Experimental analysis of Harmonic Shape Images

In our early work, a representation called Harmonic Shape Images for 3D free-form surfaces was proposed and applied to solve the surface matching problem (D. Zhang and M. Hebert, 1999). Extensive experiments using real data are conducted to analyze the performance of Harmonic Shape Images with respect to discriminability, stability and robustness to resolution and occlusion. The results show that Harmonic Shape Images are an appropriate representation for 3D surface comparison. Examples of surface comparison using real data are presented.

[1]  B. O'neill.  Elementary Differential Geometry , 1966 .

[2]  Katsushi Ikeuchi,et al.  A Spherical Representation for Recognition of Free-Form Surfaces , 1995, IEEE Trans. Pattern Anal. Mach. Intell..

[3]  Tony DeRose,et al.  Multiresolution analysis of arbitrary meshes , 1995, SIGGRAPH.

[4]  Dongmei Zhang,et al.  On Generating Multi-resolution Representations of Polygonal Meshes , 1998 .

[5]  Katsushi Ikeuchi,et al.  Building 3-D Models from Unregistered Range Images , 1995, CVGIP Graph. Model. Image Process..

[6]  J. Eells,et al.  Harmonic Mappings of Riemannian Manifolds , 1964 .

[7]  Yuanlong Xin,et al.  Geometry of Harmonic Maps , 1996 .

[8]  Jay L. Devore,et al.  Probability and statistics for engineering and the sciences , 1982 .

[9]  Gérard G. Medioni,et al.  Structural Indexing: Efficient 3-D Object Recognition , 1992, IEEE Trans. Pattern Anal. Mach. Intell..

[10]  Robert Bergevin,et al.  Estimating the 3D rigid transformation between two range views of a complex object , 1992, [1992] Proceedings. 11th IAPR International Conference on Pattern Recognition.

[11]  Dongmei Zhang,et al.  Multi-scale classification of 3-D objects , 1997, Proceedings of IEEE Computer Society Conference on Computer Vision and Pattern Recognition.

[12]  Gérard G. Medioni,et al.  Object modelling by registration of multiple range images , 1992, Image Vis. Comput..

[13]  Martial Hebert,et al.  On 3D shape similarity , 1996, Proceedings CVPR IEEE Computer Society Conference on Computer Vision and Pattern Recognition.

[14]  M. Hebert,et al.  The Representation, Recognition, and Locating of 3-D Objects , 1986 .

[15]  David J. Kriegman,et al.  HOT curves for modelling and recognition of smooth curved 3D objects , 1994, 1994 Proceedings of IEEE Conference on Computer Vision and Pattern Recognition.

[16]  Paul J. Besl.  Triangles as a Primary Representation , 1994, Object Representation in Computer Vision.

[17]  Chitra Dorai,et al.  COSMOS - A Representation Scheme for 3D Free-Form Objects , 1997, IEEE Trans. Pattern Anal. Mach. Intell..

[18]  Paul J. Besl,et al.  A Method for Registration of 3-D Shapes , 1992, IEEE Trans. Pattern Anal. Mach. Intell..

[19]  David B. Cooper,et al.  Describing Complicated Objects by Implicit Polynomials , 1994, IEEE Trans. Pattern Anal. Mach. Intell..

[20]  Gérard G. Medioni,et al.  Object modeling by registration of multiple range images , 1991, Proceedings. 1991 IEEE International Conference on Robotics and Automation.

[21]  Paul J. Besl,et al.  The Free-Form Surface Matching Problem , 1990 .

[22]  Dongmei Zhang,et al.  Harmonic maps and their applications in surface matching , 1999, Proceedings. 1999 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (Cat. No PR00149).