Gradient watersheds in morphological scale-space

Abstract

After introducing several results relating to the modification of the homotopy of gradient functions based on extrema in the base image and building on earlier results in morphological scale-space, we introduce a scale-space monotonicity theorem for regions of an image defined by watersheds of a gradient function modified to retain only the local minima or maxima of its smoothed parent image. We then illustrate the theorem with an example of the scale-space extraction of texture features from the nuclei of cervical cells.

Parallel Marker-Based Image Segmentation with Watershed Transformation

“…Thus, after cleanup, edge (3, 4, 5) has been removed, being an internal edge in the tree rooted at 3. Furthermore, edge (2,4,8) and edge (2, 3, 7) connect the same distinct trees rooted at 2 and 3. Consequently, the lighter edge, (2,3,7), is retained in the graph, while edge (2,4,8) is elided.…”

“…For the image example in Fig. 1a [5,12], [6,13]], bcg 2 =[ [9,0], [7,0], [10,13], [8,1]], bcg 3 =[ [11,0], [12,5], [13,6], [13,10]]. The local WNG, wng, is locally computed in each processor, as described in Section 2.…”

“…Suppose that in Fig. 1b pixels (3, 3), (4,6), and (8,6) ((line, col ) coordinates are relative to the (0, 0) top left corner of the image) are marked; then regions 1 and 4 have to be appended to a marked area, labeled 2 and 3. Let us first remark that merging is performed regionwise, and second that a catchment basin which contains more than one marked pixel is not further split (see region labeled 3 in Fig.…”

Application of Segmentation Techniques on Atherosclerosis Images

“…In non-homogeneous or noise embedded images there is not a one to one relation between regional minima and objects of interest. This results in an over segmentation in the majority of images, in other words, after WT each of the objects is represented by more than one region [17][18][19] [26] [30]. To avoid this over segmentation we resort to the selection of a single marker for each object of interest.…”

Image Segmentation using Multiresolution Texture Gradient and Watershed Algorithm

“…The watershed transform based segmentation approach works on morphological principles [22][23][24][25]. If we regard a grayscale image as a topographic relief, the gray value at a given location represents the elevation at that point.…”