Thesis (PDF) - Signal & Image Processing Lab

90 CHAPTER 6. EXTREMA-WATERSHED TREE EXAMPLE
(a) (b)
Figure 6.16: Trenches meaning. (a) Trench example (b) An infimum of A and B, is a
common father E. Its sons, C and D are the roots of subtree1 and subtree2. Pruning
the tree to C and D vertices, will create the required segmentation.
segmentation. The idea behind the presented method is to prune the tree, leaving
only the main objects. The tree is self-dual, and so is the resulting segmentation.
The implicit segmentation is based on the “trench” phenomenon. This phe-
nomenon is described in Chapter 4. The trench is created, during erosion, on the
border of two very different zones. The difference is defined by the path-distance
to the common parent. The trench opens a gap with the gray level of the common
parent. The sub-trees (the descendents of the common parent) are image segments.
We are going to use this feature to find basic components of an image as shown in the
example in Fig. 6.16(b). As one can see, common parent of two different subtrees, has
two sons, where each of them is the root of the corresponding subtree. An example
of a trench that opens between two zones in the Lena image is shown in Fig. 6.16(a).
If we take only those son labels, and prune every other label beneath, a segmented
image is created.
The tree-depth image, is the map of depths in the tree associated to each label
in the image. In order to obtain trenches, another definition is required. The trench