93 research outputs found

    Depth-Map Image Compression Based on Region and Contour Modeling

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    In this thesis, the problem of depth-map image compression is treated. The compilation of articles included in the thesis provides methodological contributions in the fields of lossless and lossy compression of depth-map images.The first group of methods addresses the lossless compression problem. The introduced methods are using the approach of representing the depth-map image in terms of regions and contours. In the depth-map image, a segmentation defines the regions, by grouping pixels having similar properties, and separates them using (region) contours. The depth-map image is encoded by the contours and the auxiliary information needed to reconstruct the depth values in each region.One way of encoding the contours is to describe them using two matrices of horizontal and vertical contour edges. The matrices are encoded using template context coding where each context tree is optimally pruned. In certain contexts, the contour edges are found deterministically using only the currently available information. Another way of encoding the contours is to describe them as a sequence of contour segments. Each such segment is defined by an anchor (starting) point and a string of contour edges, equivalent to a string of chain-code symbols. Here we propose efficient ways to select and encode the anchor points and to generate contour segments by using a contour crossing point analysis and by imposing rules that help in minimizing the number of anchor points.The regions are reconstructed at the decoder using predictive coding or the piecewise constant model representation. In the first approach, the large constant regions are found and one depth value is encoded for each such region. For the rest of the image, suitable regions are generated by constraining the local variation of the depth level from one pixel to another. The nonlinear predictors selected specifically for each region are combining the results of several linear predictors, each fitting optimally a subset of pixels belonging to the local neighborhood. In the second approach, the depth value of a given region is encoded using the depth values of the neighboring regions already encoded. The natural smoothness of the depth variation and the mutual exclusiveness of the values in neighboring regions are exploited to efficiently predict and encode the current region's depth value.The second group of methods is studying the lossy compression problem. In a first contribution, different segmentations are generated by varying the threshold for the depth local variability. A lossy depth-map image is obtained for each segmentation and is encoded based on predictive coding, quantization and context tree coding. In another contribution, the lossy versions of one image are created either by successively merging the constant regions of the original image, or by iteratively splitting the regions of a template image using horizontal or vertical line segments. Merging and splitting decisions are greedily taken, according to the best slope towards the next point in the rate-distortion curve. An entropy coding algorithm is used to encode each image.We propose also a progressive coding method for coding the sequence of lossy versions of a depth-map image. The bitstream is encoded so that any lossy version of the original image is generated, starting from a very low resolution up to lossless reconstruction. The partitions of the lossy versions into regions are assumed to be nested so that a higher resolution image is obtained by splitting some regions of a lower resolution image. A current image in the sequence is encoded using the a priori information from a previously encoded image: the anchor points are encoded relative to the already encoded contour points; the depth information of the newly resulting regions is recovered using the depth value of the parent region.As a final contribution, the dissertation includes a study of the parameterization of planar models. The quantized heights at three-pixel locations are used to compute the optimal plane for each region. The three-pixel locations are selected so that the distortion due to the approximation of the plane over the region is minimized. The planar model and the piecewise constant model are competing in the merging process, where the two regions to be merged are those ensuring the optimal slope in the rate-distortion curve

    Object-based video representations: shape compression and object segmentation

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    Object-based video representations are considered to be useful for easing the process of multimedia content production and enhancing user interactivity in multimedia productions. Object-based video presents several new technical challenges, however. Firstly, as with conventional video representations, compression of the video data is a requirement. For object-based representations, it is necessary to compress the shape of each video object as it moves in time. This amounts to the compression of moving binary images. This is achieved by the use of a technique called context-based arithmetic encoding. The technique is utilised by applying it to rectangular pixel blocks and as such it is consistent with the standard tools of video compression. The blockbased application also facilitates well the exploitation of temporal redundancy in the sequence of binary shapes. For the first time, context-based arithmetic encoding is used in conjunction with motion compensation to provide inter-frame compression. The method, described in this thesis, has been thoroughly tested throughout the MPEG-4 core experiment process and due to favourable results, it has been adopted as part of the MPEG-4 video standard. The second challenge lies in the acquisition of the video objects. Under normal conditions, a video sequence is captured as a sequence of frames and there is no inherent information about what objects are in the sequence, not to mention information relating to the shape of each object. Some means for segmenting semantic objects from general video sequences is required. For this purpose, several image analysis tools may be of help and in particular, it is believed that video object tracking algorithms will be important. A new tracking algorithm is developed based on piecewise polynomial motion representations and statistical estimation tools, e.g. the expectationmaximisation method and the minimum description length principle

