An efficient 3D deformable model with a self-optimising mesh

Deformable models are a powerful and popular tool for image segmentation, but in 3D imaging applications the high computational cost of fitting such models can be a problem. A further drawback is the need to select the initial size and position of a model in such a way that it is close to the desired solution. This task may require particular expertise on the part of the operator, and, furthermore, may be difficult to accomplish in three dimensions without the use of sophisticated visualisation techniques. This article describes a 3D deformable model that uses an adaptive mesh to increase computational efficiency and accuracy. The model employs a distance transform in order to overcome some of the problems caused by inaccurate initialisation. The performance of the model is illustrated by its application to the task of segmentation of 3D MR images of the human head and hand. A quantitative analysis of the performance is also provided using a synthetic test image.

[1]  Nicholas David Efford.  Knowledge-based segmentation and feature analysis of hand and wrist radiographs , 1993, Electronic Imaging.

[2]  F. Stenger,et al.  A lower bound on the angles of triangles constructed by bisecting the longest side , 1975 .

[3]  G. Borgefors.  Distance transformations in arbitrary dimensions , 1984 .

[4]  David J. Hawkes,et al.  A Strategy for Automated Multimodality Image Registration Incorporating Anatomical Knowledge and Imager Characteristics , 1993, IPMI.

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

[6]  Alex Pentland,et al.  Closed-Form Solutions for Physically Based Shape Modeling and Recognition , 1991, IEEE Trans. Pattern Anal. Mach. Intell..

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

[8]  William E. Lorensen,et al.  Marching cubes: A high resolution 3D surface construction algorithm , 1987, SIGGRAPH.

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

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

[11]  Demetri Terzopoulos,et al.  Sampling and reconstruction with adaptive meshes , 1991, Proceedings. 1991 IEEE Computer Society Conference on Computer Vision and Pattern Recognition.

[12]  H. Delingette.  Adaptive and deformable models based on simplex meshes , 1994, Proceedings of 1994 IEEE Workshop on Motion of Non-rigid and Articulated Objects.

[13]  Dimitri Metaxas,et al.  Efficient shape representation using deformable models with locally adaptive finite elements , 1993, Optics & Photonics.

[14]  Demetri Terzopoulos,et al.  Adaptive meshes and shells: irregular triangulation, discontinuities, and hierarchical subdivision , 1992, Proceedings 1992 IEEE Computer Society Conference on Computer Vision and Pattern Recognition.

[15]  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.

[16]  G. Touzot,et al.  The finite element method displayed , 1984 .

[17]  Ramesh C. Jain,et al.  Using Dynamic Programming for Solving Variational Problems in Vision , 1990, IEEE Trans. Pattern Anal. Mach. Intell..

[18]  William E. Lorensen,et al.  Decimation of triangle meshes , 1992, SIGGRAPH.

[19]  Kenneth R. Sloan,et al.  Surfaces from contours , 1992, TOGS.

[20]  Mubarak Shah,et al.  A Fast algorithm for active contours and curvature estimation , 1992, CVGIP Image Underst..