Geometric Model Reconstruction - Computational Hemodynamics: Theory, Modelling and Applications - page 52

The predefined criteria wield significant influence on the output. For example
specifying pixels too similar gives good homogeneity and coherent regions, but it
lends itself to over-segmentation where the region suffers from being smaller than
the actual object and probably won't span over separate objects. More relaxed crite-
ria can produce larger regions that fill the entire object but may lead to leaks across
the boundaries of those objects and fill multiple objects unnecessarily. Selecting the
criteria for DICOM images typically involves a threshold range on the pixel inten-
sity, or to apply an average intensity over a neighbourhood around each pixel. For
multiple regions, seed points should be selected within each of the desired regions
since the seeded points grow through neighbouring pixels that are similar, and is
expected to end at boundaries. The use of a histogram (Fig. 3.3 ) in this situation can
help reveal the appropriate range of greyscale values that should be selected as seed
pixels. Further readings regarding region growing segmentation can be found in
Haralick and Shapiro (1985), Gibbs et al. (1996), and Kallergi et al. (1992).
Region splitting is an alternate method to region growing which begins by divid-
ing up the whole image into disjointed sub-regions and then merges similar regions
together. The splitting criteria continues as long as the properties of a newly split
pair continue to differ from those of the original region by more than a threshold.
Recursively splitting an image into smaller regions becomes more efficient than
region growing which involves recursively merging individual pixels to produce
larger coherent regions. The main problem with region splitting is deciding where to
make the partition. One technique is to subdivide the image into smaller quandrants
building a quadtree structure. This involves looking at an area of interest to deter-
mine if the region satisfies a set criterion. If so, then the area retains its region, if
not, then the area is split into four equal sub-areas and each subarea is reconsidered.
This process continues until no further splitting occurs. In the worst case the areas
become so small that they are actually a single pixel. One can also allow merging
of two adjacent regions if each has similar characteristics and satisfies the set crite-
ria. Further reading can be found in Manousakas et al. (1998), Tremeau and Borel
(1997) and Goldstein et al. (2010) (Fig. 3.8 ).
The watershed algorithm concept comes from the field of topography, referring
to the division of landscape into water catchment basins or areas first proposed by
Meyer and Beucher (1990b). The grey scale image is seen as a topological surface,
where each pixel is a point situated at some height or altitude as a function of its
grey level. Thus the image is visualised in 3D as a function of x, y, g defined by
spatial coordinates ( x, y ), and greyscale values ( g ). A white colour (grey level 255)
is taken as the maximum altitude and black colour (grey level 0) the minimum. Thus
darkest pixels will exhibit deep regions, known as catchment basins, which are lo-
cal minima. These are separated by ridges in the topology called watershed lines or
simply watersheds (Fig. 3.9 ).
Two approaches may be used to extract the regions of interest. The first is to find
catchment basins, then their enclosing watershed lines by taking a set complement.
This is analogous to the topological surface being filled with water. The catchment
basins fill up with water starting at these local minima. As the flood level rises,