Ridge detection

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In a 2-D function, a (bright) ridge is a connected set of points that are maximal in at least one dimension. When extended to N dimensions, a (bright) ridge is a connected sequence of points that are maximal in N-1 dimensions. The corresponding notion of dark ridges can be defined with "maximal" replaced by "minimal".

In the scale space of an image, ridges provide an invariant description of elongated structures, and thus provide a complement to natural interest points (local extremal points). In image scale space, a ridge is a connected set of points that are maximal in one of the spatial dimensions as well as in the scale dimension. Ridges occur along the center of elongated structures, and thus provide a form of scale invariant skeleton for organizing spatial constraints on local appearance.

The notion of ridges in difference of Gaussians pyramids was introduced by Crowley in 1984 ^{[1] [2]}. The application of ridge descriptors to medical image analysis has been extensively studied by Pizer and his co-workers resulting in their notion of M-reps ^[3]. Ridge detection has been further developed by Lindeberg in ^[4] with the introduction of γ-normalized derivatives and scale-space ridges defined from local maximization of the appropriately normalized main principal curvature of the Hessian matrix (or other measures of ridge strength) over space and over scale. These notions have later been developed with application to blood vessel segmentation by Frangi et al ^[5] and to the detection of tubular structures by Krissian et al ^[6].

[edit] References

1. ^ J. L. Crowley and A. C. Parker, "A Representation for Shape Based on Peaks and Ridges in the Difference of Low Pass Transform", IEEE Transactions on PAMI, PAMI 6 (2), pp 156-170, March 1984.
2. ^ J. L. Crowley and A. Sanderson,"Multiple Resolution Representation and Probabilistic Matching of 2-D Gray-Scale Shape", IEEE Transactions on PAMI, PAMI 9(1), pp 113-121, January 1987.
3. ^ S. Pizer, S. Joshi, T. Fletcher, M. Styner, G. Tracton, J. Chen (2001) "Segmentation of Single-Figure Objects by Deformable M-reps", Proceedings of the 4th International Conference on Medical Image Computing and Computer-Assisted Intervention, Springer Lecture Notes In Computer Science; Vol. 2208, pp. 862 - 871
4. ^ T. Lindeberg: "Edge detection and ridge detection with automatic scale selection", International Journal of Computer Vision, vol 30, number 2, pp. 117--154, 1998
5. ^ A. Frangi, W. Niessen, R. Hoogeveen, T. van Walsum and M. Viergever (1999) "Model-based quantitation of 3-D magnetic resonance angiographic images", IEEE Trans Med Imaging. 1999 Oct;18(10):946-56.
6. ^ K. Krissian, G. Malandain, N. Ayache, R. Vaillan and Y. Trousset (2000) "Model-based detection of tubular structures in 3D images" Computer Vision and Image Understanding, Volume 80 , Issue 2, 130 - 171.