    Algoritmos de compressão sem perdas para imagens de microarrays e alinhamento de genomas completos

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    Doutoramento em InformáticaNowadays, in the 21st century, the never-ending expansion of information is a major global concern. The pace at which storage and communication resources are evolving is not fast enough to compensate this tendency. In order to overcome this issue, sophisticated and efficient compression tools are required. The goal of compression is to represent information with as few bits as possible. There are two kinds of compression, lossy and lossless. In lossless compression, information loss is not tolerated so the decoded information is exactly the same as the encoded one. On the other hand, in lossy compression some loss is acceptable. In this work we focused on lossless methods. The goal of this thesis was to create lossless compression tools that can be used in two types of data. The first type is known in the literature as microarray images. These images have 16 bits per pixel and a high spatial resolution. The other data type is commonly called Whole Genome Alignments (WGA), in particularly applied to MAF files. Regarding the microarray images, we improved existing microarray-specific methods by using some pre-processing techniques (segmentation and bitplane reduction). Moreover, we also developed a compression method based on pixel values estimates and a mixture of finite-context models. Furthermore, an approach based on binary-tree decomposition was also considered. Two compression tools were developed to compress MAF files. The first one based on a mixture of finite-context models and arithmetic coding, where only the DNA bases and alignment gaps were considered. The second tool, designated as MAFCO, is a complete compression tool that can handle all the information that can be found in MAF files. MAFCO relies on several finite-context models and allows parallel compression/decompression of MAF files.Hoje em dia, no século XXI, a expansão interminável de informação é uma grande preocupação mundial. O ritmo ao qual os recursos de armazenamento e comunicação estão a evoluir não é suficientemente rápido para compensar esta tendência. De forma a ultrapassar esta situação, são necessárias ferramentas de compressão sofisticadas e eficientes. A compressão consiste em representar informação utilizando a menor quantidade de bits possível. Existem dois tipos de compressão, com e sem perdas. Na compressão sem perdas, a perda de informação não é tolerada, por isso a informação descodificada é exatamente a mesma que a informação que foi codificada. Por outro lado, na compressão com perdas alguma perda é aceitável. Neste trabalho, focámo-nos apenas em métodos de compressão sem perdas. O objetivo desta tese consistiu na criação de ferramentas de compressão sem perdas para dois tipos de dados. O primeiro tipo de dados é conhecido na literatura como imagens de microarrays. Estas imagens têm 16 bits por píxel e uma resolução espacial elevada. O outro tipo de dados é geralmente denominado como alinhamento de genomas completos, particularmente aplicado a ficheiros MAF. Relativamente às imagens de microarrays, melhorámos alguns métodos de compressão específicos utilizando algumas técnicas de pré-processamento (segmentação e redução de planos binários). Além disso, desenvolvemos também um método de compressão baseado em estimação dos valores dos pixéis e em misturas de modelos de contexto-finito. Foi também considerada, uma abordagem baseada em decomposição em árvore binária. Foram desenvolvidas duas ferramentas de compressão para ficheiros MAF. A primeira ferramenta, é baseada numa mistura de modelos de contexto-finito e codificação aritmética, onde apenas as bases de ADN e os símbolos de alinhamento foram considerados. A segunda, designada como MAFCO, é uma ferramenta de compressão completa que consegue lidar com todo o tipo de informação que pode ser encontrada nos ficheiros MAF. MAFCO baseia-se em vários modelos de contexto-finito e permite compressão/descompressão paralela de ficheiros MAF

