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首页图像代数下的计算机视觉算法手册

图像代数下的计算机视觉算法手册

algorithms

computer

计算机视觉

图像算法

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"《计算机视觉图像代数手册》是一本专为工程师、科学家和学生介绍计算机视觉基础概念及其在图像处理中的应用的书籍。作者Gerhard X. Ritter和Joseph N. Wilson来自佛罗里达大学的计算机视觉与可视化中心，他们旨在通过本书提供一套核心算法，使读者能够理解和开发计算机视觉技术。本书的核心内容围绕深度学习和机器学习算法展开，涵盖了计算机视觉领域内常见的关键算法。作者强调，虽然书中并未试图涵盖计算机视觉技术的全貌和深度，因为这个领域发展迅速，但其所提供的算法集合代表了所有计算机视觉从业者应该掌握的基本知识。书的编排结构便于广泛的应用，无论是作为计算机视觉算法开发者的参考工具，还是针对使用基于图像代数的C++对象库iacc++的开发者。每一章的内容都按照抽象度逐渐提升的方式组织，确保读者可以循序渐进地学习和理解。每个技术的介绍都会先简要阐述其目的和方法论，以便读者快速掌握。作者强调理论与实践的结合，确保读者不仅能了解算法背后的原理，还能将其应用到实际项目中。此外，书中可能包含代码示例、案例分析以及对相关研究的引用，帮助读者加深对这些算法的理解和实践能力。《计算机视觉图像代数手册》是一本适合初学者入门计算机视觉领域的实用教材，也是一本深入学习者不可或缺的参考书，它将帮助读者建立起坚实的计算机视觉基础，并掌握如何利用代数思维来设计和优化视觉处理算法。"

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Symbol Explanation

Let , , and be a binary operation on . An

induced scalar operation on images is deﬁned by

Let ; .

Let

Pointwise complex conjugate of image , .

denotes reduction by a generic reduce operation

The following four items are speciﬁc examples of the global reduce operation. Each

assumes and .

Dot product, .

Complementation of a set-valued image .

Complementation of a Boolean image .

Transpose of image .

xii

Templates and Template Operations

Symbol Explanation

Bold, lowercase characters are used to represent templates.

Usually characters from the middle of the alphabet are used

as template variables.

A template is an image whose pixel values are images. In

particular, an -valued template from to is a function

. Thus, and is an -valued

image on .

Let . For each , . The image

is given by .

If and , then the support of is

denoted by and is deﬁned by

If , then .

A parameterized -valued template from to with

parameters in is a function of the form .

Let . The transpose is deﬁned as

Image-Template Operations

In the table below, is a ﬁnite subset of .

Symbol Explanation

Let be a semiring and , , then

the generic right product of with is deﬁned as

With the conditions above, except that now , the

generic left product of with is deﬁned as

xiii

Symbol Explanation

Let , , and , where .

The right linear product (or convolution) is deﬁned as

With the conditions above, except that , the left

linear product (or convolution) is deﬁned as

For and , the right additive maximum

is deﬁned by

For and , the left additive maximum is

deﬁned by

For and , the right additive minimum

is deﬁned by

For and , the left additive minimum is

deﬁned by

For and , the right

multiplicative maximum is deﬁned by

For and , the left multiplicative

maximum is deﬁned by

xiv

Symbol Explanation

For and , the right

multiplicative minimum is deﬁned by

For and , the left multiplicative

minimum is deﬁned by

Neighborhoods and Neighborhood Operations

Symbol Explanation

Italic uppercase characters are used to denote neighborhoods.

A neighborhood is an image whose pixel values are sets of

points. In particular, a neighborhood from to is a

function .

A parameterized neighborhood from to with parameters

in is a function of the form .

Let , the transpose is deﬁned as

, that is,

The dilation of by is deﬁned by

Image-Neighborhood Operations

In the table below, is a ﬁnite subset of .

Symbol Explanation

Given and , and reduce operation

, the generic right reduction of with is

deﬁned as .

With the conditions above, except that now , the

generic left reduction of with is deﬁned as

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图像代数下的计算机视觉算法手册

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