Search

The metric dimension has various applications in several fields, such as computer science, image processing, pattern recognition, integer programming problems, drug discovery, and the production of various chemical compounds. The lowest number of vertices in a set with the condition that any vertex can be uniquely identified by the list of distances from other vertices in the set is the metric dimension of a graph. A resolving function of the graph G is a map ϑ : V (G) → [ 0 , 1 ] such that ∑ u ∈ R { v , w } ϑ (u) ≥ 1 , for every pair of adjacent distinct vertices v , w ∈ V (G) . The local fractional metric dimension of the graph G is defined as ldim f (G) = min { ∑ v ∈ V (G) ϑ (v) , where ϑ is a local resolving function of G } . This paper presents a new family of planar networks namely, rotationally heptagonal symmetrical graphs by means of up to four cords in the heptagonal structure, and then find their upper-bound sequences for the local fractional metric dimension. Moreover, the comparison of the upper-bound sequence for the local fractional metric dimension is elaborated both numerically and graphically. Furthermore, the asymptotic behavior of the investigated sequences for the local fractional metric dimension is addressed. [ABSTRACT FROM AUTHOR]

Axiomatically, symmetry is a fundamental property of mathematical functions defining similarity measures, where similarity measures are important tools in many areas of computer science, including machine learning and image processing. In this paper, we investigate a new technique to measure the similarity between two images, a fixed image and a moving image, in multi-modal image registration (MIR). MIR in medical image processing is essential and useful in diagnosis and therapy guidance, but still a very challenging task due to the lack of robustness against the rotational variance in the image transformation process. Our investigation leads to a novel, local self-similarity descriptor, called the modality-independent and rotation-invariant descriptor (miRID). By relying on the mean of the intensity values, an miRID is simply computable and can effectively handle the complicated intensity relationship between multi-modal images. Moreover, it can also overcome the problem of rotational variance by sorting the numerical values, each of which is the absolute difference between each pixel's intensity and the mean of all pixel intensities within a patch of the image. The experimental result shows that our method outperforms others in both multi-modal rigid and non-rigid image registrations. [ABSTRACT FROM AUTHOR]