Abstract
This paper clarifies the nature of hierarchical relationships among singularities in the Gaussian scale-space. The hierarchy of the singular points is essentially provided by ‘stationary curves’ and flux curves of ‘figure field’. They are defined, respectively, as the trajectories of stationary points across scale, and as the gradient field of the scale-space image at fixed scale. The figure field also reveals an important fact that a stationary point at infinity is involved in catastrophe events of local minimum points. These mathematical properties define the scale-space hierarchy, which is qualitatively described as a tree.
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Sakai, T., Imiya, A. (2005). Scale-Space Hierarchy of Singularities. In: Fogh Olsen, O., Florack, L., Kuijper, A. (eds) Deep Structure, Singularities, and Computer Vision. DSSCV 2005. Lecture Notes in Computer Science, vol 3753. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11577812_16
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DOI: https://doi.org/10.1007/11577812_16
Publisher Name: Springer, Berlin, Heidelberg
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