New measures for comparing matrices and their application to image processing

Abstract

In this work we present the class of matrix resemblance functions, i.e., functions that measure the difference between two matrices. We present two construction methods and study the properties that matrix resemblance functions satisfy, which suggest that this class of functions is an appropriate tool for comparing images. Hence, we present a comparison method for grayscale images whose result is a new image, which enables to locate the areas where both images are equally similar or dissimilar. Additionally, we propose some applications in which this comparison method can be used, such as defect detection in industrial manufacturing processes and video motion detection and object tracking.

Interval Subsethood Measures with Respect to Uncertainty for the Interval-Valued Fuzzy Setting

“…Since the inclusion of the width of intervals has been proven to be useful in image processing [26,27] and so have fuzzy subsethood measures [19], our plan for future works is to apply the introduced subsethood measures in constructions of width-based indistinguishability measures and to use them in image processing problems.…”

“…Particularly, many works can be found in the literature where different types of transitivities, distance measures, similarity measures and subsethood, inclusion or equivalence measures between fuzzy sets have been proposed ( [2][3][4][5][6][7][8][9][10][11] or [12,13]). Focusing on subsethood measures, different axiomatizations have been proposed [14][15][16][17] and they have been adapted and applied in different settings [18,19].…”

Curve-based monotonicity: a generalization of directional monotonicity

“…In particular, this is the case of those based on component-wise comparison by means of the Euclidean distance |x − y|, as for restricted equivalence functions (see Bustince et al 2006;Sesma-Sara et al 2018). • Weakly increasing (decreasing) functions in the sense of Definition 2.6 are particular cases of directionally increasing (decreasing) functions in the sense of Definition 2.8, by considering the vector 1 = (1, .…”

Local Properties of Strengthened Ordered Directional and Other Forms of Monotonicity

“…The next is an example that remarks the differences between SOD and OD monotonicity from a local point of view. The function in it is a restricted equivalence function (REF) [5], which have been used for diverse applications [11,18].…”