Many problems in early vision can be formulated in terms of minimizing an energy or cost function. Examples are shape-from-shading, edge detection, motion analysis, structure from motion and surface interpolation (Poggio, Torre and Koch, 1985). It has been shown that all quadratic variational problems, an important subset of early vision tasks, can be "solved" by linear, analog electrical or chemical networks (Poggio and Koch, 1985). IN a variety of situateions the cost function is non-quadratic, however, for instance in the presence of discontinuities. The use of non-quadratic cost functions raises the question of designing efficient algorithms for computing the optimal solution. Recently, Hopfield and Tank (1985) have shown that networks of nonlinear analog "neurons" can be effective in computing the solution of optimization problems. In this paper, we show how these networks can be generalized to solve the non-convex energy functionals of early vision. We illustrate this approach by implementing a specific network solving the problem of reconstructing a smooth surface while preserving its discontinuities from sparsely sampled data (Geman and Geman, 1984; Marroquin 1984; Terzopoulos 1984). These results suggest a novel computational strategy for solving such problems for both biological and artificial vision systems.

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Magistro baigiamajam darbui pasirinkta tema yra Trimačiai objektai: atvaizdavimo ir deformacijos algoritmai. Ši tema nagrinėja paviršiaus rekonstrukciją iš taškų debesies ir galimybes pritaikyti paviršiaus deformacijos algoritmus. Analizės etapo metu išsiaiškinta, kad pagrindinė paviršiaus atstatymo iš taškų debesies problema yra lėtas algoritmų veikimas. Šiame darbe siūlomas atvirkštinės inžinerijos metodas, veikiantis 2D Delaunay trianguliacijos pagrindu. Pateikiami algoritmai padalina taškų debesį į kelias dalis, tada iš trimatės erdvės taškų debesies dalys yra transformuojamos į dvimatę erdvę, suskaičiuojama 2D Delaunay trianguliacija ir gautas trikampių tinklelis vėl transformuojamas į trimatę erdvę. Taip pat pateikiamos teorinės galimybės gautą paviršių transformuoti jau žinomu algoritmu. Po algoritmų praktinio įgyvendinimo buvo nustatyta, kad jie veikia taip kaip tikėtasi, rezultatas gaunamas greičiau nei naudojant kitus žinomus algoritmus. Taip pat buvo pastebėta, kad 2D Delaunay trianguliaciją geriau naudoti kai taškų skaičius taškų debesyje yra labai didelis, o kai taškų skaičius neviršija 2000 geriau naudoti 3D Delaunay trianguliaciją. / The chosen theme of the Master of Science degree paper is “Three dimensional objects: visualization and deformation algorithms“. This subject considers surface reconstruction from point clouds and the possibilities to apply surface deformation algorithms. During the analysis phase we found that the main problem of the algorithms of surface reconstruction from scanned point clouds is the lack of speed. So in this paper a method, based on 2D Delaunay triangulation, for reverse engineering is proposed. This method divides point clouds into several parts, and then maps all the points of those point cloud parts to the plane. Then a 2D Delaunay triangulation is computed and the mesh is mapped back to the point cloud. We also give theoretical possibilities to apply a known algorithm for surface deformation. During the implementation phase we found that our algorithms work as expected, but quicker than the other methods proposed earlier. We also noticed that it’s better to use 2D Delaunay triangulation for bigger point clouds and 3D Delaunay triangulation for point clouds, which contains no more than approximately 2000 points.

A surface reconstruction and image enhancement non-linear finite element technique based on minimization of L1 norm of the total variation of the gradient is introduced. Since minimization in the L1 norm is computationally expensive, we seek to improve the performance of this algorithm in two fronts: first, local L1- minimization, which allows parallel implementation; second, application of the Augmented Lagrangian method to solve the minimization problem. We show that local solution of the minimization problem is feasible. Furthermore, the Augmented Lagrangian method can successfully be used to solve the L1 minimization problem. This result is expected to be useful for improving algorithms computing digital elevation maps for natural and urban terrain, fitting surfaces to point-cloud data, and image super-resolution.

