taipei
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Department of Engineering Design, IIT Madras
Radius function (RF)
CAD’11, Taipei
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Department of Engineering Design, IIT Madras
Curvature function (CF)
CAD’11, Taipei
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Department of Engineering Design, IIT Madras
RF and CF
CAD’11, Taipei
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Department of Engineering Design, IIT Madras
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.
CAD’11, Taipei
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Department of Engineering Design, IIT Madras
Database details
CAD’11, Taipei
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Department of Engineering Design, IIT Madras
Models in the database
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Partially similar
MA is vastly different for similar shape
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Department of Engineering Design, IIT Madras
Retrieval results for DF
CAD’11, Taipei
All airplanes are retrieved in the firstRow.
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Department of Engineering Design, IIT Madras
Retrieval results for RF
CAD’11, Taipei
Gear is retrieved at least in the secondRow.
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Department of Engineering Design, IIT Madras
Retrieval results for CF
CAD’11, Taipei
All brackets are retrieved in the firstRow.
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Department of Engineering Design, IIT Madras
First ten results for DF
CAD’11, Taipei
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Department of Engineering Design, IIT Madras
First ten results for RF
CAD’11, Taipei
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Department of Engineering Design, IIT Madras
First ten results for CF
CAD’11, Taipei
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Department of Engineering Design, IIT Madras
First and second tier
CAD’11, Taipei
DF
RF
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Department of Engineering Design, IIT Madras
First and second tier
CAD’11, Taipei
CF
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Department of Engineering Design, IIT Madras
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.)
CAD’11, Taipei
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Department of Engineering Design, IIT Madras
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
CAD’11, Taipei
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Department of Engineering Design, IIT Madras
Robustness
CAD’11, Taipei
Retrieval results for 0.02 sample size
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Department of Engineering Design, IIT Madras
Computation Time
CAD’11, Taipei
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Department of Engineering Design, IIT Madras
Comparsion Princeton Shape
Benchmark, Engineering shape Benchmark
No freeform dataset available . Closest one Kimia dataset, silhouette in the form of images
CAD’11, Taipei
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.
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Department of Engineering Design, IIT Madras
Comparsion (contd.) Inner-distance
method Retrieval results
are comparable ID requires
alignment Shapes need to be
articulated variants.
CAD’11, Taipei
Shape geodesics method Uses Bull’s eye test Top 40 most similar
shapes are retrieved.
Second tier results are comparable to our method.
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Department of Engineering Design, IIT Madras
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.
CAD’11, Taipei
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Department of Engineering Design, IIT Madras
Future work
CAD’11, Taipei
Suitable weighting scheme. Visual saliency and other measures. Creation of freeform database. Homotopy property of MA has to be
explored.
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Department of Engineering Design, IIT Madras
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.
CAD’11, Taipei