2.2.1 is dependent highly on the type

2.2.1  Boundary peeling

This
method is based on boundary erosion process; in this process each pixel removes
the pixels while sequence of pixels remains one pixel wide. This is a repetitive,
time intensive process of testing and deletion each layer. The difficulty of
this method is that the set of rules defined for removing pixels is dependent
highly on the type of image and that different set of rules will be applied for
different type of images. However, this method is good for connectivity preservation.
The pixel level iterative thinning is like iterative erosion of the line object
boundary as introduced by 35, the kernel procedure is moving a 3 x 3 window
over the image and applying a set of rules to mark the centre of the window,
after completion of each scan, all marked points are deleted until no more
points can be deleted. The set of functions, B(P1) represents the number of
black pixels, A(P1) :- no of white –black patterns and C(P1):- no of distinct 8
connected components and rules 36 are as follows. P is marked for deletion if
all the following rules are satisfied

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·                       
P must have at least 1 white 4 connected
37 neighbors, means p is an edge point

·                       
P must have at least 2 black 8 connected
37 neighbors, means p should not be an end.

·                       
At least 1 of black 8 connected of p
must be unmarked.

·                       
P must not be a break point; deletion of
break point disconnects line in two components.

·                       
If P2 is marked setting P2
white must not make P a break point.

·                       
If P4 is marked, setting P4
white must not make P a break point.

A
fast parallel thinning 38 is proposed to perform deletion of corner points by
using two iterations. End points and pixel connectivity are preserved. Each
pattern is thinned down to a “skeleton” of unitary thickness but it
will not produce desired result in the presence of noise near corners. These
problems are resolved 39 by slight modification in conditions but it doesn’t
produce one pixel wide skeleton in sloping lines. Enhanced parallel thinning
algorithm 40 produces one pixel wide skeleton as well as it maintains 8
connectivity and removes the problems of 38,39. The main issue with pixel
level iterative thinning algorithm is the time complexity, which is O(wN),w is
line width and N is total number  of
pixels in the image and in presence of noise these algorithm may not produce
desired results.  

2.2.1  Distance transformation

These methods are based on the distance transform
and medial axis transforms (MAT), are sequential and non-iterative, the
distance coding is based on Euclidean distance or the approximation to
Euclidean distance. The skeleton produced in fixed number of passes
irrespective of image size 44. These algorithms are based on distance
transform of binary image as replacing each pixel by a number indicating the
minimum the minimum distance from that pixel to a white point after that local
maxima operation is used to find the skeleton of the object 43. The important
choice in distance transform methods is metric used in distance transform for
eg “Chamber 2-3” 41, “quasi Euclidean Metric 42″as it will directly affects
the centering of skeleton and rotation sensitivity.

Distance
transform – Voronoi Diagram:-  The Voronoi skeleton can be calculated from boundary
of an object. Henceforth, the Voronoi diagram of a (discrete) set of boundary
points will be equivalently termed the discrete Voronoi medial axis (DVMA).
The DVMA is accurate approximation of the continuous MAT46,47,48.
The Delaunay triangulation and the
Voronoi diagram are utilized to extract the skeletons that are guaranteed to be
topologically correct to extract object centrelines 49, but this
method also sensitive to noise and jagged boundaries. 

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