A standard method to perform skeletonisation is to use a distance transform. Unfortunately such an approach has the drawback that only the Symmetric axis transform can be computed and not the more practical smoothed local symmetries or the more general symmetry set. Using singularity theory we introduce an extended distance transform which may be used to capture more of the symmetries of a shap...

A non-complete geometric distance-regular graph is the point graph of a partial geometry in which the set of lines is a set of Delsarte cliques. In this paper, we prove that for fixed integer m ≥ 2, there are only finitely many non-geometric distance-regular graphs with smallest eigenvalue at least −m, diameter at least three and intersection number c2 ≥ 2.

In this paper, we present a new method for detecting curvilinear structures in a gray-scale image. The concept of skeleton extraction is introduced to detect more general structures such as tapering structures. A skeleton is extracted from the Euclidean distance map that is constructed based on the edge map of an input image. Then, skeletal points are classified into three types (RIDGE, RAVINE ...

In this paper, we use known bounds on the smallest eigenvalue of a symmetric matrix and Schoenberg’s Theorem to provide both necessary as well as sufficient trace inequalities that guarantee a matrix D is a Euclidean distance matrix, EDM. We also provide necessary and sufficient trace inequalities that guarantee a matrix D is an EDM generated by a regular figure.

It is a simple consequence of the maximum principle that a superharmonic function u on Rn(i. e. ∆u ≤ 0) which is 1 near infinity is identically 1 on Rn (throughout this paper, n ≥ 3). Geometrically this means that one can not conformally deform the Euclidean metric in a bounded region without decreasing the scalar curvature somewhere. In fact there is a much stronger result: one can not have an...

This paper proposes a grey interval relation TOPSIS for the decision making in which all of the attribute weights and attribute values are given by the interval grey numbers. The feature of our method different from other grey relation decision-making is that all of the subjective and objective weights are obtained by interval grey number and that decisionmaking is performed based on the relati...

Let A be a compact set in the right-half plane and Γ(A) the set in R 3 obtained by rotating A about the vertical axis. We investigate the support of the limit distribution of minimal energy point charges on Γ(A) that interact according to the Riesz potential 1/r, 0 < s < 1, where r is the Euclidean distance between points. Potential theory yields that this limit distribution coincides with the ...

This study investigated the effect of social skills on the facial movement asymmetry in facial expressions. Threedimensional facial landmark data of facial expressions (neutral, happy, and angry) were obtained from Japanese participants (n = 62). After the facial expression task, each participant completed KiSS-18 (Kikuchi’s Scale of Social Skills; Kikuchi, 2007). Through a generalized Procrust...

Short proofs are given to various characterizations of the (circum-)Euclidean squared distance matrices. Linear preserver problems related to these matrices are discussed.

In this paper we present an implementation of a perceptual completion model performed in the three dimensional space of position and orientation of level lines of an image. We show that the space is equipped with a natural subriemannian metric. This model allows to perform disocclusion representing both the occluding and occluded objects simultaneously in the space. The completion is accomplish...