IEEE Transactions on Pattern Analysis and Machine Intelligence
Algorithmic algebra
International Journal of Computer Vision
Journal of Mathematical Imaging and Vision
Scale-Space Theory in Computer Vision
Scale-Space Theory in Computer Vision
Gaussian Scale-Space Theory
Algebraic Geometry and Computer Vision: Polynomial Systems, Real andComplex Roots
Journal of Mathematical Imaging and Vision
Multiscale Gradient Magnitude Watershed Segmentation
ICIAP '97 Proceedings of the 9th International Conference on Image Analysis and Processing-Volume I - Volume I
Space Scale Localization, Blur, and Contour-Based Image Coding
CVPR '96 Proceedings of the 1996 Conference on Computer Vision and Pattern Recognition (CVPR '96)
Journal of Mathematical Imaging and Vision
The Relevance of Non-generic Events in Scale Space Models
ECCV '02 Proceedings of the 7th European Conference on Computer Vision-Part I
Understanding and Modeling the Evolution of Critical Points under Gaussian Blurring
ECCV '02 Proceedings of the 7th European Conference on Computer Vision-Part I
What Do Features Tell about Images?
Scale-Space '01 Proceedings of the Third International Conference on Scale-Space and Morphology in Computer Vision
The Relevance of Non-Generic Events in Scale Space Models
International Journal of Computer Vision
Using Catastrophe Theory to Derive Trees from Images
Journal of Mathematical Imaging and Vision
A Linear Image Reconstruction Framework Based on Sobolev Type Inner Products
International Journal of Computer Vision
A linear image reconstruction framework based on sobolev type inner products
Scale-Space'05 Proceedings of the 5th international conference on Scale Space and PDE Methods in Computer Vision
Tree edit distances from singularity theory
Scale-Space'05 Proceedings of the 5th international conference on Scale Space and PDE Methods in Computer Vision
International Journal of Computer Vision
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Scale space analysis combines global and local analysis in a single methodology by simplifying a signal. The simplification is indexed using a continuously varying parameter denoted scale. Different analyses can then be performed at their proper scale. We consider evolution of a polynomial by the parabolic partial differential heat equation. We first study a basis for the solution space, the heat polynomials, and subsequently the local geometry around a branch point in scale space. By a branch point of a polynomium we mean a scale and a location where two zeros of the polynomial merge. We prove that the number of branch points for a solution is \lfloor\frac{n}{2}\rfloor for an initial polynomial of degree n. Then we prove that the branch points uniquely determine a polynomial up to a constant factor. Algorithms are presented for conversion between the polynomial's coefficients and its branch points.