Colour Morphological Scale-Spaces for Image Segmentation

Abstract

Morphological scale-spaces have become an important tool for analysing greyscale images. However, their extension to colour images has proven elusive until recently. In this paper an original evaluation of two recently proposed colour sieves is presented, both algorithmically and in terms of their computational and segmentation performance. A new colour sieve structure is also proposed, motivated by the relative advantages of the two sieves previously studied. A quantitative evaluation of the segmentation performance using a set of images with human ground truth from the Berkeley dataset shows the new method to produce the best segmentation performance.

Nonlinear Operations for Colour Images Based on Pairwise Vector Ordering

“…This problem has been overcome in morphology sieves based on graph morphology where the opening and closing operations are implemented by merging regional extrema with their closest neighbours. Using this approach two colour sieves have been proposed [4,7] and evaluated [8,9].…”

“…The figure also illustrates the role played by the initial pairwise ordering in the vector ranking, producing a ranking that is subtly different from simply ordering by luminance. For example, when the vectors x (1) , x (2) , · · · , x (9) from figure 2 are ordered by their luminance their ranked positions are 2, 1, 3, 4, 5, 6, 9, 7 and 8.…”

Colour Morphological Scale-Spaces from the Positional Colour Sieve

“…A main steps of a generalised colour sieve algorithm are given in [8] Compared with its better known greyscale counterpart that processes the maxima and minima separately, colour sieves simply process extrema as they cannot distinguish between maxima and minima. The merging process in step 2 is analogous to that of the greyscale sieve and changes the colour of each extreme region to that of its closest neighbour, as assessed using the Euclidean distance.…”

“…These two approaches, although differing in the details, have algorithms that essentially follow the same steps and the main difference in their performance results from their approaches to defining extrema [8]. The CCS forms a convex hull from each pixel and its connected neighbours and then defines a pixel as extreme (resp.…”

“…However, a lower proportion of extrema also results in less image simplification for a given scale. The VAM Open-Close Sieve (VAMOCS) increases the aggressiveness of the VAMS by also sieving the minima in the scalar surface produced by the VAMS [8]. These minima correspond to "nearly flat" regions and their inclusion in the merging process was shown to produce an improved segmentation performance.…”