Analysis of Medical Images Using Fractal Geometry

Introduction

The concept of fractal geometry originally initiated by (Mandelbrot, 1982) in order to characterized to complex objects. Mostly of the objects are surrounded in environment are so complicated and abnormal pattern, hence these types of abnormal structures are decline to analyzed by Euclidean geometry described by Chen et al. (2003), Asvestas et al. (1998), and Lopes and Betrouni (2009). The concept of fractal geometry will work based upon the concept of self similarity. Medical imaging system like human vascular system, nervous system, bones and breast tissue are so complex and irregular in pattern and most of the images carry self similar and statistical self similar content. In order to analysis of this complex medical images, most of the researchers are preferring the fractal concept; This is the region why fractal dimension are most popular research area now a days in the field of medical image analysis reported by Lopes and Betrouni (2009) because most of the human body organs such as tissues, brain and breast texture show complex and irritated geometric structural pattern. These types of irritated geometry structure can be characterized by means of shape properties through dissimilar scaled value. In this regard, Fractal concept shows the primary or key role when irregular surfaces comes in computation. The concept of fractal geometry was deals with self similarity objects, that means magnifying an object by means of deeper details with different scaling value and every distinct portion is look like as similar as the whole. As we discuss earlier those biomedical images generally complex and irritated in nature, that’s way the fractal geometry, are widely techniques especially in medical image analysis field. In this context different researchers used different technique in medial image analysis but most of the researchers prefer box counting technique because of its simplicity and easiness. In recent literature survey of different applications of fractal geometry are progressed by means of box counting and its improved versions in both gray scale and color domain. In response to the gray scale domain many methods are presented by different researchers, but in this section we have reported some recent research topic which is related to this literature study like improved box counting at each box scale presented by Nayak et. al (2016), improved DBC by shifting box block gave by Nayak et. al (2016), Effect of error estimation by using box counting by same author (Nayak et. al (2016), Nayak et. al (2017)), comparative study was made in order to select appropriate algorithm for specific objects reported by Nayak et. al (2017), Fractal geometry the beauty of computer graphics presented by Das et. al (2017) and improved triangle box counting reported by Nayak et. al (2018). As concerned to color domain, there are very few technique are evolved like average box counting technique presented by Nayak et. al (2015), roughness subtraction technique by implementing improved differential box counting reported by Nayak et. al (2016), improved color box counting technique by Nayak et al (2017), fundamental color processing technique by implementing CIE based human perception model reported by Nayak et. al (2017), extended differential box counting technique into color domain by implementing maximum Euclidian distance reported by Nayak et. al (2018). These box counting (BC) and their improved versions are applied in different fields of application with different domain. However, our research analysis in this charter is to revel the different application area used by means of fractal geometry in order to analysis of medical images applications. From the above literature survey we have observed that most of the box counting principle will work based upon the concept of self similarity, and almost all bio medical images are so complex and irregular in pattern at it contains self similar and statistical self similar content. Hence, from this point of view we have motivated in order carried out our further research on bio medical image processing by means of fractal geometry. In concerned to medical image analysis there are very few research work were carried out by using fractal geometry. In our next couple of passage we have presented art of the recent investigation work relevant to the box counting technique in medical image processing. Recently Ramya et. al (2016) presented cancer detection technique using fractal texture analysis by implementing box counting algorithm. Chan and Tuszynski (2016) presented tumor malignancy prediction in breast cancer by using fractal dimension. Sumitra et. al (2017) presented a review report on medical image analysis by using fractal dimension concept. Khemis et. al (2016) reported breast tissue characterization by implementing new fractal dimension algorithm based on texture measurement. Stehlik et. al (2016) presented mammary cancer detection by implementing fractal based cancer modeling. The details work flow of medical image analysis by using fractal geometry are properly discussed in section 4, and finally provides the details investigation of these techniques and describe the key ideas related to this issue. At the end this chapter may affords the guidance to fourth coming researchers in order to successful implementation of fractal concept in medical imaging applications. The main objectives in order to write this chapter to described how fractal geometry is very useful in the field of medical image analysis. The next indication of this chapter is organized as succeed: in the following passage we described fractal analysis and its corresponding importance in medical image analysis. In section 3, we have discusses the fractal methods in medical applications. In section 4 gives the different medical application area wherever fractal concept was applied. Finally our concluding remarks are presented in subsequent sections.