Simplification, approximation and deformation of large models

The high level of realism and interaction in many computer graphic applications requires techniques for processing complex geometric models. First, we present a method that provides an accurate low-resolution approximation from a multi-chart textured model that guarantees geometric fidelity and correct preservation of the appearance attributes. Then, we introduce a mesh structure called Compact Model that approximates dense triangular meshes while preserving sharp features, allowing adaptive reconstructions and supporting textured models. Next, we design a new space deformation technique called *Cages based on a multi-level system of cages that preserves the smoothness of the mesh between neighbouring cages and is extremely versatile, allowing the use of heterogeneous sets of coordinates and different levels of deformation. Finally, we propose a hybrid method that allows to apply any deformation technique on large models obtaining high quality results with a reduced memory footprint and a high performance.

Hilbert space on probability density functions with Aitchison geometry

Compositional data analysis motivated the introduction of a complete Euclidean structure in the simplex of D parts. This was based on the early work of J. Aitchison (1986) and completed recently when Aitchinson distance in the simplex was associated with an inner product and orthonormal bases were identified (Aitchison and others, 2002; Egozcue and others, 2003). A partition of the support of a random variable generates a composition by assigning the probability of each interval to a part of the composition. One can imagine that the partition can be refined and the probability density would represent a kind of continuous composition of probabilities in a simplex of infinitely many parts. This intuitive idea would lead to a Hilbert-space of probability densities by generalizing the Aitchison geometry for compositions in the simplex into the set probability densities

Aitchison Geometry for Probability and Likelihood as a new approach to mathematical statistics

The Aitchison vector space structure for the simplex is generalized to a Hilbert space structure A2(P) for distributions and likelihoods on arbitrary spaces. Central notations of statistics, such as Information or Likelihood, can be identified in the algebraical structure of A2(P) and their corresponding notions in compositional data analysis, such as Aitchison distance or centered log ratio transform. In this way very elaborated aspects of mathematical statistics can be understood easily in the light of a simple vector space structure and of compositional data analysis. E.g. combination of statistical information such as Bayesian updating, combination of likelihood and robust M-estimation functions are simple additions/ perturbations in A2(Pprior). Weighting observations corresponds to a weighted addition of the corresponding evidence. Likelihood based statistics for general exponential families turns out to have a particularly easy interpretation in terms of A2(P). Regular exponential families form finite dimensional linear subspaces of A2(P) and they correspond to finite dimensional subspaces formed by their posterior in the dual information space A2(Pprior). The Aitchison norm can identified with mean Fisher information. The closing constant itself is identified with a generalization of the cummulant function and shown to be Kullback Leiblers directed information. Fisher information is the local geometry of the manifold induced by the A2(P) derivative of the Kullback Leibler information and the space A2(P) can therefore be seen as the tangential geometry of statistical inference at the distribution P. The discussion of A2(P) valued random variables, such as estimation functions or likelihoods, give a further interpretation of Fisher information as the expected squared norm of evidence and a scale free understanding of unbiased reasoning

Vertebrates Limb Geometry in the Simplex space

A novel metric comparison of the appendicular skeleton (fore and hind limb) of different vertebrates using the Compositional Data Analysis (CDA) methodological approach it’s presented. 355 specimens belonging in various taxa of Dinosauria (Sauropodomorpha, Theropoda, Ornithischia and Aves) and Mammalia (Prothotheria, Metatheria and Eutheria) were analyzed with CDA. A special focus has been put on Sauropodomorpha dinosaurs and the Aitchinson distance has been used as a measure of disparity in limb elements proportions to infer some aspects of functional morphology

Colour image processing

In the context of the round table the following topics related to image colour processing will be discussed: historical point of view. Studies of Aguilonius, Gerritsen, Newton and Maxwell. CIE standard (Commission International de lpsilaEclaraige). Colour models. RGB, HIS, etc. Colour segmentation based on HSI model. Industrial applications. Summary and discussion. At the end, video images showing the robustness of colour in front of B/W images will be presented