Les nanofils (NFs) de semi-conducteur (SC) sont des objets possédant des propriétés très intéressantes pour la fabrication de futurs composants électroniques à l'échelle nanométrique. Ils sont élaborés grâce à l'utilisation d'un catalyseur métallique (Au) formant un point eutectique profond en s'alliant à la phase SC (Si) permettant la germination et la croissance du NF à basses températures. Ce travail a pour but l'étude de la formation, de la structure et du comportement de ces gouttes d'alliage eutectique en interaction avec le substrat dont les propriétés futures du NF vont dépendre. L'étude a été menée in-situ, par utilisation du rayonnement synchrotron qui est un outil parfaitement dédié à la caractérisation de structures à l'échelle atomistique. Les gouttes d'eutectique ont été obtenues par le démouillage d'un film d'or. L'étude de ce procédé a révélé des changements dans les relations d'épitaxies entre l'or et le silicium. Les gouttes ainsi formées sont accompagnées d'une couche de mouillage, se révélant être une reconstruction de surface, dont les conditions de formation ainsi que la structure atomique ont été déterminées. Lors du refroidissement, une augmentation des effets de surfusion a été observée en présence de cette reconstruction et sont expliqués par la structure même de cette dernière qui semble stabiliser l'état liquide. Des expériences similaires ont été faites sur d'autres systèmes (Au-Ge, Al-Si) et une synthèse a été réalisée pour comparer les connaissances actuelles sur le ce sujet avec les résultats de ce travail. / Semiconductor (SC) nanowires (NMs) have been identified as important components for future electronic and sensor nanodevices. They are produced using a metal catalyst (Au) that forms a low eutectic point with the SC phase (Si) and enables their nucleation and their growth at low temperatures. The aim of this study is to investigate the formation, the structure as well as the behaviour of such liquid eutectic droplets in interaction with the substrates on which the futur NMs properties will later depend. This work has been performed in-situ, using synchrotron radiation which is the perfect tool to characterize this mechanism at the atomistic scale. The eutectic droplets have been obtained through the dewetting of thin gold films. This process has been found to modify the epitaxial relationships between the gold and the silicon substrate. The obtained droplets are accompanied by a wetting layer (WL) whose conditions of formation as well as atomic structure, which turned to be a surface reconstruction, have been determined. During the cooling process, the supercooling effects in such AuSi eutectic droplets have been found to be enhanced in the presence of this reconstruction. They are explained by the specific structure of the reconstruction which is likely to stabilize the liquid phase. Similar experiments on other systems (Au-Ge or Al-Si) were performed and a synthesis has been made in order to present the current knowledge on this topic in comparison with the results of this work.

Made available in DSpace on 2014-12-17T14:55:02Z (GMT). No. of bitstreams: 1 AgostinhoMBJ_ Ate_cap4.pdf: 2708709 bytes, checksum: 594003810b24cc08c34b728a0e492d9d (MD5) Previous issue date: 2005-01-14 / We propose a multi-resolution approach for surface reconstruction from clouds of unorganized points representing an object surface in 3D space. The proposed method uses a set of mesh operators and simple rules for selective mesh refinement, with a strategy based on Kohonen s self-organizing map. Basically, a self-adaptive scheme is used for iteratively moving vertices of an initial simple mesh in the direction of the set of points, ideally the object boundary. Successive refinement and motion of vertices are applied leading to a more detailed surface, in a multi-resolution, iterative scheme. Reconstruction was experimented with several point sets, induding different shapes and sizes. Results show generated meshes very dose to object final shapes. We include measures of performance and discuss robustness. / ? proposto um m?todo em multi-resolu??o para reconstru??o de superf?cies a partir de nuvens de pontos, que representam a superf?cie de um objeto no espa?o 3D. O m?todo proposto utiliza um conjunto de operadores de malha e regras simples de refinamento seletivo da malha, com um estrat?gia baseada nos mapas auto-organiz?veis de Kohonen. Basicamente, um esquema auto-adaptativo ? utilizado para mover iterativamente os v?rtices de uma malha inicial simples em dire??o ao conjunto de pontos, localizados idealmente na fronteira do objeto. Sucessivos refinamentos da malha e movimenta??es dos seus v?rtices s?o aplicados, levando a superf?cies cada vez mais detalhadas, num esquema iterativo em multi-resolu??o. Experimentos de reconstru??o foram realizados com diversos conjuntos de pontos, de diferentes formas e tamanhos. Os resultados apresentam malhas geradas que s?o muito pr?ximas das formas das superf?cies impl?citas nas amostras. S?o inclu?das medidas de erro e de qualidade e discutida a robustez do algoritmo.

