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An introduction to variational calculusapplications in image processing /

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	An introduction to variational calculusby Hebert Montegranario.
其他題名:	applications in image processing /
作者:	Montegranario, Hebert.
出版者:	Cham :Springer Nature Switzerland :2025.
面頁冊數:	x, 149 p. :ill., digital ;24 cm.
Contained By:	Springer Nature eBook
標題:	Calculus of variations.
電子資源:	https://doi.org/10.1007/978-3-031-77270-2
ISBN:	9783031772702$q(electronic bk.)

An introduction to variational calculusapplications in image processing /
Montegranario, Hebert.

An introduction to variational calculusapplications in image processing /[electronic resource] :by Hebert Montegranario. - Cham :Springer Nature Switzerland :2025. - x, 149 p. :ill., digital ;24 cm.

Introduction -- Mathematical Preliminaries -- Linear Operators and Functionals -- Minimization of Functionals -- Inverse Problems and Variational Regularization -- Variational Curve and Surface Interpolation -- Further Models and Applications.

This textbook introduces variational calculus and regularization methods for inverse problems, seamlessly blending classical concepts with contemporary computational applications, particularly in the field of image processing. The classical perspective draws upon foundational topics explored by pioneers such as Euler and Lagrange, establishing a solid theoretical groundwork. In recent decades, the advent of disciplines such as computer vision has expanded the horizons of variational calculus, showcasing its effectiveness in addressing complex problems that necessitate computational solutions. Consequently, this book places a strong emphasis on the synergy between mathematical theory, practical applications, and algorithmic development. To ensure the text is comprehensive and accessible, essential principles of functional analysis and Fourier analysis are incorporated, facilitating a deeper and more nuanced understanding of the applications presented. Covering both classic and more recent aspects of variational calculus, this book suggests that many topics of modern technology such as computer vision, robotics and especially digital image processing can be formulated in terms of variational problems.

ISBN: 9783031772702$q(electronic bk.)

Standard No.: 10.1007/978-3-031-77270-2doiSubjects--Topical Terms:

191127
Calculus of variations.

LC Class. No.: QA315 / .M66 2025

Dewey Class. No.: 515.64

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505 0 $a Introduction -- Mathematical Preliminaries -- Linear Operators and Functionals -- Minimization of Functionals -- Inverse Problems and Variational Regularization -- Variational Curve and Surface Interpolation -- Further Models and Applications.
520 $a This textbook introduces variational calculus and regularization methods for inverse problems, seamlessly blending classical concepts with contemporary computational applications, particularly in the field of image processing. The classical perspective draws upon foundational topics explored by pioneers such as Euler and Lagrange, establishing a solid theoretical groundwork. In recent decades, the advent of disciplines such as computer vision has expanded the horizons of variational calculus, showcasing its effectiveness in addressing complex problems that necessitate computational solutions. Consequently, this book places a strong emphasis on the synergy between mathematical theory, practical applications, and algorithmic development. To ensure the text is comprehensive and accessible, essential principles of functional analysis and Fourier analysis are incorporated, facilitating a deeper and more nuanced understanding of the applications presented. Covering both classic and more recent aspects of variational calculus, this book suggests that many topics of modern technology such as computer vision, robotics and especially digital image processing can be formulated in terms of variational problems.
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