Planar homography: accuracy analysis and applications

Projective homography sits at the heart of many problems in image registration. In addition to many methods for estimating the homography parameters (R.I. Hartley and A. Zisserman, 2000), analytical expressions to assess the accuracy of the transformation parameters have been proposed (A. Criminisi et al., 1999). We show that these expressions provide less accurate bounds than those based on the earlier results of Weng et al. (1989). The discrepancy becomes more critical in applications involving the integration of frame-to-frame homographies and their uncertainties, as in the reconstruction of terrain mosaics and the camera trajectory from flyover imagery. We demonstrate these issues through selected examples

A survey addressing the fundamental matrix estimation problem

Epipolar geometry is a key point in computer vision and the fundamental matrix estimation is the only way to compute it. This article surveys several methods of fundamental matrix estimation which have been classified into linear methods, iterative methods and robust methods. All of these methods have been programmed and their accuracy analysed using real images. A summary, accompanied with experimental results, is given

Visualitzation and processing of diffusion tensor MRI

Diffusion Tensor Imaging (DTI) is a new magnetic resonance imaging modality capable of producing quantitative maps of microscopic natural displacements of water molecules that occur in brain tissues as part of the physical diffusion process. This technique has become a powerful tool in the investigation of brain structure and function because it allows for in vivo measurements of white matter fiber orientation. The application of DTI in clinical practice requires specialized processing and visualization techniques to extract and represent acquired information in a comprehensible manner. Tracking techniques are used to infer patterns of continuity in the brain by following in a step-wise mode the path of a set of particles dropped into a vector field. In this way, white matter fiber maps can be obtained.

Signal processing of microstructure profiles: integrating turbulent spatial scales in aquatic ecological modeling

The main objective of this thesis was the integration of microstructure information in synoptic descriptors of turbulence, that reflects the mixing processes. Turbulent patches are intermittent in space and time, but they represent the dominant process for mixing. In this work, the properties of turbulent patches were considered the potential input for integrating the physical microscale measurements. The development of a method for integrating the properties of the turbulent patches required solving three main questions: a) how can we detect the turbulent patches from he microstructure measurements?; b) which are the most relevant properties of the turbulent patches?; and ) once an interval of time has been selected, what kind of synoptic parameters could better reflect the occurrence and properties of the turbulent patches? The answers to these questions were the final specific objectives of this thesis.

Advances in animal blood processing: development of a biopreservation system and insights on the functional properties of plasma

La sang és un subproducte amb un alt potencial de valorització que s'obté en quantitats importants en els escorxadors industrials. Actualment, la majoria de sistemes de recollida de la sang no segueixen unes mesures d'higiene estrictes, pel que esdevé un producte de baixa qualitat microbiològica. Conseqüentment, l'aprofitament de la sang és una sortida poc estimulant des del punt de vista econòmic, ja que acostuma a perdre les qualitats que permetrien l'obtenció de productes d'alt valor afegit. El capítol I del present treball s'inclou dins d'un projecte que proposa la inoculació de bacteris de l'àcid làctic (LAB) com un cultiu bioconservador de la sang, un sistema senzill i de baix cost que cerca l'estabilitat de la sang, tant microbiològica com fisicoquímica, durant el període del seu emmagatzematge. El capítol II s'emmarca dins d'un projecte que cerca la millora de l'aprofitament integral de la sang que, en el cas de la fracció plasmàtica, es centra en l'estudi de la funcionalitat dels seus principals constituents. Conèixer la contribució dels components majoritaris ha de permetre la millora de la funcionalitat dels ingredients alimentaris derivats. Els resultats presentats en aquesta tesi poden ajudar a la valorització de la sang porcina d'escorxadors industrials, mitjançant els coneixements adquirits pel que fa a la millora del seu sistema de recollida i del desenvolupament d'ingredients alimentaris amb interessants propietats funcionals.

