in this work‎, ‎we formulate chatterjea contractions using graphs in metric spaces endowed with a graph ‎‎and‏ ‎‎‎‎investigate ‎the ‎existence‎ ‎of ‎fixed ‎points ‎for such mappings ‎under two different hypotheses‎. we also discuss the uniqueness of the fixed point. the given result is a generalization of chatterjea's fixed point theorem from metric spaces to metric spaces endowed with a g...

In this short note, we extend the notion of texture symmetry to the skewed symmetry and propose a method for calculating the skewed symmetry of a non-rectangular or affine-distorted bidirectional texture. Results for a number of natural textures are shown.

In this study, the process to synthesize a human face based on the information of words is defined as a mapping from a word space, which is composed of the words expressing dimensions and shape of facial elements, into a physical model space where physical shape of the facial elements are formed. By introducing a concept of mapping, the use of whole words existing in the word space makes it pos...

The nature of the mapping between the genotype and the phenotype is vital to the performance of a genetic algorithm. We develop the notion of a phlegmatic mapping function, which encapsulates the idea that small changes in the genotype ought to produce small changes in the phenotype. After illustrating a mapping function with this property, we validate the idea using a test suite of function op...

Cockroach antennae have been extensively used for studying the multifunctional sensory appendage that generates the olfactory, gustatory, tactile, thermal, and humidity senses. Of the variety of senses, the tactile sense is thought to play a key role for perceiving physical objects. Because most cockroach species are nocturnal, the tactile sense of the antenna would be essential to determine th...

In Photometric stereo, the existence of specularities hampers to recover the normal map. To deal with this common reflective phenomenon, we introduce a novel representation for specular reflection with a set of specular basis functions with different roughness values. This representation is suitable for any intensively or weakly specular object, and is introduced into the photometric stereo alg...

This paper describes techniques for fusing the output of multiple cues to robustly and accurately segment foreground objects from the background in image sequences. Two different methods for cue integration are presented and tested. The first is a probabilistic approach which at each pixel computes the likelihood of observations over all cues before assigning pixels to foreground or background ...

Feature extraction has been recognized as a useful technique for pattern recognition. Feature extraction is accomplished by constructing a mapping from the measurement space to a feature space. Often, the mapping is chosen from an arbitrarily specified parametric family by optimizing the parameters with respect to a separability criterion. In the approach described here, a scalar distance funct...

The classical Green’s function associated to a simply connected domain in the complex plane is easily expressed in terms of a Riemann mapping function. The purpose of this paper is to express the Green’s function of a finitely connected domain in the plane in terms of a single Ahlfors mapping of the domain, which is a proper holomorphic mapping of the domain onto the unit disc that is the analo...

This is the supplementary material for the paper entitled “Deep Adaptive Image Clustering”. The supplementary material is organized as follows. Section 1 gives the mapping function described in Figure 1. Section 2 presents the proof of Theorem 1. Section 3 details the experimental settings in our experiments. 1. The Mapping Function Utilized in Figure 1 We assume that li represents the label fe...