Role of Mathematics in Image Processing

The various Image Processing technologies have revolutionized the way in which a particular image is captured, stored, or retrieved from a certain source. Most commonly used Image Processing tasks include; Image Restoration, Image Segmentation, Image Enhancement, De-Blurring, De-noising, etc. Such Images are well utilized in various ways by several of the Imaging techniques, like; Angiography, MRI (Magnetic Resonance Imaging), Arterial Spin Labeling (ASL), Computer Assisted Tomography (CT), Deep Brain Stimulation (DBS), Electroencephalography (EEG), etc. But, it is the, Mathematics that has played a crucial role in various Image Processing tasks mentioned above. Despite the innovation and rapid advances in the various Imaging Technology, one thing that has remained important throughout, is, the use of Mathematics.It has been observed that image processing has got strong connection with Mathematics. Many of the image processing methods rely on the basic Mathematical Techniques of Histogram Equalization, Probability and Statistics, Discrete Cosine Transforms, Fourier Transforms, Differential Equations, Integration, Matrix and Algebra. For computational purposes, Matlab is one of the most commonly used tool by the researchers in the area of Image Processing. Other Tools which are commonly used include SciLab, GNU Octave, SageMath, etc.This paper critically reviews the role of Mathematics in various Image Processing Applications. This paper would also present the basic Mathematical tools and techniques, used in Image processing, along with the literature review of the same.