A discrete curvature-based deformable surface model with application to segmentation of volumetric images

In this paper, we present a new curvature-based three-dimensional (3-D) deformable surface model. The model deforms under defined force terms. Internal forces are calculated from local model curvature, using a robust method by a least-squares error (LSE) approximation to the Dupin indicatrix. External forces are calculated by applying a step expansion and restoration filter (SEF) to the image data. A solution for one of the most common problems associated with deformable models, self-cutting, has been proposed in this work. We use a principal axis analysis and reslicing of the deformable model, followed by triangulation of the slices, to remedy self-cutting. We use vertex resampling, multiresolution deformation, and refinement of the mesh grid to improve the quality of the model deformation, which leads to better results. Examples of the model application to different cases (simulation, magnetic resonance imaging (MRI), computerized tomography (CT), and ultrasound images) are presented, showing diversity and flexibility of the model.

[1]  Amir A. Amini,et al.  Spatio-temporal tracking of myocardial deformations with a 4-D B-spline model from tagged MRI , 1999, IEEE Transactions on Medical Imaging.

[2]  M J Cook,et al.  Mesial temporal sclerosis and volumetric investigations , 1994, Acta neurologica Scandinavica. Supplementum.

[3]  Guido Gerig,et al.  Elastic model-based segmentation of 3-D neuroradiological data sets , 1999, IEEE Transactions on Medical Imaging.

[4]  V MillerJames,et al.  Geometrically deformed models , 1991 .

[5]  Michael W. Vannier,et al.  Hippocampal MR volumetry , 1994, Other Conferences.

[6]  Nicholas Ayache,et al.  Non-Rigid Motion Analysis in Medical Images: a Physically Based Approach , 1993, IPMI.

[7]  K. Raghunath Rao,et al.  Optimal Edge Detection using Expansion Matching and Restoration , 1994, IEEE Trans. Pattern Anal. Mach. Intell..

[8]  Robert T. Schultz,et al.  Segmentation and Measurement of the Cortex from 3D MR Images , 1998, MICCAI.

[9]  James M. Ortega,et al.  Segmentation of volumetric medical imagery using multiple geodesic-based active surfaces , 1996, Medical Imaging.

[10]  Luiz Velho,et al.  Hierarchical generalized triangle strips , 1999, The Visual Computer.

[11]  Charles Kervrann,et al.  Statistical deformable model-based segmentation of image motion , 1999, IEEE Trans. Image Process..

[12]  Demetri Terzopoulos,et al.  Constraints on Deformable Models: Recovering 3D Shape and Nonrigid Motion , 1988, Artif. Intell..

[13]  N. Peterfreund.  The velocity snake: Deformable contour for tracking in spatio-velocity space , 1997 .

[14]  Philip H. Todd,et al.  Numerical estimation of the curvature of surfaces , 1986 .

[15]  Charles L. Lawson,et al.  $C^1$ surface interpolation for scattered data on a sphere , 1984 .

[16]  J.P. Windham,et al.  A deformable model for hippocampus segmentation: improvements and extension to 3D , 1996, 1996 IEEE Nuclear Science Symposium. Conference Record.

[17]  Dimitris N. Metaxas,et al.  Dynamic 3D models with local and global deformations: deformable superquadrics , 1990, [1990] Proceedings Third International Conference on Computer Vision.

[18]  Demetri Terzopoulos,et al.  Topology adaptive deformable surfaces for medical image volume segmentation , 1999, IEEE Transactions on Medical Imaging.

[19]  H Soltanian-Zadeh,et al.  Segmentation of the hippocampus from brain MRI using deformable contours. , 1998, Computerized medical imaging and graphics : the official journal of the Computerized Medical Imaging Society.

[20]  Ramakant Nevatia,et al.  Computing volume descriptions from sparse 3-D data , 1988, International Journal of Computer Vision.

[21]  Dimitris N. Metaxas,et al.  Dynamic 3D Models with Local and Global Deformations: Deformable Superquadrics , 1991, IEEE Trans. Pattern Anal. Mach. Intell..

[22]  Hamid Soltanian-Zadeh,et al.  Knowledge-based localization of hippocampus in human brain MRI , 1999, Medical Imaging.

[23]  Y. Yoon,et al.  Triangulation of scattered data in 3D space , 1988 .

[24]  Ross T. Whitaker,et al.  Volumetric deformable models: active blobs , 1994, Other Conferences.

[25]  B. Krauskopf,et al.  Proc of SPIE , 2003 .

[26]  H Soltanian-Zadeh,et al.  A multiresolution approach for contour extraction from brain images. , 1997, Medical physics.

[27]  Laurent D. Cohen,et al.  Introducing new deformable surfaces to segment 3D images , 1991, Proceedings. 1991 IEEE Computer Society Conference on Computer Vision and Pattern Recognition.

[28]  Jeffrey A. Lieberman,et al.  Hippocampus-amygdala volumes and psychopathology in chronic schizophrenia , 1993, Biological Psychiatry.

[29]  James S. Duncan,et al.  Model-based deformable surface finding for medical images , 1996, IEEE Trans. Medical Imaging.

[30]  David J. Hawkes,et al.  Volume estimation from sparse planar images using deformable models , 1999, Image Vis. Comput..

[31]  Kenji Shimada,et al.  Automatic triangular mesh generation of trimmed parametric surfaces for finite element analysis , 1998, Comput. Aided Geom. Des..

[32]  Robert M. O'Bara,et al.  Geometrically deformed models: a method for extracting closed geometric models form volume data , 1991, SIGGRAPH.

[33]  Richard Szeliski,et al.  Modeling surfaces of arbitrary topology with dynamic particles , 1993, Proceedings of IEEE Conference on Computer Vision and Pattern Recognition.

[34]  H Soltanian-Zadeh,et al.  A 3D deformable surface model for segmentation of objects from volumetric data in medical images. , 1998, Computers in biology and medicine.

[35]  Dana H. Ballard,et al.  Computer Vision , 1982 .