An approach to coded structured light to obtain three dimensional information

The human visual ability to perceive depth looks like a puzzle. We perceive three-dimensional spatial information quickly and efficiently by using the binocular stereopsis of our eyes and, what is mote important the learning of the most common objects which we achieved through living. Nowadays, modelling the behaviour of our brain is a fiction, that is why the huge problem of 3D perception and further, interpretation is split into a sequence of easier problems. A lot of research is involved in robot vision in order to obtain 3D information of the surrounded scene. Most of this research is based on modelling the stereopsis of humans by using two cameras as if they were two eyes. This method is known as stereo vision and has been widely studied in the past and is being studied at present, and a lot of work will be surely done in the future. This fact allows us to affirm that this topic is one of the most interesting ones in computer vision. The stereo vision principle is based on obtaining the three dimensional position of an object point from the position of its projective points in both camera image planes. However, before inferring 3D information, the mathematical models of both cameras have to be known. This step is known as camera calibration and is broadly describes in the thesis. Perhaps the most important problem in stereo vision is the determination of the pair of homologue points in the two images, known as the correspondence problem, and it is also one of the most difficult problems to be solved which is currently investigated by a lot of researchers. The epipolar geometry allows us to reduce the correspondence problem. An approach to the epipolar geometry is describes in the thesis. Nevertheless, it does not solve it at all as a lot of considerations have to be taken into account. As an example we have to consider points without correspondence due to a surface occlusion or simply due to a projection out of the camera scope. The interest of the thesis is focused on structured light which has been considered as one of the most frequently used techniques in order to reduce the problems related lo stereo vision. Structured light is based on the relationship between a projected light pattern its projection and an image sensor. The deformations between the pattern projected into the scene and the one captured by the camera, permits to obtain three dimensional information of the illuminated scene. This technique has been widely used in such applications as: 3D object reconstruction, robot navigation, quality control, and so on. Although the projection of regular patterns solve the problem of points without match, it does not solve the problem of multiple matching, which leads us to use hard computing algorithms in order to search the correct matches. In recent years, another structured light technique has increased in importance. This technique is based on the codification of the light projected on the scene in order to be used as a tool to obtain an unique match. Each token of light is imaged by the camera, we have to read the label (decode the pattern) in order to solve the correspondence problem. The advantages and disadvantages of stereo vision against structured light and a survey on coded structured light are related and discussed. The work carried out in the frame of this thesis has permitted to present a new coded structured light pattern which solves the correspondence problem uniquely and robust. Unique, as each token of light is coded by a different word which removes the problem of multiple matching. Robust, since the pattern has been coded using the position of each token of light with respect to both co-ordinate axis. Algorithms and experimental results are included in the thesis. The reader can see examples 3D measurement of static objects, and the more complicated measurement of moving objects. The technique can be used in both cases as the pattern is coded by a single projection shot. Then it can be used in several applications of robot vision. Our interest is focused on the mathematical study of the camera and pattern projector models. We are also interested in how these models can be obtained by calibration, and how they can be used to obtained three dimensional information from two correspondence points. Furthermore, we have studied structured light and coded structured light, and we have presented a new coded structured light pattern. However, in this thesis we started from the assumption that the correspondence points could be well-segmented from the captured image. Computer vision constitutes a huge problem and a lot of work is being done at all levels of human vision modelling, starting from a)image acquisition; b) further image enhancement, filtering and processing, c) image segmentation which involves thresholding, thinning, contour detection, texture and colour analysis, and so on. The interest of this thesis starts in the next step, usually known as depth perception or 3D measurement.

