M ramanathan department of engineering design indian institute of technology madras
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M. Ramanathan Department of Engineering Design Indian Institute of Technology Madras. Matching of shapes bound by freeform curves. Shape Matching. A problem that finds similar shape to the query one. Prominent inputs include 3D models, images, curves . Approaches used. Global properties

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M ramanathan department of engineering design indian institute of technology madras

M. Ramanathan

Department of Engineering Design

Indian Institute of Technology Madras

Matching of shapes bound by freeform curves

Department of Engineering Design, IIT Madras


Shape matching

Shape Matching

  • A problem that finds similar shape to the query one.

  • Prominent inputs include 3D models, images, curves.

Department of Engineering Design, IIT Madras


Approaches used

Approaches used

  • Global properties

  • Manifold learning

  • Local properties such as shape diameter

  • For silhouettes - skeletal context, contour-based descriptor, region-based, graph-based.

Department of Engineering Design, IIT Madras


Skeletal based approaches

Skeletal-based approaches

  • Graph-based

  • Part-based

  • Skeletal graph, shock graph, Reeb graph

Department of Engineering Design, IIT Madras


Main contribution

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.

Department of Engineering Design, IIT Madras


Definition of medial axis ma

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.

Department of Engineering Design, IIT Madras


Examples of ma

Examples of MA

Department of Engineering Design, IIT Madras


Properties of ma

Properties of MA

  • Symmetry information

  • One to one correspondence

  • Rigid-body transformation

  • Homotopy

  • Deriving Shape functions

Department of Engineering Design, IIT Madras


Algorithm for shape matching

Algorithm for shape matching

Department of Engineering Design, IIT Madras


Shape functions and signature

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.

Department of Engineering Design, IIT Madras


Distance function df

Distance function (DF)

Department of Engineering Design, IIT Madras


Radius function rf

Radius function (RF)

Department of Engineering Design, IIT Madras


Curvature function cf

Curvature function (CF)

Department of Engineering Design, IIT Madras


Rf and cf

RF and CF

Department of Engineering Design, IIT Madras


Similarity measurement

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.

Department of Engineering Design, IIT Madras


Database details

Database details

Department of Engineering Design, IIT Madras


Models in the database

Models in the database

Partially similar

MA is vastly different for similar shape

Department of Engineering Design, IIT Madras


Retrieval results for df

Retrieval results for DF

All airplanes are retrieved in the first

Row.

Department of Engineering Design, IIT Madras


Retrieval results for rf

Retrieval results for RF

Gear is retrieved at least in the second

Row.

Department of Engineering Design, IIT Madras


Retrieval results for cf

Retrieval results for CF

All brackets are retrieved in the first

Row.

Department of Engineering Design, IIT Madras


First ten results for df

First ten results for DF

Department of Engineering Design, IIT Madras


First ten results for rf

First ten results for RF

Department of Engineering Design, IIT Madras


First ten results for cf

First ten results for CF

Department of Engineering Design, IIT Madras


First and second tier

First and second tier

DF

RF

Department of Engineering Design, IIT Madras


First and second tier1

First and second tier

CF

Department of Engineering Design, IIT Madras


Interpretation

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.)

Department of Engineering Design, IIT Madras


Interpretation contd

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

Department of Engineering Design, IIT Madras


Robustness

Robustness

Retrieval results for 0.02 sample size

Department of Engineering Design, IIT Madras


Computation time

Computation Time

Department of Engineering Design, IIT Madras


Comparsion

Comparsion

  • Princeton Shape Benchmark, Engineering shape Benchmark

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

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.

Department of Engineering Design, IIT Madras


Comparsion contd

Comparsion(contd.)

  • Shape geodesics method

    • Uses Bull’s eye test

    • Top 40 most similar shapes are retrieved.

    • Second tier results are comparable to our method.

  • Inner-distance method

    • Retrieval results are comparable

    • ID requires alignment

    • Shapes need to be articulated variants.

Department of Engineering Design, IIT Madras


Strengths and limitations

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.

Department of Engineering Design, IIT Madras


Future work

Future work

  • Suitable weighting scheme.

  • Visual saliency and other measures.

  • Creation of freeform database.

  • Homotopy property of MA has to be explored.

Department of Engineering Design, IIT Madras


Conclusions

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.

Department of Engineering Design, IIT Madras


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