Deformable triangular surfaces using fast 1-D radial Lagrangian dynamics-segmentation of 3-D MR and CT images of the wrist

We developed a new triangulated deformable surface model, which is used to detect the boundary of the bones in three-dimensional magnetic resonance (MR) and computed tomography (CT) images of the wrist. This surface model is robust to initialization and provides wide geometrical coverage and quantitative power. The surface is deformed by applying one-dimensional (1-D) radial Lagrangian dynamics. For initialization a tetrahedron is placed within the bone to be segmented. This initial surface is inflated to a binary approximation of the boundary. During inflation, the surface is refined by the addition of vertices. After the surface is fully inflated, a detailed, accurate boundary detection is obtained by the application of radial scale-space relaxation. In this optimization stage, the image intensity is filtered with a series of 1-D second-order Gaussian filters. The resolution of the triangulated mesh is adapted to the width of the Gaussian filter. To maintain the coherence between the vertices, a resampling technique is applied which is based on collapsing and splitting of edges. We regularized the triangulated mesh by a combination of volume-preserving vertex averaging and equi-angulation of edges. In this paper, we present both qualitative and quantitative results of the surface segmentations in eight MR and ten CT images.

[1]  J. B. Kneeland,et al.  Analysis of in vivo 3-D internal kinematics of the joints of the foot [MRI analysis] , 1998, IEEE Transactions on Biomedical Engineering.

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

[3]  Hong Qin,et al.  A New Dynamic FEM-Based Subdivision Surface Model for Shape Recovery and Tracking in Medical Images , 1998, MICCAI.

[4]  Robin Sibson,et al.  Locally Equiangular Triangulations , 1978, Comput. J..

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

[6]  D.E. Thompson,et al.  Construction of biological surface models from cross-sections image processing , 1993, IEEE Transactions on Biomedical Engineering.

[7]  Jacques-Olivier Lachaud,et al.  Volumic Segmentation using Hierarchical Representation and Triangulated Surface , 1996, ECCV.

[8]  Demetri Terzopoulos,et al.  Medical image segmentation using topologically adaptable surfaces , 1997, CVRMed.

[9]  Jinah Park,et al.  Deformable models with parameter functions for cardiac motion analysis from tagged MRI data , 1996, IEEE Trans. Medical Imaging.

[10]  V. Leitáo,et al.  Computer Graphics: Principles and Practice , 1995 .

[11]  Andrew P. Witkin,et al.  Dynamic simulation of non-penetrating flexible bodies , 1992, SIGGRAPH.

[12]  Jihad El-Sana,et al.  Adaptive Real-Time Level-of-Detail-Based Rendering for Polygonal Models , 1997, IEEE Trans. Vis. Comput. Graph..

[13]  David Eppstein,et al.  MESH GENERATION AND OPTIMAL TRIANGULATION , 1992 .

[14]  Demetri Terzopoulos,et al.  Deformable models in medical image analysis: a survey , 1996, Medical Image Anal..

[15]  H. Kooy,et al.  Automatic three-dimensional correlation of CT-CT, CT-MRI, and CT-SPECT using chamfer matching. , 1994, Medical physics.

[16]  James S. Duncan,et al.  Deformable boundary finding in medical images by integrating gradient and region information , 1996, IEEE Trans. Medical Imaging.

[17]  Benjamin B. Kimia,et al.  Segmentation of Carpal Bones from 3d CT Images Using Skeletally Coupled Deformable Models , 1998, MICCAI.

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

[19]  John C. Platt,et al.  Elastically deformable models , 1987, SIGGRAPH.

[20]  Dmitry B. Goldgof,et al.  Adaptive-Size Meshes for Rigid and Nonrigid Shape Analysis and Synthesis , 1993, IEEE Trans. Pattern Anal. Mach. Intell..

[21]  J. Snel,et al.  Quantitative in vivo analysis of the kinematics of carpal bones from three-dimensional CT images using a deformable surface model and a three-dimensional matching technique. , 2000, Medical physics.

[22]  Benoit M. Dawant,et al.  Registration of 3-D images using weighted geometrical features , 1996, IEEE Trans. Medical Imaging.

[23]  Demetri Terzopoulos,et al.  Medical Image Segmentation Using Topologically Adaptable Snakes , 1995, CVRMed.

[24]  Max A. Viergever,et al.  A discrete dynamic contour model , 1995, IEEE Trans. Medical Imaging.

[25]  Jean-Daniel Boissonnat,et al.  Shape reconstruction from planar cross sections , 1988, Comput. Vis. Graph. Image Process..

[26]  Hervé Delingette,et al.  General Object Reconstruction Based on Simplex Meshes , 1999, International Journal of Computer Vision.

[27]  Jeroen G. Snel,et al.  Detection of the carpal bone contours from 3-D MR images of the wrist using a planar radial scale-space snake , 1998, IEEE Transactions on Medical Imaging.

[28]  John C. Platt,et al.  Constraints methods for flexible models , 1988, SIGGRAPH.

[29]  Mathieu Desbrun,et al.  Animation of Deformable Models Using Implicit Surfaces , 1997, IEEE Trans. Vis. Comput. Graph..

[30]  Eberhard Bänsch,et al.  Local mesh refinement in 2 and 3 dimensions , 1991, IMPACT Comput. Sci. Eng..

[31]  Demetri Terzopoulos,et al.  A dynamic finite element surface model for segmentation and tracking in multidimensional medical images with application to cardiac 4D image analysis. , 1995, Computerized medical imaging and graphics : the official journal of the Computerized Medical Imaging Society.

[32]  J. J. Gerbrands.  Segmentation of noisy images , 1988 .

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

[34]  Bernd Hamann,et al.  Constructing Hierarchies for Triangle Meshes , 1998, IEEE Trans. Vis. Comput. Graph..

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

[36]  J. Shewchuk,et al.  Delaunay refinement mesh generation , 1997 .

[37]  Surendra Ranganath,et al.  Contour extraction from cardiac MRI studies using snakes , 1995, IEEE Trans. Medical Imaging.

[38]  G. Huiskamp.  Difference formulas for the surface Laplacian on a triangulated surface , 1991 .

[39]  Kenneth A. Brakke,et al.  The Surface Evolver , 1992, Exp. Math..

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

[41]  Steven K. Feiner,et al.  Computer graphics: principles and practice (2nd ed.) , 1990 .

[42]  M. Rivara.  Algorithms for refining triangular grids suitable for adaptive and multigrid techniques , 1984 .

[43]  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..

[44]  Marcel Rooze,et al.  Functional Anatomy of the Carpus in Flexion and Extension and in Radial and Ulnar Deviations: An In Vivo Two- and Three-Dimensional CT Study , 1994 .

[45]  Hemant D. Tagare.  Deformable 2-D template matching using orthogonal curves , 1997, IEEE Transactions on Medical Imaging.

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

[47]  Frederic Fol Leymarie,et al.  Tracking Deformable Objects in the Plane Using an Active Contour Model , 1993, IEEE Trans. Pattern Anal. Mach. Intell..