Thesis (PDF) - Signal & Image Processing Lab

List of Figures
1.1 (a) A noisy binary image, (b) Erosion by a 3 × 3 squared structuring
element, (c) The result of opening-closing with the same s.e., and (d)
The result of closing-opening with the same s.e. . . . . . . . . . . . . 7
2.1 Max Tree representation of images. . . . . . . . . . . . . . . . . . . . 15
2.2 Example of Binary Partition Tree creation with a region merging al-
gorithm. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
2.3 (a) The trees of connected components of upper and lower level sets of
a simple image. (b) The resulting tree of shapes corresponding to the
same image. Notice that D is a hole in F. . . . . . . . . . . . . . . . . 19
2.4 Shape decomposition and associated Tree of shapes. (a) Original gray-
scale image f and (b)-(f) its shapes. The white shapes correspond to
connected components of the collection of upper levels sets {θt(f)},
whereas the black shapes correspond to connected components of the
collection of lower level sets {θt(f) c }. . . . . . . . . . . . . . . . . . . 24
2.5 Tree of shapes associated with Fig. 2.4. (a) Original tree; the numbers
in parenthesis are the gray-levels of the shapes. (b) Modified tree; the
number in parenthesis are the differences s(τ) between the levels of
each shape τ and its parent p(τ). Notice that shape F was duplicated. 25
2.6 (a)-(b) Two grayscale images, and (c) their infimum according to ⊑.
The supremum does not exist in this case. . . . . . . . . . . . . . . . 28
2.7 Erosion in the complete inf-semilattice of shape sequences. (a) Origi-
nal gray-scale image, (b) proposed self-dual erosion, and (c) standard
erosion. The structuring element in both cases is the cross 7 × 7. . . . 29
2.8 (a) Original grayscale image, (b) shape-tree erosion, (c) opening, and
(d) top-hat. A square structuring element of size 2 × 2 was used in all
cases. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
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