A Computational Approach to Edge Detection
IEEE Transactions on Pattern Analysis and Machine Intelligence
Edge Detection and Ridge Detection with Automatic Scale Selection
International Journal of Computer Vision
Generic structure of two-dimensional dimages under Gaussian blurring
SIAM Journal on Applied Mathematics
Relative critical sets in RR(N) and applications to image analysis
Relative critical sets in RR(N) and applications to image analysis
Image Loci are Ridges in Geometric Spaces
SCALE-SPACE '97 Proceedings of the First International Conference on Scale-Space Theory in Computer Vision
Height ridges of oriented medialness
Height ridges of oriented medialness
Generic transitions of relative critical sets in parametrized families with applications to image analysis
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The maximal convexity ridge is not well suited for the analysis of medial functions or, it can be argued, for the analysis of any function that is created via convolution with a kernel based on the Gaussian. In its place one should use the maximal scale ridge, which takes scale's distinguished role into account. We present the local geometric structure of the maximal scale ridge of smooth and Gaussian blurred functions, a result that complements recent work on scale selection. We also discuss the subdimensional maxima property as it relates to the maximal scale ridge, and we prove that a generalized maximal parameter ridge has the subdimensional maxima property as well.