Ridges for image analysis

Representation of object shape by medial structures has been an important aspect of image analysis. Methods for describing objects in a binary image by medial axes are well understood. Many attempts have been made to construct similar medial structures for objects in gray scale images. In particular, researchers have studied images by analyzing the graphs of the intensity data and identifying ridge and valley structures on those surfaces. In this paper we review many of the definitions for ridges. Computational vision models require that medial structures should remain invariant under certain transformations of the spatial locations and intensities. For each ridge definition we point out which invariances the definition satisfies. We also give extensions of the concepts so that we can located-dimensional ridge structures withinn-dimensional images. A comparison of the ridge structures produced by the different definitions is given both by mathematical examples and by an application to a 2-dimensional MR image of a head.

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

[2]  HARRY BLUM,et al.  Shape description using weighted symmetric axis features , 1978, Pattern Recognit..

[3]  R. Lee,et al.  Two-Dimensional Critical Point Configuration Graphs , 1984, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[4]  Stephen M. Pizer,et al.  Ridge flow models for image segmentation , 1994, Medical Imaging.

[5]  James L. Crowley,et al.  A Representation for Shape Based on Peaks and Ridges in the Difference of Low-Pass Transform , 1984, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[6]  Max A. Viergever,et al.  Images: Regular Tempered Distributions , 1994 .

[7]  John M. Gauch,et al.  The multiresolution intensity axis of symmetry and its application to image segmentation , 1989 .

[8]  A. C. F. Colchester,et al.  Network Representation of 2-D and 3-D Images , 1990 .

[9]  C. Pearson,et al.  Handbook of Applied Mathematics , 1975 .

[10]  Robert M. Haralick,et al.  Ridges and valleys on digital images , 1983, Comput. Vis. Graph. Image Process..

[11]  Jan J. Koenderink,et al.  Local features of smooth shapes: ridges and courses , 1993, Optics & Photonics.

[12]  Glynn P. Robinson,et al.  Scale and segmentation of grey-level images using maximum gradient paths , 1991, Image Vis. Comput..

[13]  H. Blum.  Biological shape and visual science (part I) , 1973 .

[14]  Max A. Viergever,et al.  General Intensity Transformations and Second Order Invariants , 1992 .

[15]  Charles R. Johnson,et al.  Matrix analysis , 1985, Statistical Inference for Engineers and Data Scientists.

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

[17]  Lee R. Nackman,et al.  Three-Dimensional Shape Description Using the Symmetric Axis Transform I: Theory , 1985, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[18]  James M. Coggins,et al.  Object shape before boundary shape: Scale-space medial axes , 1994, Journal of Mathematical Imaging and Vision.

[19]  Lee R. Nackman.  Three-dimensional shape description using the symmetric axis transform , 1982 .