    Codage de cartes de profondeur par deformation de courbes elastiques

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    In multiple-view video plus depth, depth maps can be represented by means of grayscale images and the corresponding temporal sequence can be thought as a standard grayscale video sequence. However depth maps have different properties from natural images: they present large areas of smooth surfaces separated by sharp edges. Arguably the most important information lies in object contours, as a consequence an interesting approach consists in performing a lossless coding of the contour map, possibly followed by a lossy coding of per-object depth values.In this context, we propose a new technique for the lossless coding of object contours, based on the elastic deformation of curves. A continuous evolution of elastic deformations between two reference contour curves can be modelled, and an elastically deformed version of the reference contours can be sent to the decoder with an extremely small coding cost and used as side information to improve the lossless coding of the actual contour. After the main discontinuities have been captured by the contour description, the depth field inside each region is rather smooth. We proposed and tested two different techniques for the coding of the depth field inside each region. The first technique performs the shape-adaptive wavelet transform followed by the shape-adaptive version of SPIHT. The second technique performs a prediction of the depth field from its subsampled version and the set of coded contours. It is generally recognized that a high quality view rendering at the receiver side is possible only by preserving the contour information, since distortions on edges during the encoding step would cause a sensible degradation on the synthesized view and on the 3D perception. We investigated this claim by conducting a subjective quality assessment test to compare an object-based technique and a hybrid block-based techniques for the coding of depth maps.Dans le format multiple-view video plus depth, les cartes de profondeur peuvent être représentées comme des images en niveaux de gris et la séquence temporelle correspondante peut être considérée comme une séquence vidéo standard en niveaux de gris. Cependant les cartes de profondeur ont des propriétés différentes des images naturelles: ils présentent de grandes surfaces lisses séparées par des arêtes vives. On peut dire que l'information la plus importante réside dans les contours de l'objet, en conséquence une approche intéressante consiste à effectuer un codage sans perte de la carte de contour, éventuellement suivie d'un codage lossy des valeurs de profondeur par-objet.Dans ce contexte, nous proposons une nouvelle technique pour le codage sans perte des contours de l'objet, basée sur la déformation élastique des courbes. Une évolution continue des déformations élastiques peut être modélisée entre deux courbes de référence, et une version du contour déformée élastiquement peut être envoyé au décodeur avec un coût de codage très faible et utilisé comme information latérale pour améliorer le codage sans perte du contour réel. Après que les principales discontinuités ont été capturés par la description du contour, la profondeur à l'intérieur de chaque région est assez lisse. Nous avons proposé et testé deux techniques différentes pour le codage du champ de profondeur à l'intérieur de chaque région. La première technique utilise la version adaptative à la forme de la transformation en ondelette, suivie par la version adaptative à la forme de SPIHT.La seconde technique effectue une prédiction du champ de profondeur à partir de sa version sous-échantillonnée et l'ensemble des contours codés. Il est généralement reconnu qu'un rendu de haute qualité au récepteur pour un nouveau point de vue est possible que avec la préservation de l'information de contour, car des distorsions sur les bords lors de l'étape de codage entraînerait une dégradation évidente sur la vue synthétisée et sur la perception 3D. Nous avons étudié cette affirmation en effectuant un test d'évaluation de la qualité perçue en comparant, pour le codage des cartes de profondeur, une technique basée sur la compression d'objects et une techniques de codage vidéo hybride à blocs

