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11.1 Introduction

Breast diseases are a major concern in women's health today. Early detection of breast cancer has a substantial role in reducing fatality rates. By detecting malignant tumors and removing them at an early stage before they metastasize and spread to adjacent regions, cancer threats can be stopped.

Early detection of breast cancer by means of thermography has a long and controversial history. The availability of highly sensitive infrared cameras that produce high-resolution diagnostic images of the temperature and vascular changes of breasts, and a greater understanding of advanced image processing techniques, have recently created renewed interest in thermography. Thermography can identify the first signs of cancer formation 8 to 10 years before mammography can. In mammography, anatomical changes are detected, while in functional thermography, physiological changes can be caught. It is worthy to note that physiological changes eventually lead to anatomical changes.

Cancer is frequently described as a chaotic, poorly regulated growth.2 Cancerous cells, tumors, and vasculature have irregular shapes that cannot be described using Euclidean geometry, which is based on smooth shapes such as lines, planes, cylinders, and spheres. Since fractal geometry has a stronger means for quantifying the spatial complexity of real objects, it is useful when describing the irregularities of tumor growth.3 Moreover, cancerous cells and tumors can be depicted by a nonlinear dynamical system. A chaotic time series (CTS) can provide the tools necessary for generating procedures used to evaluate a nonlinear system.

Detection and diagnostics of dangerous malignant tumors in the breast are very important for physicians. They are generally assessed based on the skill and knowledge of a radiologist through analysis of the visual characteristics shown in a mammogram. Some experts believe that a major characteristic is the irregularity that exists on the edge of a typical cell that forms part of a tumor and tumor structures (angiogenesis).

Fractal analysis has a crucial role in identifying malignant from benign tumors in mammograms. Several studies have been presented that relate edge sharpness of malignant masses with benign masses. Benign masses are usually round and smooth with well-defined boundaries, while malignant masses are rough and have complicated boundaries. Evaluation of a tumor's geometrical complexity can be made by measuring the irregularities of its boundaries.

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