Application of continuous time quantum walks to image segmentation Micha l Krok 1 , Katarzyna Rycerz 2 , and Marian Bubak 2 1 IBM Software Laboratory, Krak´ow, Poland 2 AGH University of Science and Technology, Department of Computer Science, Krakow, Poland michal.krok@ibm.com {kzajac,bubak}@agh.edu.pl Abstract. This paper provides the algorithm that applies concept of continuous time quantum walks to image segmentation problem. The work, inspired by results from its classical counterpart [9], presents and compares two versions of the solution regarding calculation of pixel- segment association: the version using limiting distribution of the walk and the version using last step distribution. The obtained results vary in terms of accuracy and possibilities to be ported to a real quantum device. The described results were obtained by simulation on classical computer, but the algorithms were designed in a way that will allow to use a real quantum computer, when ready. Keywords: quantum walk · image segmentation · quantum algorithms 1 Introduction Image segmentation [26] is one of the most important image processing tools, as it is frequently applied in an early stage of image analysis in order to extract some high-level features of the input image and significantly simplify further computations. Image segmentation is a process of dividing entire image into multiple separate segments – areas inside which pixels expose similar charac- teristics (e.g. intensity, hue, texture). It might be also defined as an activity of assigning each pixel of an image with a label, in a way that pixels sharing similar traits of interest are labeled alike. Image segmentation has found a broad range of applications: from a very trendy in recent years computer vision (object de- tection and recognition) [13] to medical diagnostics and treatment planning [14]. Despite many efforts and development of plethora of various methods, image segmentation remains an open research area, as there is still a need for inventing more efficient and more precise solutions. A very interesting method for segmentation was invented by Grady [9]. The author proposes solution utilizing classical random walks, a very successful com- putational framework widely used for simulation of some natural and social pro- cesses in physics, biology and even economics [22]. The mechanism of random walk action is quite simple: a particle (walker) explores given space of possible ICCS Camera Ready Version 2019 To cite this paper please use the final published version: DOI: 10.1007/978-3-030-22741-8_2