    Novi algoritam za kompresiju seizmičkih podataka velike amplitudske rezolucije

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    Renewable sources cannot meet energy demand of a growing global market. Therefore, it is expected that oil & gas will remain a substantial sources of energy in a coming years. To find a new oil & gas deposits that would satisfy growing global energy demands, significant efforts are constantly involved in finding ways to increase efficiency of a seismic surveys. It is commonly considered that, in an initial phase of exploration and production of a new fields, high-resolution and high-quality images of the subsurface are of the great importance. As one part in the seismic data processing chain, efficient managing and delivering of a large data sets, that are vastly produced by the industry during seismic surveys, becomes extremely important in order to facilitate further seismic data processing and interpretation. In this respect, efficiency to a large extent relies on the efficiency of the compression scheme, which is often required to enable faster transfer and access to data, as well as efficient data storage. Motivated by the superior performance of High Efficiency Video Coding (HEVC), and driven by the rapid growth in data volume produced by seismic surveys, this work explores a 32 bits per pixel (b/p) extension of the HEVC codec for compression of seismic data. It is proposed to reassemble seismic slices in a format that corresponds to video signal and benefit from the coding gain achieved by HEVC inter mode, besides the possible advantages of the (still image) HEVC intra mode. To this end, this work modifies almost all components of the original HEVC codec to cater for high bit-depth coding of seismic data: Lagrange multiplier used in optimization of the coding parameters has been adapted to the new data statistics, core transform and quantization have been reimplemented to handle the increased bit-depth range, and modified adaptive binary arithmetic coder has been employed for efficient entropy coding. In addition, optimized block selection, reduced intra prediction modes, and flexible motion estimation are tested to adapt to the structure of seismic data. Even though the new codec after implementation of the proposed modifications goes beyond the standardized HEVC, it still maintains a generic HEVC structure, and it is developed under the general HEVC framework. There is no similar work in the field of the seismic data compression that uses the HEVC as a base codec setting. Thus, a specific codec design has been tailored which, when compared to the JPEG-XR and commercial wavelet-based codec, significantly improves the peak-signal-tonoise- ratio (PSNR) vs. compression ratio performance for 32 b/p seismic data. Depending on a proposed configurations, PSNR gain goes from 3.39 dB up to 9.48 dB. Also, relying on the specific characteristics of seismic data, an optimized encoder is proposed in this work. It reduces encoding time by 67.17% for All-I configuration on trace image dataset, and 67.39% for All-I, 97.96% for P2-configuration and 98.64% for B-configuration on 3D wavefield dataset, with negligible coding performance losses. As a side contribution of this work, HEVC is analyzed within all of its functional units, so that the presented work itself can serve as a specific overview of methods incorporated into the standard

    The Fifth NASA Symposium on VLSI Design

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    The fifth annual NASA Symposium on VLSI Design had 13 sessions including Radiation Effects, Architectures, Mixed Signal, Design Techniques, Fault Testing, Synthesis, Signal Processing, and other Featured Presentations. The symposium provides insights into developments in VLSI and digital systems which can be used to increase data systems performance. The presentations share insights into next generation advances that will serve as a basis for future VLSI design

    MedLAN: Compact mobile computing system for wireless information access in emergency hospital wards

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    This thesis was submitted for the degree of Doctor of Philosophy and awarded by Brunel University.As the need for faster, safer and more efficient healthcare delivery increases, medical consultants seek new ways of implementing a high quality telemedical system, using innovative technology. Until today, teleconsultation (the most common application of Telemedicine) was performed by transferring the patient from the Accidents and Emergency ward, to a specially equipped room, or by moving large and heavy machinery to the place where the patient resided. Both these solutions were unpractical, uneconomical and potentially dangerous. At the same time wireless networks became increasingly useful in point-of-care areas such as hospitals, because of their ease of use, low cost of installation and increased flexibility. This thesis presents an integrated system called MedLAN dedicated for use inside the A&E hospital wards. Its purpose is to wirelessly support high-quality live video, audio, high-resolution still images and networks support from anywhere there is WLAN coverage. It is capable of transmitting all of the above to a consultant residing either inside or outside the hospital, or even to an external place, thorough the use of the Internet. To implement that, it makes use of the existing IEEE 802.11b wireless technology. Initially, this thesis demonstrates that for specific scenarios (such as when using WLANs), DICOM specifications should be adjusted to accommodate for the reduced WLAN bandwidth. Near lossless compression has been used to send still images through the WLANs and the results have been evaluated by a number of consultants to decide whether they retain their diagnostic value. The thesis further suggests improvements on the existing 802.11b protocol. In particular, as the typical hospital environment suffers from heavy RF reflections, it suggests that an alternative method of modulation (OFDM) can be embedded in the 802.11b hardware to reduce the multipath effect, increase the throughput and thus the video quality sent by the MedLAN system. Finally, realising that the trust between a patient and a doctor is fundamental this thesis proposes a series of simple actions aiming at securing the MedLAN system. Additionally, a concrete security system is suggested, that encapsulates the existing WEP security protocol, over IPSec

