Shape Matching Using Sets of Curve Geometric Invariant Point

We introduce a non-iterative geometric-based method for shape matching using a novel set of geometric landmarks residing on a 2D contours. These landmarks are intrinsic and are computed from the differential geometry of the curve. We exploit the invariant properties of geometric landmarks that are local and preserved under the affine and some perspective transformation. Geometric invariant exploits coplanar five-point invariant and ration of area constructed from a sequence of consecutive landmarks. These invariants are preserved not only in affine map but weak perspective map as well. To reduce the sensitivity of the landmarks to noise, we use a B-Spline surface representation that smoothes out the curve prior to the computation of the landmarks. The matching is achieved by establishing correspondences between the landmarks after a conformal sorting based on derived absolute invariant and registering the contours. The experiments have shown that the purposed methods are robust and promising even in the presence of noise.

[1]  Manfredo P. do Carmo,et al.  Differential geometry of curves and surfaces , 1976 .

[2]  David Salesin,et al.  Fast multiresolution image querying , 1995, SIGGRAPH.

[3]  R. Bolles,et al.  Recognizing and Locating Partially Visible Objects: The Local-Feature-Focus Method , 1982 .

[4]  Venu Madhav Govindu,et al.  Alignment Using Distributions of Local Geometric Properties , 1999, IEEE Trans. Pattern Anal. Mach. Intell..

[5]  Andrew Zisserman,et al.  Appendix—projective geometry for machine vision , 1992 .

[6]  Eamon B. Barrett,et al.  General methods for determining projective invariants in imagery , 1991, CVGIP Image Underst..

[7]  Azriel Rosenfeld,et al.  A Min-Max Medial Axis Transformation , 1981, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[8]  幹男 山本.  “IEEE Trans. on Medical Imaging”誌と本誌 , 1983 .

[9]  Edward J. Delp,et al.  Partial Shape Recognition: A Landmark-Based Approach , 1990, IEEE Trans. Pattern Anal. Mach. Intell..

[10]  F. S. Cohen,et al.  Registering coronal histological 2-D sections of a rat brain with coronal sections of a 3-D brain atlas using geometric curve invariants and B-spline representation , 1998, IEEE Transactions on Medical Imaging.

[11]  Carl de Boor,et al.  A Practical Guide to Splines , 1978, Applied Mathematical Sciences.

[12]  George C. Stockman,et al.  Matching Images to Models for Registration and Object Detection via Clustering , 1982, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[13]  Robert C. Bolles,et al.  Locating Partially Visible Objects: The Local Feature Focus Method , 1980, AAAI.

[14]  HARRY BLUM,et al.  Shape description using weighted symmetric axis features , 1978, Pattern Recognit..

[15]  James Ze Wang,et al.  Wavelet-based image indexing techniques with partial sketch retrieval capability , 1997, Proceedings of ADL '97 Forum on Research and Technology. Advances in Digital Libraries.

[16]  Evangelos E. Milios,et al.  Shape matching using curvature processes , 1988, ICASSP-88., International Conference on Acoustics, Speech, and Signal Processing.

[17]  Jake K. Aggarwal,et al.  Model Construction and Shape Recognition from Occluding Contours , 1989, IEEE Trans. Pattern Anal. Mach. Intell..

[18]  A. Ardeshir Goshtasby,et al.  Piecewise linear mapping functions for image registration , 1986, Pattern Recognit..

[19]  M. Docarmo.  Differential geometry of curves and surfaces , 1976 .

[20]  Peter J. van Otterloo,et al.  A contour-oriented approach to shape analysis , 1991 .

[21]  Dinggang Shen,et al.  Affine-invariant image retrieval by correspondence matching of shapes , 1999, Image Vis. Comput..

[22]  P. Besl.  Geometric modeling and computer vision , 1988, Proc. IEEE.