Thesis (PDF) - Signal & Image Processing Lab

x LIST OF FIGURES
4.17 A Simba image with Salt&Pepper noise cleaned with an combined fil-
ter. Maximal size of structuring element here is 2 × 2. (a) erosion of
Noisy Image (b) opening of Noisy Image . . . . . . . . . . . . . . . . 59
4.18 Traditional erosion and dilation of gray scale image . . . . . . . . . . 60
4.19 Traditional opening and closing of gray scale image. . . . . . . . . . . 60
4.20 Traditional pseudo-dual open-close and close-open operators. . . . . . 61
4.21 Median operator compared to the combined method of self-dual open-
ing of AS image. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
5.1 Tree-based morphology. . . . . . . . . . . . . . . . . . . . . . . . . . . 62
5.2 An example of image tree representation. An image with V1, V2, V3
and V4 zones is represented as a tree. Each pixel in this zone is mapped
to a corresponding label. . . . . . . . . . . . . . . . . . . . . . . . . . 63
5.3 An example of order of trees. The tree representation (a) is bigger
than (b), because of two reasons: tree (b) is included in tree (a), and
there exists pixels in (b) that belong to label 1, while the same pixels
belong to labels 2 and 3 in (a). . . . . . . . . . . . . . . . . . . . . . 64
5.4 An example of trees intersection that is not a tree. . . . . . . . . . . 65
5.5 An example of a projection of the mapping function. Mapping func-
tions M1(x) and M2(x) of point x are projected to a subtree t1 ∧ t2. 66
5.6 Problem of existence of image semilattice, based on tree representation 73
6.1 EWT-based morphology. . . . . . . . . . . . . . . . . . . . . . . . . . 76
6.2 Example of extrema watershed tree creation. . . . . . . . . . . . . . . 79
6.3 The Extrema Watershed Tree associated to the example in Fig. 6.2. . 80
6.4 Inverse transform of Extrema watershed tree of Lena image eroded by
structuring element 2 × 2. (a) Original Image (b) Eroded Image . . . 82
6.5 Inverse transform of Extrema watershed tree of Lena image opened by
structuring element 2 × 2. (a) Original Image (b) Opened Image . . . 82
6.6 A Lena image corrupted by the Salt&Pepper noise. (a) Original Image
(b) Noisy Lena Image . . . . . . . . . . . . . . . . . . . . . . . . . . . 83