• Journal of Broadcast Engineering
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• v.13 no.6
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• pp.962-965
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• 2008

2-D shape descriptors, which are vectors representing characteristics of shapes, enable comparison and classification of shapes and are mainly applied to image and 3-D model retrieval. Existing descriptors have limitations that they only describe shapes of single closed contours or lack in precision, making it difficult to be applied to shapes with multiple contours. Therefore, in this paper, we propose a new shape descriptor called Multi-Curvature-Scale Space that can be applied to shapes with multiple contours. Specifically, we represent the topology of the sub-contours in the multi-contour along with Curvature-Scale Space descriptors to represent the shapes of each sub-contours. Also, by allowing the weight of each component to be controlled when computing the distance between descriptors the weight, we deal with ambiguities in measuring similarity between shapes. Results of various experiments that prove the effectiveness of proposed descriptor are presented.

• Journal of the Chungcheong Mathematical Society
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• v.34 no.1
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• pp.37-53
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• 2021

In this paper we define scaled visual curvature and visual Frenet frame that can be visually accepted for discrete space curves. Scaled visual curvature is relatively simple compared to multi-scale visual curvature and easy to control the influence of noise. We adopt scaled minimizing directions of height functions on each neighborhood. Minimizing direction at a point of a curve is a direction that makes the point a local minimum. Minimizing direction can be given by a small noise around the point. To reduce this kind of influence of noise we exmine the direction whether it makes the point minimum in a neighborhood of some size. If this happens we call the direction scaled minimizing direction of C at p ∈ C in a neighborhood Br(p). Normal vector of a space curve is a second derivative of the curve but we characterize the normal vector of a curve by an integration of minimizing directions. Since integration is more robust to noise, we can find more robust definition of discrete normal vector, visual normal vector. On the other hand, the set of minimizing directions span the normal plane in the case of smooth curve. So we can find the tangent vector from minimizing directions. This lead to the definition of visual tangent vector which is orthogonal to the visual normal vector. By the cross product of visual tangent vector and visual normal vector, we can define visual binormal vector and form a Frenet frame. We examine these concepts to some discrete curve with noise and can see that the scaled visual curvature and visual Frenet frame approximate the original geometric invariants.