This site contains: mathematics courses and book; covers: image analysis, data analysis, and discrete modelling; provides: image analysis software. Created and run by Peter Saveliev.

# Books on computer vision

Elementary computer vision and image analysis.

## 1 Introduction

Current textbooks either have extensive prerequisites or take too long to get the student to use what’s been learned in real-life computer vision projects.

Let’s consider an example. Suppose we know freshman or sophomore students in a technical discipline. They have to take their first course in image processing. What are they capable of doing at the end of a typical course? They know about image representation and how to handle image files. They know how to increase contrast and remove noise. They are familiar with image restoration, image enhancement, and image compression. All good, but this choice of topics draws students toward photo editing and away from scientific and industrial applications.

I am talking about the image processing vs. image analysis dilemma. The former produces images and the latter produces data.

As image processing is a time consuming topic, the students may only get a little taste of image analysis (image segmentation and related topics about image content).

The result is that in order to make their skills applicable to scientific image analysis, they will need to take a more advanced course on the subject. Such a course would require (some combination of) calculus 1-3, linear algebra, probability. Even then, 3D images, especially their topology, are rarely discussed.

Below three very different books on computer vision are briefly reviewed. My suggestion, consider The mathematics of computer vision: course.

## 2 Digital Image Processing Using MATLAB by Gonzalez, Woods, and Eddins

This book one of the best and closest to what I have in mind. Here is a short analysis.

 Pros: Cons: “[T]extbook format not a software manual”. Comprehensive coverage of image processing. A loose collection of “tools”. More about image processing than image analysis. No video analysis. No 3D analysis. Many illustrations. Some mathematics is explained. Required: Good understanding of calculus, Some linear algebra. Many examples of MATLAB code. Website: a lot of supplementary material (even PowerPoint slides for instructors). Many projects online. No exercises in the book. Based on MATLAB which is ubiquitous. MATLAB is expensive. MATLAB is good for education and possibly research, problematic for industry. Accessible to “individuals with a basic background in digital image processing, mathematical analysis, and computer programming, all at the level typical of that found in a junior/senior curriculum in a technical discipline.” These requirements make it an intermediate book.

## 3 Computer Vision by Shapiro and Stockman

 Pros: Cons: Some mathematics is explained. Required: Calculus and beyond, Good understanding of linear algebra. Many illustrations are available. Illustrations are in black and white except for inserts. Comprehensive coverage. 3D topology is not addressed (specifically, tunnels = 1-cycles). Algorithms are presented in pseudocode. Prior experience with algorithms is required. Does not rely on any programming language. Software is not provided. No website. The prerequisites make it an advanced book.

## 4 Computational Homology by Kaczynski, Mischaikow, and Mrozek

 Pros: Cons: Thorough presentation of all the mathematics is given. A solid course in modern algebra is required for the student. Prior experience with algebraic topology is required for the instructor. Algorithms are presented in pseudocode. Prior experience with algorithms is required. Software (CHomP) is provided. Prior experience with C++ is required. The homology of n-dimensional images is addressed in full generality (but not persistent homology). Not addressed: Website contains examples and downloads. Projects provided online are geared toward academic research. Numerous exercises are provided. The prerequisites make it a graduate course.
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