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If the criterion of optimality is defined, globally optimal borders can be determined using
(heuristic) graph searching or dynamic programming. Graph search based border detection
represents as extremely powerful segmentation approach.
The border detection process is transformed into a search for the optimal path in the weighted
graph. Costs are associated with each graph node that reflects the likelihood that the border
passes through the particular node (pixel). The aim is to find the optimal path (optimal border,
with respect to some objective function) that connects two specified nodes or sets of nodes that
represent the border’s beginning and end.
Cost definition (evaluation functions) is the key to successful border detection. Cost
calculation complexity may range from simple inverted edge strength to complex
representation of a priori knowledge about the sought borders, segmentation task, image
Graph searching uses Nilsson’s A-algorithm and guarantees optimally. Heuristic graph
search may substantially increase search speed, although the heuristics must satisfy
additional constraints to guarantee optimally.
Dynamic programming is based on the principle of optimality and presents an efficient
way of simultaneously searching for optimal paths from multiple starting and ending
Using the A-algorithm to search a graph, it is not necessary to construct the entire graph
since the costs associated with expended nodes are calculated only if needed. In dynamic
programming, a complete graph must be constructed.
If calculation of the local cost functions is computationally inexpensive, dynamic
programming may represent a computationally less demanding choice. However, which
of the two graph searching approaches ( A- algorithm, dynamic programming) is more
efficient for a particular problem depends on the evaluation functions and on the quality
of heuristics for an A-algorithm.
Hough transform segmentation is applicable if objects of known shape are to be detected
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This document was uploaded on 03/12/2014 for the course MECHANICAL 214 at University of Manchester.
- Spring '14