Weighted Corner Angle FeatureTo extract the rotationinvariant shape features from the SR, we propose a novel feature that can incorporate simultaneously variations of the curvature and shape of the SR object. For this purpose, for a corner point of the SR, the angle between two points of boundary in the left and right sides of that corner point is weighted with Euclidean distance of those two points. Therefore, valuable properties of the curvature of boundary points and shape of the SR based on a special corner point are integrated in a feature that is called weighted corner angle feature.
Suppose is a closed set of boundary points of a selected SR and is an extracted corner point on the selected SR’s boundary. Then, we compute the angle between each pair of its neighbor points (right handed and left handed) as,
(9)
where is the number of boundary points belong to selected SR and and are the lefthanded and righthanded neighborhood pixels of the corner point , respectively. Then, Euclidean distance between each pair of these neighborhood points is computed as in the following,
(10)
To integrate two terms of the angle and distance in the weighted corner angle feature, we normalize the angle term in range of [0, 1] by sinusoidal function and then multiply this normalized term to distance term as,
(11)
Since each SR of a query image has more than one corner point, the scenario of corner point selection will be described in section (2.3.1). Fig. 6 illustrates the process of weighted corner angle feature for one corner point of the selected SR in Fig. (3a).
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Fig. 6: Extraction process of weighted corner angle feature for one corner point of the selected SR in Fig. (3a). (a) Softened boundary of the selected SR in Fig. (3a) and description of the weighted corner angle feature, the green point shows one of selected corner points as a sample, blue vectors represent each pair of left and righthanded neighbors of selected corner point used in Eq. 9 to compute angles between each two vectors, red lines show the distances between each pair of left and righthanded neighbors of selected corner point described in Eq. 10, (b) Angle vector of , (c) Distance vector of , (d) Weighted corner angle feature .
Date: 20160422; view: 116