New Methods for Triangulation-based Shape Acquisition using Laser Scanners

Tradicionalment, la reproducció del mon real se'ns ha mostrat a traves d'imatges planes. Aquestes imatges se solien materialitzar mitjançant pintures sobre tela o be amb dibuixos. Avui, per sort, encara podem veure pintures fetes a ma, tot i que la majoria d'imatges s'adquireixen mitjançant càmeres, i es mostren directament a una audiència, com en el cinema, la televisió o exposicions de fotografies, o be son processades per un sistema computeritzat per tal d'obtenir un resultat en particular. Aquests processaments s'apliquen en camps com en el control de qualitat industrial o be en la recerca mes puntera en intel·ligència artificial. Aplicant algorismes de processament de nivell mitja es poden obtenir imatges 3D a partir d'imatges 2D, utilitzant tècniques ben conegudes anomenades Shape From X, on X es el mètode per obtenir la tercera dimensió, i varia en funció de la tècnica que s'utilitza a tal nalitat. Tot i que l'evolució cap a la càmera 3D va començar en els 90, cal que les tècniques per obtenir les formes tridimensionals siguin mes i mes acurades. Les aplicacions dels escàners 3D han augmentat considerablement en els darrers anys, especialment en camps com el lleure, diagnosi/cirurgia assistida, robòtica, etc. Una de les tècniques mes utilitzades per obtenir informació 3D d'una escena, es la triangulació, i mes concretament, la utilització d'escàners laser tridimensionals. Des de la seva aparició formal en publicacions científiques al 1971 [SS71], hi ha hagut contribucions per solucionar problemes inherents com ara la disminució d'oclusions, millora de la precisió, velocitat d'adquisició, descripció de la forma, etc. Tots i cadascun dels mètodes per obtenir punts 3D d'una escena te associat un procés de calibració, i aquest procés juga un paper decisiu en el rendiment d'un dispositiu d'adquisició tridimensional. La nalitat d'aquesta tesi es la d'abordar el problema de l'adquisició de forma 3D, des d'un punt de vista total, reportant un estat de l'art sobre escàners laser basats en triangulació, provant el funcionament i rendiment de diferents sistemes, i fent aportacions per millorar la precisió en la detecció del feix laser, especialment en condicions adverses, i solucionant el problema de la calibració a partir de mètodes geomètrics projectius.

Texture recognition under varying imaging geometries

La visió és probablement el nostre sentit més dominant a partir del qual derivem la majoria d'informació del món que ens envolta. A través de la visió podem percebre com són les coses, on són i com es mouen. En les imatges que percebem amb el nostre sistema de visió podem extreure'n característiques com el color, la textura i la forma, i gràcies a aquesta informació som capaços de reconèixer objectes fins i tot quan s'observen sota unes condicions totalment diferents. Per exemple, som capaços de distingir un mateix objecte si l'observem des de diferents punts de vista, distància, condicions d'il·luminació, etc. La Visió per Computador intenta emular el sistema de visió humà mitjançant un sistema de captura d'imatges, un ordinador, i un conjunt de programes. L'objectiu desitjat no és altre que desenvolupar un sistema que pugui entendre una imatge d'una manera similar com ho realitzaria una persona. Aquesta tesi es centra en l'anàlisi de la textura per tal de realitzar el reconeixement de superfícies. La motivació principal és resoldre el problema de la classificació de superfícies texturades quan han estat capturades sota diferents condicions, com ara distància de la càmera o direcció de la il·luminació. D'aquesta forma s'aconsegueix reduir els errors de classificació provocats per aquests canvis en les condicions de captura. En aquest treball es presenta detalladament un sistema de reconeixement de textures que ens permet classificar imatges de diferents superfícies capturades en diferents condicions. El sistema proposat es basa en un model 3D de la superfície (que inclou informació de color i forma) obtingut mitjançant la tècnica coneguda com a 4-Source Colour Photometric Stereo (CPS). Aquesta informació és utilitzada posteriorment per un mètode de predicció de textures amb l'objectiu de generar noves imatges 2D de les textures sota unes noves condicions. Aquestes imatges virtuals que es generen seran la base del nostre sistema de reconeixement, ja que seran utilitzades com a models de referència per al nostre classificador de textures. El sistema de reconeixement proposat combina les Matrius de Co-ocurrència per a l'extracció de característiques de textura, amb la utilització del Classificador del veí més proper. Aquest classificador ens permet al mateix temps aproximar la direcció d'il·luminació present en les imatges que s'utilitzen per testejar el sistema de reconeixement. És a dir, serem capaços de predir l'angle d'il·luminació sota el qual han estat capturades les imatges de test. Els resultats obtinguts en els diferents experiments que s'han realitzat demostren la viabilitat del sistema de predicció de textures, així com del sistema de reconeixement.