Unformatted text preview: tly. The smaller the number of
direction changes, the straighter the boundary. The evaluation algorithm is based on the
detection of angles between line segments positioned b boundary pixels from the
Faculty of Engineering Robotics Technology MECH 4041 26
B.Eng (Hons.) Mechatronics S. Venkannah Mechanical and Production Engineering Department evaluated boundary in both directions. The angle need not be represented numerically;
rather, relative position of line segments can be used as a property.
Bending energy- The bending of a border may be understood as the energy necessary to
bend a rod to the desired shape, and can be computed as a sum of squares of the border
curvature c(k) over the border length L.
BE = 1/L Σ c2(k)
Bending energy can easily be computed from Fourier descriptors using Parseval’s theorem. To
represent the border, Freeman’s chain code or its smoothed version may be used. Bending
energy does not permit shape reconstruction.
Signature- the signature of a region may be obtained as a sequence of normal contour
distances. The normal contour distance is calculated for each boundary element as a
function of the path length. For each border point A, the shortest distance to an opposite
border point B is sought in a direction perpendicular to the border tangent at point A.
Signatures are noise sensitive., and using smoothed signatures or signatures of smoothed
contours reduces noise sensitivity. Chord distribution- a line joining any two points of the region boundary is a chord, and
the distribution of lengths and angles of all chords on a contour may be used for shape
Boundary description using segment sequences.
Polygonal representation approximates a region by a polygon, the region being
represented using vertices. Polygonal representations are obtained as a result of a simple
boundary segmentation. The boundary can be approximated with varying precision; if a
more precise description is necessary, a larger number of line segments may be
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