    Algorithms for the reconstruction, analysis, repairing and enhancement of 3D urban models from multiple data sources

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    Over the last few years, there has been a notorious growth in the field of digitization of 3D buildings and urban environments. The substantial improvement of both scanning hardware and reconstruction algorithms has led to the development of representations of buildings and cities that can be remotely transmitted and inspected in real-time. Among the applications that implement these technologies are several GPS navigators and virtual globes such as Google Earth or the tools provided by the Institut Cartogràfic i Geològic de Catalunya. In particular, in this thesis, we conceptualize cities as a collection of individual buildings. Hence, we focus on the individual processing of one structure at a time, rather than on the larger-scale processing of urban environments. Nowadays, there is a wide diversity of digitization technologies, and the choice of the appropriate one is key for each particular application. Roughly, these techniques can be grouped around three main families: - Time-of-flight (terrestrial and aerial LiDAR). - Photogrammetry (street-level, satellite, and aerial imagery). - Human-edited vector data (cadastre and other map sources). Each of these has its advantages in terms of covered area, data quality, economic cost, and processing effort. Plane and car-mounted LiDAR devices are optimal for sweeping huge areas, but acquiring and calibrating such devices is not a trivial task. Moreover, the capturing process is done by scan lines, which need to be registered using GPS and inertial data. As an alternative, terrestrial LiDAR devices are more accessible but cover smaller areas, and their sampling strategy usually produces massive point clouds with over-represented plain regions. A more inexpensive option is street-level imagery. A dense set of images captured with a commodity camera can be fed to state-of-the-art multi-view stereo algorithms to produce realistic-enough reconstructions. One other advantage of this approach is capturing high-quality color data, whereas the geometric information is usually lacking. In this thesis, we analyze in-depth some of the shortcomings of these data-acquisition methods and propose new ways to overcome them. Mainly, we focus on the technologies that allow high-quality digitization of individual buildings. These are terrestrial LiDAR for geometric information and street-level imagery for color information. Our main goal is the processing and completion of detailed 3D urban representations. For this, we will work with multiple data sources and combine them when possible to produce models that can be inspected in real-time. Our research has focused on the following contributions: - Effective and feature-preserving simplification of massive point clouds. - Developing normal estimation algorithms explicitly designed for LiDAR data. - Low-stretch panoramic representation for point clouds. - Semantic analysis of street-level imagery for improved multi-view stereo reconstruction. - Color improvement through heuristic techniques and the registration of LiDAR and imagery data. - Efficient and faithful visualization of massive point clouds using image-based techniques.Durant els darrers anys, hi ha hagut un creixement notori en el camp de la digitalització d'edificis en 3D i entorns urbans. La millora substancial tant del maquinari d'escaneig com dels algorismes de reconstrucció ha portat al desenvolupament de representacions d'edificis i ciutats que es poden transmetre i inspeccionar remotament en temps real. Entre les aplicacions que implementen aquestes tecnologies hi ha diversos navegadors GPS i globus virtuals com Google Earth o les eines proporcionades per l'Institut Cartogràfic i Geològic de Catalunya. En particular, en aquesta tesi, conceptualitzem les ciutats com una col·lecció d'edificis individuals. Per tant, ens centrem en el processament individual d'una estructura a la vegada, en lloc del processament a gran escala d'entorns urbans. Avui en dia, hi ha una àmplia diversitat de tecnologies de digitalització i la selecció de l'adequada és clau per a cada aplicació particular. Aproximadament, aquestes tècniques es poden agrupar en tres famílies principals: - Temps de vol (LiDAR terrestre i aeri). - Fotogrametria (imatges a escala de carrer, de satèl·lit i aèries). - Dades vectorials editades per humans (cadastre i altres fonts de mapes). Cadascun d'ells presenta els seus avantatges en termes d'àrea coberta, qualitat de les dades, cost econòmic i esforç de processament. Els dispositius LiDAR muntats en avió i en cotxe són òptims per escombrar àrees enormes, però adquirir i calibrar aquests dispositius no és una tasca trivial. A més, el procés de captura es realitza mitjançant línies d'escaneig, que cal registrar mitjançant GPS i dades inercials. Com a alternativa, els dispositius terrestres de LiDAR són més accessibles, però cobreixen àrees més petites, i la seva estratègia de mostreig sol produir núvols de punts massius amb regions planes sobrerepresentades. Una opció més barata són les imatges a escala de carrer. Es pot fer servir un conjunt dens d'imatges capturades amb una càmera de qualitat mitjana per obtenir reconstruccions prou realistes mitjançant algorismes estèreo d'última generació per produir. Un altre avantatge d'aquest mètode és la captura de dades de color d'alta qualitat. Tanmateix, la informació geomètrica resultant sol ser de baixa qualitat. En aquesta tesi, analitzem en profunditat algunes de les mancances d'aquests mètodes d'adquisició de dades i proposem noves maneres de superar-les. Principalment, ens centrem en les tecnologies que permeten una digitalització d'alta qualitat d'edificis individuals. Es tracta de LiDAR terrestre per obtenir informació geomètrica i imatges a escala de carrer per obtenir informació sobre colors. El nostre objectiu principal és el processament i la millora de representacions urbanes 3D amb molt detall. Per a això, treballarem amb diverses fonts de dades i les combinarem quan sigui possible per produir models que es puguin inspeccionar en temps real. La nostra investigació s'ha centrat en les següents contribucions: - Simplificació eficaç de núvols de punts massius, preservant detalls d'alta resolució. - Desenvolupament d'algoritmes d'estimació normal dissenyats explícitament per a dades LiDAR. - Representació panoràmica de baixa distorsió per a núvols de punts. - Anàlisi semàntica d'imatges a escala de carrer per millorar la reconstrucció estèreo de façanes. - Millora del color mitjançant tècniques heurístiques i el registre de dades LiDAR i imatge. - Visualització eficient i fidel de núvols de punts massius mitjançant tècniques basades en imatges