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Given the importance of color processing in computer vision and computer graphics, estimating and rendering illumination spectral reflectance of image scenes is important to advance the capability of a large class of applications such as scene reconstruction, rendering, surface segmentation, object recognition, and reflectance estimation. Consequently, this dissertation proposes effective methods for reflection components separation and rendering in single scene images. Based on the dichromatic reflectance model, a novel decomposition technique, named the Mean-Shift Decomposition (MSD) method, is introduced to separate the specular from diffuse reflectance components. This technique provides a direct access to surface shape information through diffuse shading pixel isolation. More importantly, this process does not require any local color segmentation process, which differs from the traditional methods that operate by aggregating color information along each image plane. Exploiting the merits of the MSD method, a scene illumination rendering technique is designed to estimate the relative contributing specular reflectance attributes of a scene image. The image feature subset targeted provides a direct access to the surface illumination information, while a newly introduced efficient rendering method reshapes the dynamic range distribution of the specular reflectance components over each image color channel. This image enhancement technique renders the scene illumination reflection effectively without altering the scene’s surface diffuse attributes contributing to realistic rendering effects. As an ancillary contribution, an effective color constancy algorithm based on the dichromatic reflectance model was also developed. This algorithm selects image highlights in order to extract the prominent surface reflectance that reproduces the exact illumination chromaticity. This evaluation is presented using a novel voting scheme technique based on histogram analysis. In each of the three main contributions, empirical evaluations were performed on synthetic and real-world image scenes taken from three different color image datasets. The experimental results show over 90% accuracy in illumination estimation contributing to near real world illumination rendering effects.

Representações computacionais de formas podem ser criadas em ferramentas CAD ou geradas a partir de um objeto físico já existente. Esta última abordagem oferece como vantagens rapidez e fidelidade ao objeto original, que são os aspectos fundamentais em muitas aplicações, como Simulações Numéricas de Equações Diferenciais Parciais e Imagens Médicas. A reconstrução (ou geração de malhas superficiais) a partir de pontos amostrados de uma superfície de um objeto é um problema clássico de representação de formas. Nesta dissertação apresentamos um vasto levantamento bibliográfico deste tipo de reconstrução, classificando e descrevendo os principais trabalhos presentes na literatura. A partir do levantamento bibliográfico, selecionamos um conjunto de algoritmos sobre os quais foram realizadas comparações teóricas e empíricas cujos resultados são apresentados. Para finalizar, apresentamos aplicações de nossas implementações em Simulação Numérica de Equações Diferenciais Parciais e processamento de Imagens / Computational representations of shapes can be developed using CAD applications or created from data acquired from a real physical object. This latter is advantageous with respect to time and fidelity to the original object which are essential to several applications, such as Numerical Simulation of Partial Differential Equations and Medical Imaging. A classical shape representation problem is that of reconstruction (or superficial mesh generation) from points sampled over the surface of an object. In this Master\'s thesis we describe a broad survey of these reconstruction methods. We focus in the classification and characterization of the main algorithms proposed in the literature. From this survey, we selected some algorithms and conducted some theoretical and practical comparisons. We conclude this work describing applications of the algorithms implemented in Numerical Simulations of Differential Partial Equations and Image Processing

We consider the problem of reconstructing a surface from noisy samples by approximating the point set with non-uniform rational B-spline surfaces. We focus on the fact that the knot sequences should also be part of the unknown variables that include the control points and the weights in order to find their optimal positions. We show how to set up the free knot problem such that constrained nonlinear optimization can be applied efficiently. We describe in detail a parallel implementation of our approach that give almost linear speedup. Finally, we provide numerical results obtained on the Chemnitzer Linux Cluster supercomputer.