A Network Approach to Reconstructions From Zero Crossings
A Network Approach to Reconstructions From Zero Crossings
R a Hummel
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T + v. + ij-i, t + 2v/ + ij, k + Vi+ij + i, t]. We can then formulate equation error as a sum of square difference of the left and right sides of this discretized Heat Equation over all nodes, and seek to minimize the resulting quadratic functional. In practice, things are complicated by the need to define boundary conditions, choose an appropriate constrained minimization procedure, and to ensure numerical stability and reasonable convergence rates. We will briefly discuss some of these concer...ns in the case of one space dimen- sion. In this case, we are given initial data /(/), and construct the scale-space func- tion Vj^j. This function is computed recursively from the formulas: «i, o =/(»■), v, -, jt = «i, t+i-«i, t- For the border points, let us assume that /(z) is defined for —N^i^N. Then we Page 5 A Network Approach to Reconstructions from Zero-Crossings replace in the above formulas, for i = ±N, the formulas: U-N. K + 1 = -^"-N + l, k + -^U-N, k, and otherwise things are the same.
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