CAD’11, TaipeiDepartment of Engineering Design, IIT Madras M. Ramanathan Department of Engineering Design Indian Institute of Technology Madras

Shape Matching  A problem that finds similar shape to the query one.  Prominent inputs include 3D models, images, curves. CAD’11, TaipeiDepartment 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, TaipeiDepartment of Engineering Design, IIT Madras

Skeletal-based approaches  Graph-based  Part-based  Skeletal graph, shock graph, Reeb graph CAD’11, TaipeiDepartment 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, TaipeiDepartment 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, TaipeiDepartment of Engineering Design, IIT Madras

Examples of MA CAD’11, TaipeiDepartment of Engineering Design, IIT Madras

Properties of MA  Symmetry information  One to one correspondence  Rigid-body transformation  Homotopy  Deriving Shape functions CAD’11, TaipeiDepartment of Engineering Design, IIT Madras

Algorithm for shape matching CAD’11, TaipeiDepartment 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, TaipeiDepartment of Engineering Design, IIT Madras

Distance function (DF) CAD’11, TaipeiDepartment of Engineering Design, IIT Madras

Radius function (RF) CAD’11, TaipeiDepartment of Engineering Design, IIT Madras

Curvature function (CF) CAD’11, TaipeiDepartment of Engineering Design, IIT Madras

RF and CF CAD’11, TaipeiDepartment of Engineering Design, IIT Madras

Similarity Measurement  Given two shape signatures, its similarity can be computed using distance measures such as χ2, Minkowski’s L N, Mahalanobis.  For its simplicity, L 2 has been employed. CAD’11, TaipeiDepartment of Engineering Design, IIT Madras

Database details CAD’11, TaipeiDepartment of Engineering Design, IIT Madras

Models in the database CAD’11, TaipeiDepartment of Engineering Design, IIT Madras Partially similar MA is vastly different for similar shape

Retrieval results for DF CAD’11, TaipeiDepartment of Engineering Design, IIT Madras All airplanes are retrieved in the first Row.

Retrieval results for RF CAD’11, TaipeiDepartment of Engineering Design, IIT Madras Gear is retrieved at least in the second Row.

Retrieval results for CF CAD’11, TaipeiDepartment of Engineering Design, IIT Madras All brackets are retrieved in the first Row.

First ten results for DF CAD’11, TaipeiDepartment of Engineering Design, IIT Madras

First ten results for RF CAD’11, TaipeiDepartment of Engineering Design, IIT Madras

First ten results for CF CAD’11, TaipeiDepartment of Engineering Design, IIT Madras

First and second tier CAD’11, TaipeiDepartment of Engineering Design, IIT Madras DF RF

First and second tier CAD’11, TaipeiDepartment of Engineering Design, IIT Madras 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.) CAD’11, TaipeiDepartment 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, TaipeiDepartment of Engineering Design, IIT Madras

Robustness CAD’11, TaipeiDepartment of Engineering Design, IIT Madras Retrieval results for 0.02 sample size

Computation Time CAD’11, TaipeiDepartment 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, TaipeiDepartment of Engineering Design, IIT Madras 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. CAD’11, TaipeiDepartment of Engineering Design, IIT Madras  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. CAD’11, TaipeiDepartment of Engineering Design, IIT Madras

CAD’11, TaipeiDepartment of Engineering Design, IIT Madras  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. CAD’11, TaipeiDepartment of Engineering Design, IIT Madras