A morphological polynomial transform

Authors:
H. Cha;L. F. Chaparro
Affiliations:
Real Time Signal Processing Laboratory, Department of Electrical Engineering, University of Pittsburgh, Pittsburgh, PA;Real Time Signal Processing Laboratory, Department of Electrical Engineering, University of Pittsburgh, Pittsburgh, PA
Venue:
ICASSP'93 Proceedings of the 1993 IEEE international conference on Acoustics, speech, and signal processing: image and multidimensional signal processing - Volume V
Year:
1993

Citing 3
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Grayscale morphology

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Computer Vision, Graphics, and Image Processing
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Abstract

In this paper, we show that using grayscale morphology and a set of functions related to orthogonal polynomials - defined on a window - as structuring elements, a signal representation analogous to the polynomial transform can be developed. The geometric decomposition of a signal is achieved by windowing and using a morphological opening operation to approximate the windowed signal with each of the structuring elements. The resulting representation is made to resemble an orthogonal expansion by constraining the result of opening to be equal to the structuring function. Properties of our recursive decomposition algorithm permit us to develop an algorithm to calculate a set of coefficients used in the reconstruction. The analysis and synthesis of one-dimensional signals are illustrated with an image data compression example.