The Topological Structure of Scale-Space Images
Journal of Mathematical Imaging and Vision
Scale-Space '01 Proceedings of the Third International Conference on Scale-Space and Morphology in Computer Vision
On the Axioms of Scale Space Theory
Journal of Mathematical Imaging and Vision
The monogenic scale space on a bounded domain and its applications
Scale Space'03 Proceedings of the 4th international conference on Scale space methods in computer vision
α scale spaces on a bounded domain
Scale Space'03 Proceedings of the 4th international conference on Scale space methods in computer vision
Review article: Edge and line oriented contour detection: State of the art
Image and Vision Computing
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We compare the topology and deep structure of alternative scale space representations, so called α-scale spaces, 1/2 ≤ α ≤ 1, which are subject to a first order pseudo partial differential equation on the upper half plane {(x,s)∈ℝd ×ℝ|s0}. In particular, the cases α = 1 and α = 1/2, which correspond to respectively Poisson scale space and Gaussian scale space, are considered. Poisson scale space is equivalent to harmonic extension to the upper half plane, inducing potential physics, whereas Gaussian scale space is generated by the diffusion equation on the upper half plane, inducing heat physics. Despite the continuous connection (by parameter 1/2 ≤ α ≤ 1) between these scale spaces and the similarity between their convolution convolution kernels, we show both theoretically and experimentally that there is a strong difference between the topology in the deep structure of these scale spaces.