Video Data Compression by Progressive Iterative Approximation

In the present paper, the B-spline curve is used for reducing the entropy of video data. We consider the color or luminance variations of a spatial position in a series of frames as input data points in Euclidean space R or R3. The progressive and iterative approximation (PIA) method is a direct and intuitive way of generating curve series of high and higher fitting accuracy. The video data points are approximated using progressive and iterative approximation for least square (LSPIA) fitting. The Lossless video data compression is done through storing the B-spline curve control points (CPs) and the difference between fitted and original video data. The proposed method is applied to two classes of synthetically produced and naturally recorded video sequences and makes a reduction in the entropy of both. However, this reduction is higher for syntactically created than those naturally produced. The comparative analysis of experiments on a variety of video sequences suggests that the entropy of output video data is much less than that of input video data

Preconditioned geometric iterative methods for cubic B-spline interpolation curves

The geometric iterative method (GIM) is widely used in data interpolation/fitting, but its slow convergence affects the computational efficiency. Recently, much work was done to guarantee the acceleration of GIM in the literature. In this work, we aim to further accelerate the rate of convergence by introducing a preconditioning technique. After constructing the preconditioner, we preprocess the progressive iterative approximation (PIA) and its variants, called the preconditioned GIMs. We show that the proposed preconditioned GIMs converge and the extra computation cost brought by the preconditioning technique is negligible. Several numerical experiments are given to demonstrate that our preconditioner can accelerate the convergence rate of PIA and its variants

An Iterative Method Based on the Marginalized Particle Filter for Nonlinear B-Spline Data Approximation and Trajectory Optimization

The B-spline function representation is commonly used for data approximation and trajectory definition, but filter-based methods for nonlinear weighted least squares (NWLS) approximation are restricted to a bounded definition range. We present an algorithm termed nonlinear recursive B-spline approximation (NRBA) for an iterative NWLS approximation of an unbounded set of data points by a B-spline function. NRBA is based on a marginalized particle filter (MPF), in which a Kalman filter (KF) solves the linear subproblem optimally while a particle filter (PF) deals with nonlinear approximation goals. NRBA can adjust the bounded definition range of the approximating B-spline function during run-time such that, regardless of the initially chosen definition range, all data points can be processed. In numerical experiments, NRBA achieves approximation results close to those of the Levenberg–Marquardt algorithm. An NWLS approximation problem is a nonlinear optimization problem. The direct trajectory optimization approach also leads to a nonlinear problem. The computational effort of most solution methods grows exponentially with the trajectory length. We demonstrate how NRBA can be applied for a multiobjective trajectory optimization for a battery electric vehicle in order to determine an energy-efficient velocity trajectory. With NRBA, the effort increases only linearly with the processed data points and the trajectory length

FITTING A PARAMETRIC MODEL TO A CLOUD OF POINTS VIA OPTIMIZATION METHODS

Computer Aided Design (CAD) is a powerful tool for designing parametric geometry. However, many CAD models of current configurations are constructed in previous generations of CAD systems, which represent the configuration simply as a collection of surfaces instead of as a parametrized solid model. But since many modern analysis techniques take advantage of a parametrization, one often has to re-engineer the configuration into a parametric model. The objective here is to generate an efficient, robust, and accurate method for fitting parametric models to a cloud of points. The process uses a gradient-based optimization technique, which is applied to the whole cloud, without the need to segment or classify the points in the cloud a priori. First, for the points associated with any component, a variant of the Levenberg-Marquardt gradient-based optimization method (ILM) is used to find the set of model parameters that minimizes the least-square errors between the model and the points. The efficiency of the ILM algorithm is greatly improved through the use of analytic geometric sensitivities and sparse matrix techniques. Second, for cases in which one does not know a priori the correspondences between points in the cloud and the geometry model\u27s components, an efficient initialization and classification algorithm is introduced. While this technique works well once the configuration is close enough, it occasionally fails when the initial parametrized configuration is too far from the cloud of points. To circumvent this problem, the objective function is modified, which has yielded good results for all cases tested. This technique is applied to a series of increasingly complex configurations. The final configuration represents a full transport aircraft configuration, with a wing, fuselage, empennage, and engines. Although only applied to aerospace applications, the technique is general enough to be applicable in any domain for which basic parametrized models are available

Verbesserung der Prozesskette zur Herstellung mikrostrukturierter Linsen für automobile Scheinwerfer

Diese Arbeit befasst sich mit der Auslegung, Herstellung und Qualitätskontrolle mikrostrukturierter Linsen für Scheinwerfer-Projektionssysteme. Es wird ein Algorithmus beschrieben, um glatte Linsenflächen zu strukturieren. Die Datenweitergabe zur Herstellung von Stahlwerkzeugen für den Spritzgussprozess werden erläutert. Um die Werkzeuge zu qualifizieren wird ein „Reverse Engineering“-Prozess vorgestellt

Razvoj izogeometrijske metode konačnih elemenata i njena primena u strukturnoj analizi nosećih struktura transportnih mašina

