Adaptive B-splines and boundary estimation

This paper describes a boundary estimation scheme based on a new adaptive approach to B-spline curve fitting. The number of control points of the spline, their locations, and the observation parameters, are all considered unknown. The optimal number of control points is estimated via a new minimum description length (MDL) type criterion. The result is an adaptive parametrically deformable contour which also estimates the observation model parameters. Experiments on synthetic and real (medical) images confirm the adequacy and good performance of the approach.

[1]  James L. McClelland,et al.  B-Spline Contour Representation and Symmetry Detection , 1993 .

[2]  Demetri Terzopoulos,et al.  Topologically adaptable snakes , 1995, Proceedings of IEEE International Conference on Computer Vision.

[3]  José M. N. Leitão,et al.  Unsupervised image restoration and edge location using compound Gauss-Markov random fields and the MDL principle , 1997, IEEE Trans. Image Process..

[4]  Mário A. T. Figueiredo,et al.  Bayesian estimation of ventricular contours in angiographic images , 1992, IEEE Trans. Medical Imaging.

[5]  Gerald Farin,et al.  Curves and surfaces for computer aided geometric design , 1990 .

[6]  Baba C. Vemuri,et al.  Shape Modeling with Front Propagation: A Level Set Approach , 1995, IEEE Trans. Pattern Anal. Mach. Intell..

[7]  Jorma Rissanen,et al.  Fisher information and stochastic complexity , 1996, IEEE Trans. Inf. Theory.

[8]  Fernand S. Cohen,et al.  Part I: Modeling Image Curves Using Invariant 3-D Object Curve Models-A Path to 3-D Recognition and Shape Estimation from Image Contours , 1994, IEEE Trans. Pattern Anal. Mach. Intell..

[9]  Jorge L. C. Sanz,et al.  Periodic quasi-orthogonal spline bases and applications to least-squares curve fitting of digital images , 1996, IEEE Trans. Image Process..

[10]  Anil K. Jain,et al.  Vehicle Segmentation and Classification Using Deformable Templates , 1996, IEEE Trans. Pattern Anal. Mach. Intell..

[11]  J. Rissanen.  Stochastic Complexity in Statistical Inquiry Theory , 1989 .

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

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

[14]  C. R. Deboor,et al.  A practical guide to splines , 1978 .

[15]  Alan L. Yuille,et al.  Deformable templates , 1993 .

[16]  James S. Duncan,et al.  Boundary Finding with Parametrically Deformable Models , 1992, IEEE Trans. Pattern Anal. Mach. Intell..

[17]  Alan L. Yuille,et al.  Region Competition: Unifying Snakes, Region Growing, and Bayes/MDL for Multiband Image Segmentation , 1996, IEEE Trans. Pattern Anal. Mach. Intell..

[18]  Geir Storvik,et al.  A Bayesian Approach to Dynamic Contours Through Stochastic Sampling and Simulated Annealing , 1994, IEEE Trans. Pattern Anal. Mach. Intell..

[19]  Laurent D. Cohen,et al.  Finite-Element Methods for Active Contour Models and Balloons for 2-D and 3-D Images , 1993, IEEE Trans. Pattern Anal. Mach. Intell..

[20]  Anil K. Jain,et al.  Object Matching Using Deformable Templates , 1996, IEEE Trans. Pattern Anal. Mach. Intell..

[21]  Michael I. Miller,et al.  REPRESENTATIONS OF KNOWLEDGE IN COMPLEX SYSTEMS , 1994 .

[22]  M.N.M. vanLieshout.  Discussion contribution to U. Grenander and M.I. Miller: Representations of knowledge in complex systems , 1994 .

[23]  James S. Duncan,et al.  Deformable boundary finding influenced by region homogeneity , 1994, 1994 Proceedings of IEEE Conference on Computer Vision and Pattern Recognition.