A Decomposition and Noise Removal Method Combining Diffusion Equation and Wave Atoms for Textured Images

We propose a new method that is aimed at denoising images having textures. The method combines a balanced nonlinear partial differential equation driven by optimal parameters, mathematical morphology operators, weighting techniques, and some recent works in harmonic analysis. Furthermore, the new scheme decomposes the observed image into three components that are well defined as structure/cartoon, texture, and noise-background. Experimental results are provided to show the improved performance of our method for the texture-preserving denoising problem

Laplacian coordinates for seeded image segmentation

Seed-based image segmentation methods have gained\ud much attention lately, mainly due to their good performance\ud in segmenting complex images with little user interaction.\ud Such popularity leveraged the development of many new\ud variations of seed-based image segmentation techniques,\ud which vary greatly regarding mathematical formulation and\ud complexity. Most existing methods in fact rely on complex\ud mathematical formulations that typically do not guarantee\ud unique solution for the segmentation problem while still being\ud prone to be trapped in local minima. In this work we\ud present a novel framework for seed-based image segmentation\ud that is mathematically simple, easy to implement, and\ud guaranteed to produce a unique solution. Moreover, the formulation\ud holds an anisotropic behavior, that is, pixels sharing\ud similar attributes are kept closer to each other while\ud big jumps are naturally imposed on the boundary between\ud image regions, thus ensuring better fitting on object boundaries.\ud We show that the proposed framework outperform\ud state-of-the-art techniques in terms of quantitative quality\ud metrics as well as qualitative visual resultsFAPESP (processos nos. 2009/17801-0 e 2011/22749-8 e 2012/14021-7)CNPq (processo no. 302643/2013-3)NSF (subvenções IIS-0808718 e 0915661-CCF

Estudo do Laplaciano do grafo para o problema de clusterização espectral e segmentação interativa de imagens

Image segmentation is an essential tool to enhance the ability of computer systems to efficiently perform elementary cognitive tasks such as detection, recognition and tracking. In this thesis we concentrate on the investigation of two fundamental topics in the context of image segmentation: spectral clustering and seeded image segmentation. We introduce two new algorithms for those topics that, in summary, rely on Laplacian-based operators, spectral graph theory, and minimization of energy functionals. The effectiveness of both segmentation algorithms is verified by visually evaluating the resulting partitions against state-of-the-art methods as well as through a variety of quantitative measures typically employed as benchmark by the image segmentation community. Our spectral-based segmentation algorithm combines image decomposition, similarity metrics, and spectral graph theory into a concise and powerful framework. An image decomposition is performed to split the input image into texture and cartoon components. Then, an affinity graph is generated and weights are assigned to the edges of the graph according to a gradient-based inner-product function. From the eigenstructure of the affinity graph, the image is partitioned through the spectral cut of the underlying graph. Moreover, the image partitioning can be improved by changing the graph weights by sketching interactively. Visual and numerical evaluation were conducted against representative spectral-based segmentation techniques using boundary and partition quality measures in the well-known BSDS dataset. Unlike most existing seed-based methods that rely on complex mathematical formulations that typically do not guarantee unique solution for the segmentation problem while still being prone to be trapped in local minima, our segmentation approach is mathematically simple to formulate, easy-to-implement, and it guarantees to produce a unique solution. Moreover, the formulation holds an anisotropic behavior, that is, pixels sharing similar attributes are preserved closer to each other while big discontinuities are naturally imposed on the boundary between image regions, thus ensuring better fitting on object boundaries. We show that the proposed approach significantly outperforms competing techniques both quantitatively as well as qualitatively, using the classical GrabCut dataset from Microsoft as a benchmark. While most of this research concentrates on the particular problem of segmenting an image, we also develop two new techniques to address the problem of image inpainting and photo colorization. Both methods couple the developed segmentation tools with other computer vision approaches in order to operate properly.Segmentar uma image é visto nos dias de hoje como uma prerrogativa para melhorar a capacidade de sistemas de computador para realizar tarefas complexas de natureza cognitiva tais como detecção de objetos, reconhecimento de padrões e monitoramento de alvos. Esta pesquisa de doutorado visa estudar dois temas de fundamental importância no contexto de segmentação de imagens: clusterização espectral e segmentação interativa de imagens. Foram propostos dois novos algoritmos de segmentação dentro das linhas supracitadas, os quais se baseiam em operadores do Laplaciano, teoria espectral de grafos e na minimização de funcionais de energia. A eficácia de ambos os algoritmos pode ser constatada através de avaliações visuais das segmentações originadas, como também através de medidas quantitativas computadas com base nos resultados obtidos por técnicas do estado-da-arte em segmentação de imagens. Nosso primeiro algoritmo de segmentação, o qual ´e baseado na teoria espectral de grafos, combina técnicas de decomposição de imagens e medidas de similaridade em grafos em uma única e robusta ferramenta computacional. Primeiramente, um método de decomposição de imagens é aplicado para dividir a imagem alvo em duas componentes: textura e cartoon. Em seguida, um grafo de afinidade é gerado e pesos são atribuídos às suas arestas de acordo com uma função escalar proveniente de um operador de produto interno. Com base no grafo de afinidade, a imagem é então subdividida por meio do processo de corte espectral. Além disso, o resultado da segmentação pode ser refinado de forma interativa, mudando-se, desta forma, os pesos do grafo base. Experimentos visuais e numéricos foram conduzidos tomando-se por base métodos representativos do estado-da-arte e a clássica base de dados BSDS a fim de averiguar a eficiência da metodologia proposta. Ao contrário de grande parte dos métodos existentes de segmentação interativa, os quais são modelados por formulações matemáticas complexas que normalmente não garantem solução única para o problema de segmentação, nossa segunda metodologia aqui proposta é matematicamente simples de ser interpretada, fácil de implementar e ainda garante unicidade de solução. Além disso, o método proposto possui um comportamento anisotrópico, ou seja, pixels semelhantes são preservados mais próximos uns dos outros enquanto descontinuidades bruscas são impostas entre regiões da imagem onde as bordas são mais salientes. Como no caso anterior, foram realizadas diversas avaliações qualitativas e quantitativas envolvendo nossa técnica e métodos do estado-da-arte, tomando-se como referência a base de dados GrabCut da Microsoft. Enquanto a maior parte desta pesquisa de doutorado concentra-se no problema específico de segmentar imagens, como conteúdo complementar de pesquisa foram propostas duas novas técnicas para tratar o problema de retoque digital e colorização de imagens

