Unformatted text preview: neighbors. The
directions of these line segments are then encoded as small integers from zero to the number of
Determine the boundary coding for the region shown in Fig Qu. 1 below. Faculty of Engineering Robotics Technology MECH 4041 24
B.Eng (Hons.) Mechatronics S. Venkannah Mechanical and Production Engineering Department Fig Qu.1
When the boundary does not have to be exact, the boundary pixels can be approximated by
straight line segments, forming a polygonal approximation to the boundary.
A digital boundary can be approximated with arbitrary accuracy by a polygon. For a closed
curve, the approximation is exact when the number of segments in the polygon is equal to the
number of points in the boundary so that each pair of adjacent points defines a segment in the
polygon. In practice, the goal of a polygonal approximation is to capture the essence of the
boundary shape with the fewest possible polygonal segments. This problem in general is not
trivial and can quickly turn into a time consuming iterative search. Explain what you understand by the polygonal approximations with reference to Fig Qu. 1.
2.4 Quad trees
The quad-tree is another space saving region representation that encodes the whole region, not
just its border. In general, each region of interest would be represented by a quad tree structure.
Each node of a quad tree represents a square region in the image and can have one of three
labels: full, empty or mixed. If the node is labeled full, then every pixel of the square region it
represents is a pixel of the region of interest. If the node is labeled empty, then there is no
Faculty of Engineering Robotics Technology MECH 4041 25
B.Eng (Hons.) Mechatronics S. Venkannah Mechanical and Production Engineering Department intersection between the square region it represents and the region of interest. If the node is
labeled mixed, then some of the pixels of the square region are pixels of the region of interest
and some are not....
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