Fast Approximation of Color Morphology

EasyChair Preprint 6694

Abstract

The basic filters in mathematical morphology are dilation and erosion. They are defined by a flat or non-flat structuring element that is usually shifted pixel-wise over an image and a comparison process that takes place within the corresponding mask. The algorithmic complexity of fast algorithms that realise dilation and erosion for color images usually depends on size and shape of the structuring element. In this paper we propose and investigate an easy and fast way to make use of the fast Fourier transform for an approximate computation of dilation and erosion for color images. Similarly in construction as many other fast algorithms, the method extends a recent scheme proposed for single channel filtering. It is by design highly flexible, as it can be used with flat and non-flat structuring elements of any size and shape. Moreover, its complexity only depends on the number of pixels in the filtered images. We analyse here some important aspects of the approximation, and we show experimentally that we obtain results of very reasonable quality while the method has very attractive computational properties.

Keyphrases: Fourier transform, fast algorithms, mathematical morphology

@booklet{EasyChair:6694,
  author    = {Vivek Sridhar and Michael Breuß and Marvin Kahra},
  title     = {Fast Approximation of Color Morphology},
  howpublished = {EasyChair Preprint 6694},
  year      = {EasyChair, 2021}}