Learning and Bayesian Shape Extraction for Object Recognition

We present a novel algorithm for extracting shapes of contours of (possibly partially occluded) objects from noisy or low-contrast images. The approach taken is Bayesian: we adopt a region-based model that incorporates prior knowledge of specific shapes of interest. To quantify this prior knowledge, we address the problem of learning probability models for collections of observed shapes. Our method is based on the geometric representation and algorithmic analysis of planar shapes introduced and developed in [15]. In contrast with the commonly used approach to active contours using partial differential equation methods [12,20,1], we model the dynamics of contours on vector fields on shape manifolds.

[1]  K. Mardia,et al.  Statistical Shape Analysis , 1998 .

[2]  Olivier D. Faugeras,et al.  Statistical shape influence in geodesic active contours , 2000, Proceedings IEEE Conference on Computer Vision and Pattern Recognition. CVPR 2000 (Cat. No.PR00662).

[3]  C. Small.  The statistical theory of shape , 1996 .

[4]  Stefano Soatto,et al.  A Pseudo-distance for Shape Priors in Level Set Segmentation , 2003 .

[5]  Asger Hobolth,et al.  On the Relation between Edge and Vertex Modelling in Shape Analysis , 2002 .

[6]  U. Grenander,et al.  Computational anatomy: an emerging discipline , 1998 .

[7]  Anil K. Jain,et al.  Automatic Construction of 2D Shape Models , 2001, IEEE Trans. Pattern Anal. Mach. Intell..

[8]  James A. Sethian,et al.  Level Set Methods and Fast Marching Methods: Evolving Interfaces in Computational Geometry, Fluid , 2012 .

[9]  Michael I. Miller,et al.  Group Actions, Homeomorphisms, and Matching: A General Framework , 2004, International Journal of Computer Vision.

[10]  J. Sethian.  Level set methods : evolving interfaces in geometry, fluid mechanics, computer vision, and materials science , 1996 .

[11]  H. Piaggio.  Differential Geometry of Curves and Surfaces , 1952, Nature.

[12]  Xiao Liu,et al.  Geometric analysis of constrained curves for image understanding , 2003 .

[13]  H. Karcher.  Riemannian center of mass and mollifier smoothing , 1977 .

[14]  D. Mumford,et al.  Optimal approximations by piecewise smooth functions and associated variational problems , 1989 .

[15]  I. Dryden,et al.  Using circulant symmetry to model featureless objects , 2000 .

[16]  Milan Sonka,et al.  Learning Shape Models from Examples Using Automatic Shape Clustering and Procrustes Analysis , 1999, IPMI.

[17]  Anuj Srivastava,et al.  Hierarchical Organization of Shapes for Efficient Retrieval , 2004, ECCV.

[18]  Jiří Matas,et al.  Computer Vision - ECCV 2004 , 2004, Lecture Notes in Computer Science.

[19]  D. Kendall,et al.  The Riemannian Structure of Euclidean Shape Spaces: A Novel Environment for Statistics , 1993 .

[20]  Anuj Srivastava,et al.  Analysis of planar shapes using geodesic paths on shape spaces , 2004, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[21]  Tony F. Chan,et al.  Variational PDE models in image processing , 2002 .

[22]  D. Kendall.  SHAPE MANIFOLDS, PROCRUSTEAN METRICS, AND COMPLEX PROJECTIVE SPACES , 1984 .

[23]  Ulf Grenander,et al.  General Pattern Theory: A Mathematical Study of Regular Structures , 1993 .

[24]  Laurent Younes,et al.  Computable Elastic Distances Between Shapes , 1998, SIAM J. Appl. Math..

[25]  Demetri Terzopoulos,et al.  Snakes: Active contour models , 2004, International Journal of Computer Vision.

[26]  Daniel Cremers,et al.  Diffusion Snakes: Introducing Statistical Shape Knowledge into the Mumford-Shah Functional , 2002, International Journal of Computer Vision.