Measuring Resemblances Between Swarm Behaviours: A Perceptual Tolerance Near Set Approach

Abstract

The problem considered in this article is how to detect and measure resemblances between swarm behaviours. The solution to this problem stems from an extension of recent work on tolerance near sets and image correspondence. Instead of considering feature extraction from subimages in digital images, we compare swarm behaviours by considering feature extraction from subsets of tuples of feature-values representing the behaviour of observed swarms of organisms. Thanks to recent work on the foundations of near sets, it is possible to formulate a rigorous approach to measuring the extent that swarm behaviours resemble each other. Fundamental to this approach is what is known as a recent description-based set intersection, a set containing objects with matching or . this work is a new approach to comparing information tables representing N. Tinbergen's ethology (study of animal behaviour) and direct result of recent work on what is known as rough ethology. Included in this article is a comparison of recent nearness measures that includes a new form of F. Hausdorff's distance measure. The contribution of this article is a tolerance near set approach to measuring the degree of resemblance between swarm behaviours.

Arthritic Hand‐Finger Movement Similarity Measurements: Tolerance Near Set Approach

“…Near set theory has connections in topology [ 8 ], proximity spaces [ 9 , 10 ], metric spaces [ 11 ], tolerance spaces [ 12 , 13 ], and approach spaces [ 14 , 15 ]. Near sets have proved to be useful in solving problems based on human perception [ 8 ] that arise in areas such as image analysis [ 2 , 4 , 14 , 16 ], image processing [ 2 , 4 , 12 , 13 , 16 – 18 ], face recognition [ 19 ], ethology [ 20 ], image morphology, and segmentation evaluation [ 21 , 22 ] as well as many engineering and science problems.…”

Perceptual Systems Approach to Measuring Image Resemblance

“…Near sets, introduced in 1980s by Zdzislaw Pawlak are useful for solving problems based on human perception [1] that arise in areas such as image analysis [2,3], image processing [2,4], face recognition [5], ethology [6], as well as engineering and science problems As an illustration of the degree of nearness between two sets, consider an example of the Henry color model for varying degrees of nearness between sets. The two pairs of ovals in Figures 1 and 2 contain colored segments.…”

Applications of Near Sets

“…Resemblance is determined by considering set descriptions defined by feature vectors (n-dimensional vectors of numerical features that represent characteristics of objects such as digital image pixels). Near sets are useful in solving problems based on human perception [44,76, 49,51,56] that arise in areas such as image analysis [52,14,41, 48,17,18], image processing [41], face recognition [13], ethology [63], as well as engineering and science problems [53,63,44,19,17,18].As an illustration of the degree of nearness between two sets, consider an example of the Henry color model for varying degrees of nearness between sets [17, §4.3].…”