Texture classification using deterministic walk and the influence of the neighbor set

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ORIGINAL PAPER

Texture classification using deterministic walk and the influence of the neighbor set André Ricardo Backes1 Received: 1 January 2020 / Revised: 24 March 2020 / Accepted: 30 April 2020 © Springer-Verlag London Ltd., part of Springer Nature 2020

Abstract Recently, the deterministic partially self-avoiding walk was proposed as an approach for texture characterization. Unfortunately, tourist walk is subjected to different parameters and these parameters may influence its performance. Although the influence of some parameters is well known, there is a lack of information concerning about the influence of the neighbor set used during the walk. As our contribution, we investigated the influence of the neighbor set, thus providing a better understanding on how neighborhood affects the method’s ability to characterize texture samples. To accomplish that, we evaluated three different types of neighborhood and how the radius value used to generate each neighborhood affects the method’s performance. Keywords Texture analysis · Cellular automata · Deterministic walk · Complex systems

1 Introduction First described by John von Neumann and Stanislaw Ulam in late 1940s, cellular automata is a time- and space- discrete mathematical model. It is usually defined by a grid of cell and a transition rule which determines the new state of each cell. Due its characteristics such as local interaction, simplicity of design, and inherent parallelism, cellular automata has achieved considerable attention in last several years to analyze digital images, being nowadays used for task such texture classification [19,26], content-based image retrieval [30], noise filtration [15] and edge detection [21]. Inspired on the idea of cellular automata, we proposed a novel approach for texture analysis, the deterministic partially self-avoiding walk (also known as Deterministic Tourist Walk) [5]. This method uses independent walkers to explorer an image, where a walker moves from its current André R. Backes gratefully acknowledges the financial support of CNPq (National Council for Scientific and Technological Development, Brazil) (Grant #301715/2018-1). This study was financed in part by the Coordenação de Aperfeiçoamento de Pessoal de Nível Superior—Brazil (CAPES)—Finance Code 001.

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André Ricardo Backes [email protected] School of Computer Science, Federal University of Uberlândia, Uberlândia, MG 38408-100, Brazil

pixel to one of its neighboring pixels according to the difference of intensity between them. However, this movement is restricted by memory, i.e., it can only visit a pixel which has not been visited in the last μ steps. After some transient time, the tourist walk usually ends in an attractor, i.e., a cycle of pixels from where the it cannot escape. By performing the tourist walk for each pixel in the image we are able to compute the joint probability distribution between transients and attractors, a bidimensional histogram that can be used as the basis for feasible feature vectors. Besides its good results, recent