Biological Cybernetics
A Multiresolution Hierarchical Approach to Image Segmentation Based on Intensity Extrema
IEEE Transactions on Pattern Analysis and Machine Intelligence
Scale-Space for Discrete Signals
IEEE Transactions on Pattern Analysis and Machine Intelligence
International Journal of Computer Vision
The Topological Structure of Scale-Space Images
Journal of Mathematical Imaging and Vision
Scale-Space Theory in Computer Vision
Scale-Space Theory in Computer Vision
Linear Scale-Space has First been Proposed in Japan
Journal of Mathematical Imaging and Vision
An Extended Class of Scale-Invariant and Recursive Scale Space Filters
IEEE Transactions on Pattern Analysis and Machine Intelligence
International Journal of Computer Vision
What Do Features Tell about Images?
Scale-Space '01 Proceedings of the Third International Conference on Scale-Space and Morphology in Computer 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: A Unifying Approach to Phase-Based Image Processing in Scale-Space
Journal of Mathematical Imaging and Vision
IJCAI'83 Proceedings of the Eighth international joint conference on Artificial intelligence - Volume 2
Image reconstruction from multiscale critical points
Scale Space'03 Proceedings of the 4th international conference on Scale space methods in computer vision
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A sufficient condition is presented for two-dimensional images on a finite rectangular domain Ω=(-A,A)×(-B,B) to be completely determined by features on curves t→(ξ(t),t) in the three-dimensional domain Ω×(0,∞) of an α-scale space. For any fixed finite set of points in the image, the values of the α-scale space at these points at all scales together do not provide sufficient information to reconstruct the image, even if spatial derivatives up to any order are included as well. On the other hand, the image is completely fixed by the values of the scale space and its derivative along any straight line in Ω×(0,∞) for which ξ:(0,∞)→Ω is linear but not constant. A similar result holds for curves for which ξ is of the form ξ(t)=(ξ1(t),0) with ξ1 periodic and not constant. If the locations at which the scale space is evaluated form a curve on a cylinder in Ω×(0,∞) with some periodic structure, like a helix, then it is sufficient to evaluate the α-scale space without spatial derivatives.