Fórum de Matemática
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Gostaria de saber se alguém tem alguma bibliografia ou referências a filtragem de imagens, por exemplo, baseada em matrizes aleatórias.

Obrigado

_________________
José Sousa
_{se gostou da resposta, divulgue o fórumdematemática.org}

O Binômio de Newton é tão belo como a Vênus de Milo.
O que há é pouca gente para dar por isso.

óóóó---óóóóóó óóó---óóóóóóó óóóóóóóó
(O vento lá fora.)

Álvaro de Campos, 15-1-1928

Boas caro José Sousa

Como presumo que queira a bibliografia, para fazer processamento de imagem com a intenção de remover manchas, borrões ou nódoas nas imagens, provocadas por exemplo em fotografias aéreas, por nuvens ou nevoeiro, encontrei este livro que aborda exatamente esses tópicos, por exemplo através de matrizes, e ainda tem exemplos MATLAB

http://www.amazon.com/Deblurring-Images-Filtering-Fundamentals-Algorithms/dp/0898716187/ref=sr_1_1?s=books&ie=UTF8&qid=1342994395

Deblurring Images: Matrices, Spectra, and Filtering

“The book’s focus on imaging problems is very unique among the competing books on inverse and ill-posed problems. …It gives a nice introduction into the MATLAB world of images and deblurring problems.”
— Martin Hanke, Professor, Institut für Mathematik, Johannes-Gutenberg-Universität. When we use a camera, we want the recorded image to be a faithful representation of the scene that we see, but every image is more or less blurry. In image deblurring, the goal is to recover the original, sharp image by using a mathematical model of the blurring process. The key issue is that some information on the lost details is indeed present in the blurred image, but this “hidden” information can be recovered only if we know the details of the blurring process. Deblurring Images: Matrices, Spectra, and Filtering describes the deblurring algorithms and techniques collectively known as spectral filtering methods, in which the singular value decomposition—or a similar decomposition with spectral properties—is used to introduce the necessary regularization or filtering in the reconstructed image. The concise MATLAB® implementations described in the book provide a template of techniques that can be used to restore blurred images from many applications. This book’s treatment of image deblurring is unique in two ways: it includes algorithmic and implementation details; and by keeping the formulations in terms of matrices, vectors, and matrix computations, it makes the material accessible to a wide range of readers. Students and researchers in engineering will gain an understanding of the linear algebra behind filtering methods, while readers in applied mathematics, numerical analysis, and computational science will be exposed to modern techniques to solve realistic large-scale problems in image processing. With a focus on practical and efficient algorithms, Deblurring Images: Matrices, Spectra, and Filtering includes many examples, sample image data, and MATLAB codes that allow readers to experiment with the algorithms. It also incorporates introductory material, such as how to manipulate images within the MATLAB environment, making it a stand-alone text. Pointers to the literature are given for techniques not covered in the book. Audience
This book is intended for beginners in the field of image restoration and regularization. Readers should be familiar with basic concepts of linear algebra and matrix computations, including the singular value decomposition and orthogonal transformations. A background in signal processing and a familiarity with regularization methods or with ill-posed problems are not needed. For readers who already have this knowledge, this book gives a new and practical perspective on the use of regularization methods to solve real problems. Preface; How to Get the Software; List of Symbols; Chapter 1: The Image Deblurring Problem; Chapter 2: Manipulating Images in MATLAB; Chapter 3: The Blurring Function; Chapter 4: Structured Matrix Computations; Chapter 5: SVD and Spectral Analysis; Chapter 6: Regularization by Spectral Filtering; Chapter 7: Color Images, Smoothing Norms, and Other Topics; Appendix: MATLAB Functions; Bibliography; Index.

Saudações, espero ter ajudado

_________________
João Pimentel Ferreira
 
_{Partilhe dúvidas e resultados, ajude a comunidade com a sua pergunta!
Não lhe dês o peixe, ensina-o a pescar (provérbio chinês)
Fortalecemos a quem ajudamos pouco, mas prejudicamos se ajudarmos muito (pensamento budista)}

Obrigado pela dica. Tem sido difícil arranjar boa bibliografia!

Saudações Pitagóricas!

_________________
José Sousa
_{se gostou da resposta, divulgue o fórumdematemática.org}

O Binômio de Newton é tão belo como a Vênus de Milo.
O que há é pouca gente para dar por isso.

óóóó---óóóóóó óóó---óóóóóóó óóóóóóóó
(O vento lá fora.)

Álvaro de Campos, 15-1-1928

Eu não li o livro, mas quem leu deixou o seguinte comentário

I enjoy reading this book very much. From introductory material to algorithmic and implementation details, it is packed with interesting material.

I especially like the `Pointer' and `Very Important Point (VIP)' sections throughout the book. Many times, the VIP and Pointer sections help me focus on what was covered even though the material may be a bit unclear to me or I may have forgotten a piece of the mathematics. Another nice feature is that you don't need to have MATLAB Image Processing Toolbox (IPT) to implement the algorithm in the book, the authors provide a HNO MATLAB package to supplement the IPT functions.

To understand the material, you should be comfortable with numerical analysis and linear algebra. A good grasp on Numerical Linear algebra at Demmel's or Trefethen's or Golub's book would not hurt. My minor complaint is the high price for such a small book.

Highly recommended. A real gem!

E uma coisa boa deste livro, apenas 130 páginas, pois já sabemos que é tipico na bibliografia americana levarmos com pelo menos 600 páginas, sendo que mais de metade é pouco útil/importante

Saudações pitagóricas

_________________
João Pimentel Ferreira
 
_{Partilhe dúvidas e resultados, ajude a comunidade com a sua pergunta!
Não lhe dês o peixe, ensina-o a pescar (provérbio chinês)
Fortalecemos a quem ajudamos pouco, mas prejudicamos se ajudarmos muito (pensamento budista)}