    MedLAN : compact mobile computing system for wireless information access in emergency hospital wards

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    As the need for faster, safer and more efficient healthcare delivery increases, medical consultants seek new ways of implementing a high quality telemedical system, using innovative technology. Until today, teleconsultation (the most common application of Telemedicine) was performed by transferring the patient from the Accidents and Emergency ward, to a specially equipped room, or by moving large and heavy machinery to the place where the patient resided. Both these solutions were unpractical, uneconomical and potentially dangerous. At the same time wireless networks became increasingly useful in point-of-care areas such as hospitals, because of their ease of use, low cost of installation and increased flexibility. This thesis presents an integrated system called MedLAN dedicated for use inside the A;E hospital wards. Its purpose is to wirelessly support high-quality live video, audio, high-resolution still images and networks support from anywhere there is WLAN coverage. It is capable of transmitting all of the above to a consultant residing either inside or outside the hospital, or even to an external place, thorough the use of the Internet. To implement that, it makes use of the existing IEEE 802.11b wireless technology. Initially, this thesis demonstrates that for specific scenarios (such as when using WLANs), DICOM specifications should be adjusted to accommodate for the reduced WLAN bandwidth. Near lossless compression has been used to send still images through the WLANs and the results have been evaluated by a number of consultants to decide whether they retain their diagnostic value. The thesis further suggests improvements on the existing 802.11b protocol. In particular, as the typical hospital environment suffers from heavy RF reflections, it suggests that an alternative method of modulation (OFDM) can be embedded in the 802.11b hardware to reduce the multipath effect, increase the throughput and thus the video quality sent by the MedLAN system. Finally, realising that the trust between a patient and a doctor is fundamental this thesis proposes a series of simple actions aiming at securing the MedLAN system. Additionally, a concrete security system is suggested, that encapsulates the existing WEP security protocol, over IPSec.EThOS - Electronic Theses Online ServiceGBUnited Kingdo

