ISSN:
1573-7683
Keywords:
scale space
;
branch points
;
reconstruction
;
representation
;
real algebra
;
heat polynomial
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Abstract 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 $$ \left\lfloor {\frac{n}{2}} \right\rfloor $$ 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.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1023/A:1011241531216
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