Mathematics of Shape Description: A Morphological Approach to Image Processing and Computer Graphics

Image processing problems are often not well defined because real images are contaminated with noise and other uncertain factors. In Mathematics of Shape Description, the authors take a mathematical approach to address these problems using the morphological and set-theoretic approach to image processing and computer graphics by presenting a simple shape model using two basic shape operators called Minkowski addition and decomposition.

This book is ideal for professional researchers and engineers in Information Processing, Image Measurement, Shape Description, Shape Representation and Computer Graphics. Post-graduate and advanced undergraduate students in pure and applied mathematics, computer sciences, robotics and engineering will also benefit from this book.

 Key Features

• Explains the fundamental and advanced relationships between algebraic system and shape description through the set-theoretic approach
• Promotes interaction of image processing geochronology and mathematics in the field of algebraic geometry
• Provides a shape description scheme that is a notational system for the shape of objects
• Offers a thorough and detailed discussion on the mathematical characteristics and significance of the Minkowski operators

圖像處理問題通常定義不清楚，因為真實圖像受到噪音和其他不確定因素的干擾。在《形狀描述的數學》一書中，作者們採用數學方法來解決這些問題，使用形態學和集合論方法進行圖像處理和計算機圖形學，並提出了一個簡單的形狀模型，使用了兩個基本的形狀運算符，稱為明可夫斯基加法和分解。

這本書非常適合資訊處理、圖像測量、形狀描述、形狀表示和計算機圖形學的專業研究人員和工程師。純粹和應用數學、計算機科學、機器人學和工程的研究生和高年級本科生也會從這本書中受益。

主要特點：
- 通過集合論方法解釋了代數系統和形狀描述之間的基本和高級關係
- 促進了圖像處理地質年代學和數學在代數幾何領域的交互作用
- 提供了一種形狀描述方案，即對物體形狀的符號系統
- 對明可夫斯基運算符的數學特性和重要性進行了全面而詳細的討論