Journal
JOURNAL OF MATHEMATICAL IMAGING AND VISION
Volume 13, Issue 3, Pages 193-203Publisher
SPRINGER
DOI: 10.1023/A:1011241531216
Keywords
scale space; branch points; reconstruction; representation; real algebra; heat polynomial
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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 [n/2] for an initial polynomial of degree it. 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.
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