    Modelado jerárquico de objetos 3D con superficies de subdivisión

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    Las SSs (Superficies de Subdivisión) son un potente paradigma de modelado de objetos 3D (tridimensionales) que establece un puente entre los dos enfoques tradicionales a la aproximación de superficies, basados en mallas poligonales y de parches alabeados, que conllevan problemas uno y otro. Los esquemas de subdivisión permiten definir una superficie suave (a tramos), como las más frecuentes en la práctica, como el límite de un proceso recursivo de refinamiento de una malla de control burda, que puede ser descrita muy compactamente. Además, la recursividad inherente a las SSs establece naturalmente una relación de anidamiento piramidal entre las mallas / NDs (Niveles de Detalle) generadas/os sucesivamente, por lo que las SSs se prestan extraordinariamente al AMRO (Análisis Multiresolución mediante Ondículas) de superficies, que tiene aplicaciones prácticas inmediatas e interesantísimas, como la codificación y la edición jerárquicas de modelos 3D. Empezamos describiendo los vínculos entre las tres áreas que han servido de base a nuestro trabajo (SSs, extracción automática de NDs y AMRO) para explicar como encajan estas tres piezas del puzzle del modelado jerárquico de objetos de 3D con SSs. El AMRO consiste en descomponer una función en una versión burda suya y un conjunto de refinamientos aditivos anidados jerárquicamente llamados "coeficientes ondiculares". La teoría clásica de ondículas estudia las señales clásicas nD: las definidas sobre dominios paramétricos homeomorfos a R" o (0,1)n como el audio (n=1), las imágenes (n=2) o el vídeo (n=3). En topologías menos triviales, como las variedades 2D) (superficies en el espacio 3D), el AMRO no es tan obvio, pero sigue siendo posible si se enfoca desde la perspectiva de las SSs. Basta con partir de una malla burda que aproxime a un bajo ND la superficie considerada, subdividirla recursivamente y, al hacerlo, ir añadiendo los coeficientes ondiculares, que son los detalles 3D necesarios para obtener aproximaciones más y más finas a la superficie original. Pasamos después a las aplicaciones prácticas que constituyen nuestros principal desarrollo original y, en particular, presentamos una técnica de codificación jerárquica de modelos 3D basada en SSs, que actúa sobre los detalles 3D mencionados: los expresa en un referencial normal loscal; los organiza según una estructura jerárquica basada en facetas; los cuantifica dedicando menos bits a sus componentes tangenciales, menos energéticas, y los "escalariza"; y los codifica dinalmente gracias a una técnica similar al SPIHT (Set Partitioning In Hierarchical Tress) de Said y Pearlman. El resultado es un código completamente embebido y al menos dos veces más compacto, para superficies mayormente suaves, que los obtenidos con técnicas de codificación progresiva de mallas 3D publicadas previamente, en las que además los NDs no están anidados piramidalmente. Finalmente, describimos varios métodos auxiliares que hemos desarrollado, mejorando técnicas previas y creando otras propias, ya que una solución completa al modelado de objetos 3D con SSs requiere resolver otros dos problemas. El primero es la extracción de una malla base (triangular, en nuestro caso) de la superficie original, habitualmente dada por una malla triangular fina con conectividad arbitraria. El segundo es la generación de un remallado recursivo con conectividad de subdivisión de la malla original/objetivo mediante un refinamiento recursivo de la malla base, calculando así los detalles 3D necesarios para corregir las posiciones predichas por la subdivisión para nuevos vértices
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