From Extrema Relationships to Image Simplification Using Non-flat Structuring Functions
Image simplification plays a fundamental role in Image Processing to improve results in complex tasks such as segmentation. The field of Mathematical Morphology (MM) itself has established many ways to perform such improvements. In this paper, we present a new approach for image simplification which takes into account erosion and dilation from MM. The proposed method is not self-dual and only single-band signals under a discrete domain are considered. Our main focus is on the creation of concave structuring functions based on a relation between signal extrema. This relation is given by two extrema according to their degree of separation (distance) and the respective heights (contrast). From these features, a total order relation is produced, thus supplying a way to progressively simplify the signal. Some two-dimensional images are considered here to illustrate in practice this simplification behavior.
KeywordsMathematical Morphology Regional Extrema Concave Structuring Functions Image Simplification
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