A new shape decomposition scheme for graph-based representation

Nowadays, the part-based representation of a given shape plays a significant role in shape-related applications, such as those involving content-based retrieval, object recognition, and so on. In this paper, to represent both 2-D and 3-D shapes as a relational structure, i.e. a graph, a new shape decomposition scheme, which recursively performs constrained morphological decomposition (CMD), is proposed. The CMD method adopts the use of the opening operation with the ball-shaped structuring element, and weighted convexity to select the optimal decomposition. For the sake of providing a compact representation, the merging criterion is applied using the weighted convexity difference. Therefore, the proposed scheme uses the split-and-merge approach. Finally, we present experimental results for various, modified 2-D shapes, as well as 3-D shapes represented by triangular meshes. Based on the experimental results, it is believed that the decomposition of a given shape coincides with that based on human insight for both 2-D and 3-D shapes, and also provides robustness to scaling, rotation, noise, shape deformation, and occlusion.

[1]  Ayellet Tal,et al.  Polyhedral surface decomposition with applications , 2002, Comput. Graph..

[2]  Marc Rioux,et al.  Nefertiti: a query by content system for three-dimensional model and image databases management , 1999, Image Vis. Comput..

[3]  Petros Maragos,et al.  Morphological skeleton representation and coding of binary images , 1984, IEEE Trans. Acoust. Speech Signal Process..

[4]  Kaleem Siddiqi,et al.  Parts of Visual Form: Computational Aspects , 1995, IEEE Trans. Pattern Anal. Mach. Intell..

[5]  Carlo Arcelli,et al.  From discs to parts of visual form , 1997, Image Vis. Comput..

[6]  Jianning Xu Morphological decomposition of 2-D binary shapes into convex polygons: a heuristic algorithm , 2001, IEEE Trans. Image Process..

[7]  A. Pentland Recognition by Parts , 1987 .

[8]  Mark de Berg,et al.  Computational geometry: algorithms and applications , 1997 .

[9]  Jianning Xu Efficient morphological shape representation with overlapping disk components , 2001, IEEE Trans. Image Process..

[10]  Sang Uk Lee,et al.  Graph representation by medial axis transform for 3D image retrieval , 2001, IS&T/SPIE Electronic Imaging.

[11]  Thomas S. Huang,et al.  Relevance feedback: a power tool for interactive content-based image retrieval , 1998, IEEE Trans. Circuits Syst. Video Technol..

[12]  Paul L. Rosin Shape partitioning by convexity , 2000, IEEE Trans. Syst. Man Cybern. Part A.

[13]  Ioannis Pitas,et al.  Morphological Shape Decomposition , 1990, IEEE Trans. Pattern Anal. Mach. Intell..

[14]  Luc Vincent,et al.  Morphological transformations of binary images with arbitrary structuring elements , 1991, Signal Process..

[15]  Philip N. Klein,et al.  Recognition of Shapes by Editing Shock Graphs , 2001, ICCV.

[16]  Ioannis Pitas,et al.  A fast implementation of 3-D binary morphological transformations , 2000, IEEE Trans. Image Process..

[17]  Joseph Ronsin,et al.  Shape decomposition and representation using a recursive morphological operation , 1995, Pattern Recognit..

[18]  Longin Jan Latecki,et al.  Convexity Rule for Shape Decomposition Based on Discrete Contour Evolution , 1999, Comput. Vis. Image Underst..