The subject of doctoral dissertation is the isogeometric structural analysis. The isogeometric analysis represents a special approach in the finite element method (FEM) which aims at closing the gap between the actual geometry of modeled structures and the geometry generated upon the finite element discretization. In the isogeometric FE analysis, NURBS (non-uniform rational basis spline) functions usually form the basis for the definition of both the geometric models and interpolation functions of the FE models. Regardless of the mesh density, the geometry is exactly described in the FE model. The aim of the dissertation is the systematization of procedures and methods necessary for isogeometric analysis by creating general mathematical forms and program procedures. Isogeometric FE models are defined by using the NURBS and T-spline basis functions. An isogeometric solid element is formulated as well as a Kirchhoff-Love shell element with the NURBS basic functions. The method of modeling complex structures formed from several surfaces by using Kirchhoff-Love elements is presented. The results of the performed isogeometric analyses were compared with analytical results, the results yielded by the classical finite element method and experimental results. The developed isogeometric models were tested in the field of linear static, modal and explicit dynamic analyses. A particular part of the dissertation is dedicated to the benefits of isogeometric analysis in the field of structural analysis of transport machines complex structures. The conclusions related to advantages and disadvantages of NURBS ant Tsplines basis functions in the finite element method are presented through examples and tests done in this dissertation. The directions of further research are proposed

Modelado geométrico personalizado de la córnea humana y su aplicación a la detección de ectasias corneales

[SPA] La córnea es una estructura biológica viva cuya arquitectura presenta una morfología singular, ya sea en un estado natural o patológico. Esta singularidad ha sido caracterizada a lo largo de toda la historia en el campo de la oftalmología y la óptica a través de la generación de modelos genéricos o de modelos personalizados de la córnea humana. Hoy en día, el desarrollo de nuevas tecnologías permite caracterizar la morfología corneal a partir de los denominados equipos topográficos; estos equipos aportan una caracterización personalizada de índole cualitativa y cuantitativa al médico oftalmólogo. Sin embargo, los sistemas de diagnóstico de las patologías corneales están basados en unos índices de valoración de la irregularidad de las superficies corneales que son calculados a partir de algoritmos específicos internos para cada topógrafo corneal y de los cuales se desconoce su programación. Por este motivo en esta tesis doctoral se establece un nuevo procedimiento fundamentado en la geometría computacional para obtener un modelo sólido 3D personalizado in vivo de la córnea humana utilizando herramientas de Diseño Geométrico Asistido por Ordenador. Este modelo virtual reconstruye fidedignamente las superficies de la cara anterior y posterior de la córnea, a partir de unos datos aportados por los topógrafos corneales denominados datos en bruto (sin ningún trato mediante algoritmo) tanto para los ojos de pacientes sanos como para los ojos de pacientes diagnosticados con la patología ectásica más común, el queratocono. A partir del nuevo modelo sólido obtenido, se definen unos índices de caracterización de la morfología corneal basados en variables geométricas, los cuales pueden ser utilizados como unos nuevos índices de diagnóstico de la patología ectásica objeto de estudio debido a que presentan una elevada sensibilidad y especificidad para su diagnóstico. [ENG] The cornea is a living biological structure whose architecture has a unique morphology, either in a natural or diseased condition. This uniqueness has been characterized throughout all history in the field of ophthalmology and optics through the generation of generic or customized models of human cornea. Today, the development of new technologies leads to characterize the corneal morphology from the so‐called topographic devices; these devices provide a personalized qualitative and quantitative characterization of its nature for the ophthalmologist. However corneal pathological diagnosis systems are based on indicators of the irregularity of the corneal surfaces, which are calculated from specific internal algorithms for each corneal topographer and whose programming is unknown. For that reason, this doctoral thesis establishes a new procedure based on computational geometry to obtain a 3D solid model, personalized and in vivo of the human cornea by using Computer Aided Geometrical Design tools. This virtual model represents accurately both the anterior and posterior corneal surfaces from a set of raw data (without any algorithm treatment) provided by the corneal topographers for both healthy corneas and corneas with the most common ectasic disease, the keratoconus. The new solid model obtained is later analyzed to define a set of indices that enable the characterization of the corneal morphology and that are based on geometric variables. These indices can be used as new indicators for the diagnosis of the keratoconus disease due to their high sensibility and specificity.[ENG] The cornea is a living biological structure whose architecture has a unique morphology, either in a natural or diseased condition. This uniqueness has been characterized throughout all history in the field of ophthalmology and optics through the generation of generic or customized models of human cornea. Today, the development of new technologies leads to characterize the corneal morphology from the so‐called topographic devices; these devices provide a personalized qualitative and quantitative characterization of its nature for the ophthalmologist. However corneal pathological diagnosis systems are based on indicators of the irregularity of the corneal surfaces, which are calculated from specific internal algorithms for each corneal topographer and whose programming is unknown. For that reason, this doctoral thesis establishes a new procedure based on computational geometry to obtain a 3D solid model, personalized and in vivo of the human cornea by using Computer Aided Geometrical Design tools. This virtual model represents accurately both the anterior and posterior corneal surfaces from a set of raw data (without any algorithm treatment) provided by the corneal topographers for both healthy corneas and corneas with the most common ectasic disease, the keratoconus. The new solid model obtained is later analyzed to define a set of indices that enable the characterization of the corneal morphology and that are based on geometric variables. These indices can be used as new indicators for the diagnosis of the keratoconus disease due to their high sensibility and specificity.Esta tesis se ha realizado en parte gracias a la financiación del proyecto del Fondo Europeo de Desarrollo Regional (FEDER) y del Ministerio Español de Economía y Competitividad, Instituto Carlos III, Red Temática de Investigación Cooperativa en Salud (RETICS) «Prevención, detección precoz y tratamiento de la patología ocular prevalente, degenerativa y crónica». Subprograma «dioptrio ocular y patologías frecuentes» (RD12/0034/0007).Escuela Internacional de DoctoradoUniversidad Politécnica de CartagenaPrograma Oficial de Doctorado en Tecnologías Industriale