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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
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更新于2024-07-17
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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 .
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![](https://csdnimg.cn/release/download_crawler_static/10926486/bgd.jpg)
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 .
If , then .
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
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![](https://csdnimg.cn/release/download_crawler_static/10926486/bge.jpg)
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
![](https://csdnimg.cn/release/download_crawler_static/10926486/bgf.jpg)
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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