Multi-scale Singularity Trees: Soft-Linked Scale-Space Hierarchies

We consider images as manifolds embedded in a hybrid of a high dimensional space of coordinates and features. Using the proposed energy functional and mathematical landmarks, images are partitioned into segments. The nesting of image segments occurring at catastrophe points in the scale-space is used to construct image hierarchies called Multi-Scale Singularity Trees (MSSTs). We propose two kinds of mathematical landmarks: extrema and saddles. Unlike all other similar methods proposed hitherto, our method produces soft-linked image hierarchies in the sense that all possible connections are suggested along with their energies. The information added makes possible for directly estimating the stability of the connection and hence the costs of transitions. Aimed applications of MSSTs include multi-scale pre-segmentation, image matching, sub-object extraction, and hierarchical image retrieval.

[1]  Stephen M. Pizer,et al.  A Multiresolution Hierarchical Approach to Image Segmentation Based on Intensity Extrema , 1990, IEEE Trans. Pattern Anal. Mach. Intell..

[2]  Ron Kimmel,et al.  From High Energy Physics to Low Level Vision , 1997, Scale-Space.

[3]  Lewis D. Griffin,et al.  Scale Space Methods in Computer Vision , 2003, Lecture Notes in Computer Science.

[4]  Sven Kreiborg,et al.  Transitions of Multi-scale Singularity Trees , 2005, DSSCV.

[5]  Lucas J. van Vliet,et al.  Recursive Gaussian derivative filters , 1998, Proceedings. Fourteenth International Conference on Pattern Recognition (Cat. No.98EX170).

[6]  Peter Johansen,et al.  Gaussian Scale-Space Theory , 1997, Computational Imaging and Vision.

[7]  Andrew P. Witkin,et al.  Scale-Space Filtering , 1983, IJCAI.

[8]  Luc Florack,et al.  Using multiscale top points in image matching , 2004, 2004 International Conference on Image Processing, 2004. ICIP '04..

[9]  Arjan Kuijper,et al.  The deep structure of Gaussian scale space images , 2002 .

[10]  Laurent D. Cohen,et al.  The Extrema Edges , 2003, Scale-Space.

[11]  Andy Harter,et al.  Parameterisation of a stochastic model for human face identification , 1994, Proceedings of 1994 IEEE Workshop on Applications of Computer Vision.

[12]  Mads Nielsen,et al.  Multiscale Gradient Magnitude Watershed Segmentation , 1997, ICIAP.

[13]  Luc Florack,et al.  Multiscale hierarchical segmentation , 2003 .

[14]  Bram van Ginneken,et al.  Applications of Locally Orderless Images , 1999, J. Vis. Commun. Image Represent..

[15]  Joachim Weickert,et al.  Parallel implementations of AOS schemes: a fast way of nonlinear diffusion filtering , 1997, Proceedings of International Conference on Image Processing.

[16]  J. Koenderink.  The structure of images , 2004, Biological Cybernetics.

[17]  J. A. Sethian,et al.  Fast Marching Methods , 1999, SIAM Rev..

[18]  Stefano Levialdi,et al.  Image Analysis and Processing , 1987 .

[19]  James Damon,et al.  Local Morse Theory for Gaussian Blurred Functions , 1997, Gaussian Scale-Space Theory.