Abstract
In order to investigate the deep structure of Gaussian scale space images, one needs to understand the behaviour of critical points under the influence of parameter-driven blurring. During this evolution two different types of special points are encountered, the so-called scale space saddles and the catastrophe points, the latter describing the pairwise annihilation and creation of critical points. The mathematical framework of catastrophe theory is used to model non-generic events that might occur due to e.g. local symmetries in the image. It is shown how this knowledge can be exploited in conjunction with the scale space saddle points, yielding a scale space hierarchy tree that can be used for segmentation. Furthermore the relevance of creations of pairs of critical points with respect to the hierarchy is discussed. We clarify the theory with an artificial image and a simulated MR image.
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© 2002 Springer-Verlag Berlin Heidelberg
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Kuijper, A., Florack, L. (2002). Understanding and Modeling the Evolution of Critical Points under Gaussian Blurring. In: Heyden, A., Sparr, G., Nielsen, M., Johansen, P. (eds) Computer Vision — ECCV 2002. ECCV 2002. Lecture Notes in Computer Science, vol 2350. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-47969-4_10
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DOI: https://doi.org/10.1007/3-540-47969-4_10
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