An Image Processing Tour of College Mathematics

The topics covered include a library of elementary functions, basic concepts of descriptive statistics, probability distributions of functions of random variables, definitions and concepts behind first- and second-order derivatives,　 most concepts and techniques of traditional linear algebra courses, an introduction to Fourier analysis, and a variety of discrete wavelet transforms - all of that in the context of digital image processing.
Features
Pre-calculus material and basic concepts of descriptive statistics are reviewed in the context of image processing in the spatial domain.
Key concepts of linear algebra are reviewed both in the context of fundamental operations with digital images and in the more advanced context of discrete wavelet transforms.
Some of the key concepts of probability theory are reviewed in the context of image equalization and histogram matching.
The convolution operation is introduced painlessly and naturally in the context of naïve filtering for denoising and is subsequently used for edge detection and image restoration.
An accessible elementary introduction to Fourier analysis is provided in the context of image restoration.
Discrete wavelet transforms are introduced in the context of image compression, and the readers become more aware of some of the recent developments in applied mathematics.
This text helps students of mathematics ease their way into mastering the basics of scientific computer programming.


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