An Approach to Determine the Features of Dental X-ray Images Based on the Fractal Dimension

Applications of the fractal dimension include the analysis and interpretation of medical images. The article presents a method for determining image features that are based on fractal dimension. In the proposed method, an optimization process (modified semi-multifractal optimization algorithm) creates a division into sub-areas similarly to a multi-resolution method. Using this division, a characteristic spectrum based on the fractal dimensions is calculated. This spectrum is applied to the recognition method of X-ray images of teeth. The obtained experimental results showed that the proposed method can effectively recognize such images

Semi-multifractal optimization algorithm

Observations on living organism systems are the inspiration for the creation of modern computational techniques. The article presents an algorithm implementing the division of a solution space in the optimization process. A method for the algorithm operation controlling shows the wide range of its use possibilities. The article presents properties of fractal dimensions of subareas created in the process of optimization. The paper also presents the possibilities of using this method to determine function extremes. The approach proposed in the paper gives more opportunities for its use.Alrawi A, Sagheer A, Ibrahim D (2012) Texture segmentation based on multifractal dimension. Int J Soft Comput ( IJSC ) 3(1):1–10Belussi A, Catania B, Clementini E, Ferrari EE (eds) (2007) Spatial data on the web modeling and management. Springer, Berlin. doi: 10.1007/978-3-540-69878-4Corso G, Freitas J, Lucena L (2004) A multifractal scale-free lattice. Phys A Stat Mech Appl 342(1–2):214–220. doi: 10.1016/j.physa.2004.04.081Corso G, Lucena L (2005) Multifractal lattice and group theory. Phys A Stat Mech Appl 357(1):64–70. doi: 10.1016/j.physa.2005.05.049Gosciniak I (2017) Discussion on semi-immune algorithm behaviour based on fractal analysis. Soft Comput 21(14):3945–3956. doi: 10.1007/s00500-016-2044-yHwang WJ, Derin H (1995) Multiresolution multiresource progressive image transmission. IEEE Trans Image Process 4:1128–1140. doi: 10.1109/83.403418Iwanicki K, van Steen M (2009) Using area hierarchy for multi-resolution storage and search in large wireless sensor networks. In: Communications, 2009. ICC ’09. IEEE international conference on, pp 1–6. doi: 10.1109/ICC.2009.5199556Juliany J, Vose M (1994) The genetic algorithm fractal. Evol Comput 2(2):165–180. doi: 10.1162/evco.1994.2.2.165Kies P (2001) Information dimension of a population’s attractor a binary genetic algorithm. In: Artificial neural nets and genetic algorithms: proceedings of the international conference in Prague, Czech Republic. Springer, pp 232–235. doi: 10.1007/978-3-7091-6230-9_57Kotowski S, Kosinski W, Michalewicz Z, Nowicki J, Przepiorkiewicz B (2008) Fractal dimension of trajectory as invariant of genetic algorithms. In: Artificial intelligence and soft computing (ICAISC 2008). Springer, pp 414–425. doi: 10.1007/978-3-540-69731-2_41Lu Y, Huo X, Tsiotras P (2012) A beamlet-based graph structure for path planning using multiscale information. IEEE Trans Autom Control 57(5):1166–1178. doi: 10.1109/TAC.2012.2191836Marinov M, Kobbelt L (2005) Automatic generation of structure preserving multiresolution models. In: Eurographics, pp 1–8Masayoshi K, Masaru N, Yoshio S (1996) Identification of complicated shape objects by fractal characteristic variables categorizing dust particles on LSI wafer surface. Syst Comput Jpn 27(6):82–91. doi: 10.1002/scj.4690270608Michalewicz Z (1996) Genetic algorithms + data structures = evolution programs. Springer, Berlin. doi: 10.1007/978-3-662-03315-9Mo H (2008) Handbook of research on artificial immune systems and natural computing: applying complex adaptive technologies. Information Science Reference - Imprint of: IGI Publishing. doi: 10.4018/978-1-60566-310-4Pereira M, Corso G, Lucena L, Freitas J (2005) A random multifractal tilling. Chaos Solitons Fractals 23:1105–1110. doi: 10.1016/j.chaos.2004.06.045Rejaur Rahman M, Saha SK (2009) Multi-resolution segmentation for object-based classification and accuracy assessment of land use/land cover classification using remotely sensed data. J Indian Soc Remote Sens 36:189–201. doi: 10.1007/s12524-008-0020-4Song J, Qian F (2006) Fractal algorithm for finding global optimal solution. In: International conference on computational intelligence for modelling control and automation, and international conference on intelligent agents, web technologies and internet commerce (CIMCA–IAWTIC’06). IEEE Computer Society, pp 149–153Urrutia J, Sack JR (eds) (2000) Handbook of computational geometry. North-Holland, Amsterdam. doi: 10.1016/B978-0-444-82537-7.50027-9Weise T (2009) Global Optimization Algorithms—Theory and Applications, 2nd edn. University of Kassel, Distributed Systems Group. http://www.it-weise.deWeller R (2013) New geometric data structures for collision detection and haptics. Springer, Cham. doi: 10.1007/978-3-319-01020-5Vujovic I (2014) Multiresolution approach to processing images for different applications: interaction of lower processing with higher vision. Springer, Cham. doi: 10.1007/978-3-319-14457-3 Google Scholar Virtual library of simulation experiments: test functions and datasets, optimization test problems. https://www.sfu.ca/ssurjano/optimization.html. Accessed 28 July 201