Restauração de imagens digitais com texturas utilizando técnicas de decomposição e equações diferenciais parciais

Neste trabalho propomos quatro novas abordagens para tratar o problema de restauração de imagens reais contendo texturas sob a perspectiva dos temas: reconstrução de regiões danificadas, remoção de objetos, e eliminação de ruídos. As duas primeiras abor dagens são designadas para recompor partes perdias ou remover objetos de uma imagem real a partir de formulações envolvendo decomposiçãode imagens e inpainting por exem- plar, enquanto que as duas últimas são empregadas para remover ruído, cujas formulações são baseadas em decomposição de três termos e equações diferenciais parciais não lineares. Resultados experimentais atestam a boa performace dos protótipos apresentados quando comparados à modelagens correlatas da literatura.In this paper we propose four new approaches to address the problem of restoration of real images containing textures from the perspective of reconstruction of damaged areas, object removal, and denoising topics. The first two approaches are designed to reconstruct missing parts or to remove objects of a real image using formulations based on image de composition and exemplar based inpainting, while the last two other approaches are used to remove noise, whose formulations are based on decomposition of three terms and non- linear partial di®erential equations. Experimental results attest to the good performance of the presented prototypes when compared to modeling related in literature.Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP

Class-specific metrics for multidimensional data projection applied to CBIR

Content-based image retrieval is still a challenging issue due to the inherent complexity of images and choice of the most discriminant descriptors. Recent developments in the field have introduced multidimensional projections to burst accuracy in the retrieval process, but many issues such as introduction of pattern recognition tasks and deeper user intervention to assist the process of choosing the most discriminant features still remain unaddressed. In this paper, we present a novel framework to CBIR that combines pattern recognition tasks, class-specific metrics, and multidimensional projection to devise an effective and interactive image retrieval system. User interaction plays an essential role in the computation of the final multidimensional projection from which image retrieval will be attained. Results have shown that the proposed approach outperforms existing methods, turning out to be a very attractive alternative for managing image data sets.FAPESPCAPES-Brazi

Similarity preserving snippet-based visualization of web search results

Internet users are very familiar with the results of a search query displayed as a ranked list of snippets. Each textual snippet\ud shows a content summary of the referred document (or webpage) and a link to it. This display has many advantages, for example, it\ud affords easy navigation and is straightforward to interpret. Nonetheless, any user of search engines could possibly report some\ud experience of disappointment with this metaphor. Indeed, it has limitations in particular situations, as it fails to provide an overview of\ud the document collection retrieved. Moreover, depending on the nature of the query—for example, it may be too general, or ambiguous,\ud or ill expressed—the desired information may be poorly ranked, or results may contemplate varied topics. Several search tasks would\ud be easier if users were shown an overview of the returned documents, organized so as to reflect how related they are, content wise.\ud We propose a visualization technique to display the results of web queries aimed at overcoming such limitations. It combines the\ud neighborhood preservation capability of multidimensional projections with the familiar snippet-based representation by employing a\ud multidimensional projection to derive two-dimensional layouts of the query search results that preserve text similarity relations, or\ud neighborhoods. Similarity is computed by applying the cosine similarity over a “bag-of-words” vector representation of collection built\ud from the snippets. If the snippets are displayed directly according to the derived layout, they will overlap considerably, producing a poor\ud visualization. We overcome this problem by defining an energy functional that considers both the overlapping among snippets and the\ud preservation of the neighborhood structure as given in the projected layout. Minimizing this energy functional provides a neighborhood\ud preserving two-dimensional arrangement of the textual snippets with minimum overlap. The resulting visualization conveys both a\ud global view of the query results and visual groupings that reflect related results, as illustrated in several examples shown.FAPESPCNPqCAPE