Active shape focusing

This paper presents a framework for hierarchical shape description which enables quantitative and qualitative shape studies at multiple levels of image detail. It allows the capture of the global object shape at higher image scales, and to focus it down to finer details at decreasing levels of image scale. A multi-scale active contour model, whose energy function is regularized with respect to underlying geometric image structure in a natural scale setting, is developed for the purpose of implicit shape extraction or regularization with respect to scale. The resulting set of shapes is formulated and visualized as a multi-scale shape stack for the investigation of shape changes across scales. We demonstrate the functionality of this framework by applying it to a set of true fractal structures, and to 3D brain MRI. The framework is shown to be capable of recovering the fractal dimension of the fractal shapes directly from their embedding image context. The equivalent measure on the medical images and its potential for medical shape analysis is discussed. (C) 1999 Elsevier Science B.V. All rights reserved.

[1]  Simon R. Arridge,et al.  Active Contour Models for Shape Description using Multiscale Differential Invariants , 1995, BMVC.

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

[3]  B. Kimia,et al.  Volumetric segmentation of medical images by three-dimensional bubbles , 1995, Proceedings of the Workshop on Physics-Based Modeling in Computer Vision.

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

[5]  Max A. Viergever,et al.  Scale-Space: Its Natural Operators and Differential Invariants , 1991, IPMI.

[6]  Max A. Viergever,et al.  Scale and the differential structure of images , 1992, Image Vis. Comput..

[7]  Alan Liu,et al.  MuItiscale medial analysis of medical images , 1994, Image Vis. Comput..

[8]  Fredrik Bergholm,et al.  Edge Focusing , 1987, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[9]  Farzin Mokhtarian,et al.  A Theory of Multiscale, Curvature-Based Shape Representation for Planar Curves , 1992, IEEE Trans. Pattern Anal. Mach. Intell..

[10]  M. Gage,et al.  The heat equation shrinking convex plane curves , 1986 .

[11]  D R Fish,et al.  Three-dimensional fractal analysis of the white matter surface from magnetic resonance images of the human brain. , 1996, Cerebral cortex.

[12]  Andrew P. Witkin,et al.  Scale-Space Filtering , 1983, IJCAI.

[13]  Simon R. Arridge,et al.  Multi-Scale Active Shape Description , 1997, Scale-Space.

[14]  Thomas W. Sederberg,et al.  Conversion of complex contour line definitions into polygonal element mosaics , 1978, SIGGRAPH.

[15]  Daniel P. Huttenlocher,et al.  Comparing Images Using the Hausdorff Distance , 1993, IEEE Trans. Pattern Anal. Mach. Intell..

[16]  J. Brickmann.  B. Mandelbrot: The Fractal Geometry of Nature, Freeman and Co., San Francisco 1982. 460 Seiten, Preis: £ 22,75. , 1985 .

[17]  C. Sparrow.  The Fractal Geometry of Nature , 1984 .

[18]  Julia A. Schnabel,et al.  Multi-scale active shape description in medical imaging. , 1998 .

[19]  Max A. Viergever,et al.  Probabilistic Multiscale Image Segmentation , 1997, IEEE Trans. Pattern Anal. Mach. Intell..

[20]  Daniel Rueckert,et al.  Automatic tracking of the aorta in cardiovascular MR images using deformable models , 1997, IEEE Transactions on Medical Imaging.

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

[22]  David H. Eberly,et al.  Ridges in Image and Data Analysis , 1996, Computational Imaging and Vision.

[23]  Alan Liu,et al.  Multiscale Medial Analysis of Medical Images , 1993, IPMI.

[24]  Gunilla Borgefors,et al.  Distance transformations in digital images , 1986, Comput. Vis. Graph. Image Process..

[25]  P. Saint-Marc,et al.  Active contour models: overview, implementation and applications , 1990, 1990 IEEE International Conference on Systems, Man, and Cybernetics Conference Proceedings.