Synopses & Reviews
Synopsis
Excerpt from The Scale-Space Formulation of Pyramid Data Structures
Pyramid data structures can be analyzed in an analytic formulation based on notions of scale-space and partial differential operators. We've seen that the Gaussian pyramid can be viewed as a method of solving the Heat Equation using the image intensity values for the initial data. The Laplacian pyramid can be viewed as a partial derivative, in the scale parameter, of the Gaussian pyramid data, from the standpoint of this continuous formulation. We are also able to use the continuous formulation to define and study zero-crossings in scale-space, particularly of the Laplacian pyramid data.
We've given three examples of how the continuous formulation assists in our understanding of pyramid data structures. The first example concerned border affects, and we discussed three ways of handling borders when constructing pyramids of images defined on a bounded domain. Each of these methods is motivated by a different formulation of the Heat Equation problem: namely, (1)
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