An Image Processing Tour of College Mathematics

An Image Processing Tour of College Mathematics aims to provide meaningful context for reviewing key topics of the college mathematics curriculum, to help students gain confidence in using concepts and techniques of applied mathematics, to increase student awareness of recent developments in mathematical sciences, and to help students prepare for graduate studies.

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.

《大學數學的影像處理之旅》旨在為大學數學課程的關鍵主題提供有意義的背景，幫助學生在應用數學的概念和技巧上增加信心，提高學生對數學科學最新發展的認識，並幫助學生為研究生學習做好準備。

所涵蓋的主題包括基本函數庫、描述性統計的基本概念、隨機變量函數的概率分佈、一階和二階導數背後的定義和概念、傳統線性代數課程的大多數概念和技巧、傅立葉分析的介紹，以及各種離散小波變換 - 所有這些都在數字影像處理的背景下進行。

特點：
- 在空間域中，以影像處理的背景回顧預計算材料和描述性統計的基本概念。
- 在數字影像的基本操作和離散小波變換的更高級背景下，回顧線性代數的關鍵概念。
- 在影像均衡和直方圖匹配的背景下，回顧概率論的一些關鍵概念。
- 在去噪的天真濾波背景下，輕鬆自然地介紹卷積運算，並隨後用於邊緣檢測和影像恢復。
- 在影像恢復的背景下，提供易於理解的傅立葉分析初級介紹。
- 在影像壓縮的背景下引入離散小波變換，讓讀者更加了解應用數學的一些最新發展。
- 本書幫助數學學生輕鬆掌握科學計算機編程的基礎知識。

Yevgeniy V. Galperin is Associate Professor of Mathematics at East Stroudsburg University of Pennsylvania. He holds a PhD in mathematics and has published several papers in the field of time-frequency analysis and related areas of Fourier analysis. His research and academic interests also include numerical methods, simulation of stochastic processes for real-life applications, and mathematical pedagogy. He has given numerous conference presentations on instructional and course-design approaches directed at increasing student motivation and awareness of societal value of mathematics and on incorporating signal and image processing into the undergraduate mathematics curriculum.

Yevgeniy V. Galperin是賓夕法尼亞州東斯特勞茲堡大學的數學副教授。他擁有數學博士學位，並在時頻分析和傅立葉分析相關領域發表了多篇論文。他的研究和學術興趣還包括數值方法、模擬隨機過程應用於實際問題以及數學教學法。他在教學和課程設計方法方面做了許多會議演講，旨在提高學生的動機和對數學的社會價值的認識，並將信號和圖像處理納入本科數學課程中。