Journal of Mathematical Imaging and Vision
Zoom-invariant vision of figural shape: the mathematics of cores
Computer Vision and Image Understanding
Topological Numbers and Singularities in Scalar Images: Scale-Space Evolution Properties
Journal of Mathematical Imaging and Vision
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
The Influence of the gamma-Parameter on Feature Detection with Automatic Scale Selection
Scale-Space '01 Proceedings of the Third International Conference on Scale-Space and Morphology in Computer Vision
Segmentation subject to stitching constraints: finding many small structures in a large image
MICCAI'10 Proceedings of the 13th international conference on Medical image computing and computer-assisted intervention: Part I
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In this paper we investigate scale space based structural grouping in images. Our strategy is to detect (relative) critical point sets in scale space, which we consider as an extended image representation. In this way the multi-scale behavior of the original image structures is taken into account and automatic scale space grouping and scale selection is possible. We review a constructive and efficient topologically based method to detect the (relative) critical points. The method is presented for arbitrary dimensions. Relative critical point sets in a Hessian vector frame provide us with a generalization of height ridges. Automatic scale selection is accomplished by a proper reparameterization of the scale axis. As the relative critical sets are in general connected sub-manifolds, it provides a robust method for perceptual grouping with only local measurements.