Abstract
The Discrete Pulse Transform (DPT) for images and videos has been developed over the past few years and provides aВ theoretically sound setting for a nonlinear decomposition of an image or video. In [1] the theoretical basis of the DPT was presented. In this paper we now present a soundВ characterization of this useful nonlinear hierarchical decomposition by referring to its ability as a separator, the consistency of the decomposition, as well as the smoothing ability of the decomposition.
Highlights
The Discrete Pulse Transform (DPT) is a nonlinear hierarchical decomposition obtained by the successive application of the LULU operators Ln and Un where n increases from 1 to N, where N is the number of data points in the signal
The LULU operators were extended in detail to multidimensional arrays in [1], which provides a framework for the obvious areas of image processing in two dimensions, as well as video processing in three dimensions
This is the important advantage of the LULU operators, which are only concerned about size, and morphological filters, which operate in conjunction with a specified structuring element with a specified size
Summary
The Discrete Pulse Transform (DPT) is a nonlinear hierarchical decomposition obtained by the successive application of the LULU operators Ln and Un where n increases from 1 to N , where N is the number of data points in the signal. For a concise overview of the onedimensional LULU operators see [2] as well as further collaboration with Laurie and Wild. The LULU operators were extended in detail to multidimensional arrays in [1], which provides a framework for the obvious areas of image processing in two dimensions, as well as video processing in three dimensions. We provide a short overview of these operators and the DPT here for completeness
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