Thesis (PDF) - Signal & Image Processing Lab

78 CHAPTER 6. EXTREMA-WATERSHED TREE EXAMPLE
arbitrary, because v1 and v8 have identical sizes and same gray level difference.
The resulting tree is depicted in Fig. 6.3.
Algorithm 2 Compare 2 extremum regions for a merge candidate selection
function CompareExtrema(e1,e2) ⊲ e1 = (V 1
extr, V 1
2 ), e2 = (V 2
extr, V 2
2 )
⊲ return value 0 means e1 is smaller,value 1 means e2 is smaller
if Size(V 1
extr) < Size(V 2
extr) then
return 0
else if Size(V 2
extr) < Size(V 1
extr) then
return 1
else ⊲ sizes are equal
∆1 1
GL = |GL(Vextr) − GL(V 1
2 )|
2 = |GL(V 2 )|
∆2 GL extr) − GL(V 2
if ∆1 GL < ∆2GL then
return 0
else
return 1
end if
end if
end function
6.2 Morphological operations on the extrema-watershed
tree
As described in the Chapter 5, once a tree transform is defined, morphological op-
erations (such as erosion and opening) in the tree-domain can be obtained. In this
section, we investigate the results of applying this technique to the extrema-watershed
tree.
6.2.1 Erosion and opening
Consider the erosion and opening operators derived from the extrema-watershed tree,
using the general framework developed in Chapter 5. In the following examples the
two operators: erosion and opening are applied on synthetic and natural noisy and
not noisy images.