Combining anisotropic diffusion, transport equation and texture synthesis for inpainting textured images

Casaca, Wallace; Boaventura, Maurílio; Almeida, Marcos Proença de; Nonato, Luís Gustavo

doi:10.1016/j.patrec.2013.08.023

Cited by 31 publications

(26 citation statements)

References 41 publications

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“…The proposed algorithms rely on Laplace operators, spectral graph theory, and optimization tools towards reaching highly fitting on object boundaries which demand a reduced amount of user involvement while still being mathematically easy to solve and computationally efficient. While most of our research has been focused on the particular problem of segmentation, we developed as side results new methods for the problem of inpainting [8] and photo colorization [9], both of which derived from the previous segmentation methodologies combined with PDE-based approaches. The list below provides the main publications originated during the development of the PhD work: …”

Section: Contributionsmentioning

confidence: 99%

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On the Graph Laplacian for Spectral Image Segmentation and Energy Minimization on Graphs

Casaca¹,

Nonato²,

Taubin³

2017

Proceeding Series of the Brazilian Society of Computational and Applied Mathematics

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Abstract. Image segmentation is an indispensable tool to enhance the ability of computer systems to perform elementary cognitive tasks such as recognition and tracking. In particular, graph-based algorithms have gained a lot of attention lately, specially due to their good performance in clustering complex images and easy usability. However, most traditional approaches rely on sophisticated mathematical tools whose effectiveness strongly depends on how good the boundaries reflect the partitions of the image. In fact, sharp adherence to the contours of image segments, uniqueness of solution, high computational burden, and extensive user intervention are some of the weaknesses of most representative techniques. In this work we proposed two novel graph-based image segmentation techniques that sort out the issues discussed above. The proposed methods rely on Laplace operators, spectral graph theory, and optimization approaches towards enabling highly accurate segmentation tools which demand a small amount of user involvement while still being mathematically easy-to-handle and computationally efficient. The effectiveness of our segmentation algorithms is attested by a comprehensive set of comparisons against state-of-the-art methods. As additional contribution, we have also proposed two new techniques for image inpainting and photo colorization, both of which rely on the accuracy of our segmentation apparatus.

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Section: Contributionsmentioning

confidence: 99%

“…The methods rely on the accuracy of our segmentation apparatus and numerical PDEs to properly work, as reported in [3,8,14]. For general illustrations, see Fig.…”

Section: Image Inpainting and Photo Colorizationmentioning

confidence: 99%

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On the Graph Laplacian for Spectral Image Segmentation and Energy Minimization on Graphs

Casaca¹,

Nonato²,

Taubin³

2017

Proceeding Series of the Brazilian Society of Computational and Applied Mathematics

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“…The proposed methods rely on Laplace operators, spectral graph theory, and optimization schemes towards enabling highly accurate segmentation tools which demand a reduced amount of user interaction while still being mathematically simple and computationally efficient. While most of our research has been focused on the particular problem of image segmentation, we develop as side results new methodologies for the problem of image inpainting [Casaca et al 2014a] and photo colorization [Casaca et al 2012], both of which derived from the proposed segmentation approaches. A summary of the main results obtained during the development of this thesis is presented in the following sections.…”

Section: Contributionsmentioning

confidence: 99%

Graph Laplacian for Spectral Clustering and Seeded Image Segmentation

Casaca¹,

Taubin²,

Nonato³

2015

Anais Do XXVIII Concurso De Teses E Dissertações (CTD 2015)

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Interactive segmentation methods have gained much attention lately, specially due to their good performance in segmenting complex images and easy utilization. However, most interactive segmentation algorithms rely on sophisticated mathematical formulations whose effectiveness highly depends on the kind of image to be processed. In fact, sharp adherence to the contours of image segments, uniqueness of solution, high computational burden, and extensive user interaction are some of the weaknesses of most existing methods. In this thesis we proposed two novel interactive image segmentation techniques that sort out the issues raised above. The proposed methods rely on Laplace operators, spectral graph theory, and optimization schemes towards enabling highly accurate segmentation tools which demand a reduced amount of user interaction while still being mathematically simple and computationally efficient. The good performance of our segmentation algorithms is attested by a comprehensive set of comparisons against representative state-of-the-art methods. As additional contribution, we have also proposed two new algorithms for inpainting and photo colorization, both of which rely on the accuracy of our segmentation apparatus

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“…(f), (g) e (h) Gráfico do termo de confiabilidade proposto C para k = 0:5; 1:0; 1:5, respectivamente, por número de iterações quando aplicamos o retoque na imagem (a). Fonte: (CASACA et al, 2014) TOYAMA, 2004). Segunda linha, método DTAS com: (d) janelamento de 3; (e) janelamento de 5; (f) janelamento de 7.…”

Section: Introductionunclassified

Eliminação de ruídos e retoque digital em imagens com textura via difusão anisotrópica

Almeida¹

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Agradeço a todos aqueles que me ajudaram em minha vida acadêmica e pessoal, pois o apoio e ajuda de vocês tornou possível esta conquista. Foi um período de muito aprendizado e crescimento, com alegria e tristezas, mudanças e viagens, cafezinhos e mais cafezinhos, além de muitas amizades e momentos que serão lembrados com muito afeto. Uma conquista nuncaé fruto do trabalho individual. Há sempre contribuições diretas e indiretas que tornam possível a realização de nossas tarefas. Neste sentigo, sou extremamente grato a todos aqueles me deram suporte e contribuíram na realização deste trabalho de doutoramento. Contudo, acredito ser de grande valia e certamente muito merecido explicitar meu sentimento de gratidão para com algumas pessoas em particular. Agradeço a Deus pelas oportunidades e, principalmente, pelas pessoas que encontrei em meu caminho, pois cada uma delas trouxe mais luz e significado à minha existência. Agradeço também à minha noiva, Amanda Coto, uma pessoa forte e determinada que me ajudou imensamente durante todos os momentos desta etapa tão significante de minha vida, sempre com muita atenção, dedicação e carinho. Expresso também minha gratidão ao meu amigo, Prof. Dr. Wallace Casaca, pela amizade, companhia e auxílio prestado nas questões acadêmicas e nas experiências de vida. À minha família, agradeço por todo apoio, suporte e carinho com o qual me recebem toda vez que retorno para casa. Afinal, mesmo distantes sempre estiveram presentes em minha vida. Agradeço ao Prof. Dr. Antonio Castelo Filho pela orientação deste trabalho e também por todo apoio e ensinamentos oferecidos durante a execução deste trabalho e ao Prof. Dr. António Gaspar-Cunha agradeço pela coorientação e auxílio prestado no decorrer de meu de doutoramento. Além disso, agradeço ao Prof. Dr. Alexandre Delbem pela disponibilidade, atenção e auxílio no desenvolvimento deste trabalho. Deixo também meus agradecimentos aos membros da banca, Prof.

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Combining anisotropic diffusion, transport equation and texture synthesis for inpainting textured images

Cited by 31 publications

References 41 publications

On the Graph Laplacian for Spectral Image Segmentation and Energy Minimization on Graphs

On the Graph Laplacian for Spectral Image Segmentation and Energy Minimization on Graphs

Graph Laplacian for Spectral Clustering and Seeded Image Segmentation

Eliminação de ruídos e retoque digital em imagens com textura via difusão anisotrópica

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