An Image Processing Tour of College Mathematics

The Image Processing Tour of College Mathematics provides a comprehensive overview of key topics in college mathematics, focusing on their applications in digital image processing. It covers elementary functions, descriptive statistics, probability distributions, derivatives, linear algebra, Fourier analysis, and discrete wavelet transforms. The book aims to increase student confidence, awareness of recent developments, and preparation for graduate studies in the field.

Format: Paperback / softback
Length: 336 pages
Publication date: 01 August 2022
Publisher: Taylor & Francis Ltd

An Image Processing Tour of College Mathematics is a comprehensive guide designed to provide students with a meaningful context for reviewing key topics in college mathematics. Its primary objectives include helping students gain confidence in applying concepts and techniques of applied mathematics, increasing their awareness of recent developments in mathematical sciences, and preparing them for graduate studies.

The topics covered in this text are diverse and encompass a wide range of subjects relevant to digital image processing. These topics 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.

One of the unique features of this text is its integration of pre-calculus material and basic concepts of descriptive statistics into the context of image processing in the spatial domain. This approach helps students connect mathematical concepts with practical applications, making the learning process more engaging and meaningful.

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. This integration provides students with a comprehensive understanding of linear algebra, which is essential for many applications in image processing.

Some of the key concepts of probability theory are also reviewed in the context of image equalization and histogram matching. This helps students understand how probability theory can be applied to image processing tasks such as image restoration and compression.

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. This approach helps students understand the importance of convolution in image processing and its applications in various fields.

An accessible elementary introduction to Fourier analysis is provided in the context of image restoration. This introduction helps students understand the underlying principles of Fourier analysis, which are crucial for many image processing techniques.

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 integration provides students with a glimpse into the latest advancements in the field, which are essential for staying up-to-date with the latest technologies and techniques.

Overall, An Image Processing Tour of College Mathematics is a valuable resource for students studying college mathematics. It provides a comprehensive and engaging approach to learning key topics in applied mathematics, while also increasing student awareness of recent developments in mathematical sciences. The text's unique integration of pre-calculus material and basic concepts of descriptive statistics into the context of image processing makes it an ideal tool for students preparing for graduate studies in the field of image processing.

Weight: 640g
Dimension: 234 x 156 (mm)
ISBN-13: 9780367694487