Necklaces: Inhomogeneous and Point-Enhanced Deformable Models

Abstract In many advanced segmentation problems objects have inhomogeneous boundaries, hindering segmentation under uniform boundary assumption. We present a multifeature image segmentation method, called necklaces, that exploits local inhomogeneities to reduce the complexity of the segmentation problem. Multiple continuous boundary features, deduced from a set of training objects, are statistically analyzed and encoded into a deformable model. On the deformable model salient features are identified on the basis of the local differential geometric characteristics of the features, yielding a classification into point landmarks, curve landmarks, and sheet points. Salient features are exploited within a priority segmentation scheme that tries to find complete boundaries in an unknown image, first by landmarks and then by sheet points. The application of our method to segment vertebrae from CT data shows promising results despite their articulated morphology and despite the presence of interfering structures.

[1]  Tosiyasu L. Kunii,et al.  Shape Modeling and Shape Analysis Based on Singularities , 1996, Int. J. Shape Model..

[2]  ISAAC COHEN,et al.  Using deformable surfaces to segment 3-D images and infer differential structures , 1992, CVGIP Image Underst..

[3]  B. S. Duran,et al.  Cluster Analysis: A Survey , 1974 .

[4]  Jan J. Koenderink,et al.  Solid shape , 1990 .

[5]  Ron Kohavi,et al.  A Study of Cross-Validation and Bootstrap for Accuracy Estimation and Model Selection , 1995, IJCAI.

[6]  M. Nakahara Geometry, Topology and Physics , 2018 .

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

[8]  Ramesh C. Jain,et al.  Invariant surface characteristics for 3D object recognition in range images , 1985, Comput. Vis. Graph. Image Process..

[9]  Walter Murray,et al.  Construction of a three-dimensional geometric model for segmentation and visualization of cervical spine images , 1996 .

[10]  R. Brent Table errata: Algorithms for minimization without derivatives (Prentice-Hall, Englewood Cliffs, N. J., 1973) , 1975 .

[11]  James F. Brinkley,et al.  Shape-based interactive three-dimensional medical image segmentation , 1997, Medical Imaging.

[12]  Lawrence H. Staib,et al.  Boundary Finding with Prior Shape and Smoothness Models , 2000, IEEE Trans. Pattern Anal. Mach. Intell..

[13]  Jean-Philippe Thirion,et al.  Extremal points: definition and application to 3D image registration , 1994, 1994 Proceedings of IEEE Conference on Computer Vision and Pattern Recognition.

[14]  Arnold W. M. Smeulders,et al.  Strings: Variational Deformable Models of Multivariate Ordered Features , 2001 .

[15]  Cristian Lorenz,et al.  Generation of Point-Based 3D Statistical Shape Models for Anatomical Objects , 2000, Comput. Vis. Image Underst..

[16]  Dimitris N. Metaxas,et al.  Constrained deformable superquadrics and nonrigid motion tracking , 1991, Proceedings. 1991 IEEE Computer Society Conference on Computer Vision and Pattern Recognition.

[17]  Laurent D. Cohen,et al.  On active contour models and balloons , 1991, CVGIP Image Underst..

[18]  Karl Rohr,et al.  Multi-Step Procedures for the Localization of 2D and 3D Point Landmarks and Automatic ROI Size Selection , 1998, ECCV.

[19]  Timothy F. Cootes,et al.  Automatic Interpretation and Coding of Face Images Using Flexible Models , 1997, IEEE Trans. Pattern Anal. Mach. Intell..

[20]  Carl-Fredrik Westin,et al.  Using local 3D structure for segmentation of bone from computer tomography images , 1997, Proceedings of IEEE Computer Society Conference on Computer Vision and Pattern Recognition.

[21]  Piet W. Verbeek,et al.  Scale-adaptive landmark detection, classification and size estimation in 3D object-background images , 2000, Proceedings 15th International Conference on Pattern Recognition. ICPR-2000.

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

[23]  Les A. Piegl,et al.  The NURBS Book , 1995, Monographs in Visual Communication.

[24]  Nicholas Ayache,et al.  Automatic Retrieval of Anatomical Structures in 3D Medical Images , 1995, CVRMed.

[25]  Fred L. Bookstein,et al.  Principal Warps: Thin-Plate Splines and the Decomposition of Deformations , 1989, IEEE Trans. Pattern Anal. Mach. Intell..

[26]  Jürgen Weese,et al.  Point-Based Elastic Registration of Medical Image Data Using Approximating Thin-Plate Splines , 1996, VBC.

[27]  Laurent D. Cohen,et al.  Global Minimum for Active Contour Models: A Minimal Path Approach , 1997, International Journal of Computer Vision.

[28]  D. Struik Lectures on classical differential geometry , 1951 .