Snapshot-Based Methods and Algorithms

An increasing complexity of models used to predict real-world systems leads to the need for algorithms to replace complex models with far simpler ones, while preserving the accuracy of the predictions. This two-volume handbook covers methods as well as applications. This second volume focuses on applications in engineering, biomedical engineering, computational physics and computer science

Overview of database projects

The use of entity and object oriented data modeling techniques for managing Computer Aided Design (CAD) is explored

Model Order Reduction

An increasing complexity of models used to predict real-world systems leads to the need for algorithms to replace complex models with far simpler ones, while preserving the accuracy of the predictions. This two-volume handbook covers methods as well as applications. This second volume focuses on applications in engineering, biomedical engineering, computational physics and computer science

Applied Mathematics and Computational Physics

As faster and more efficient numerical algorithms become available, the understanding of the physics and the mathematical foundation behind these new methods will play an increasingly important role. This Special Issue provides a platform for researchers from both academia and industry to present their novel computational methods that have engineering and physics applications

Multi-scale active shape description in medical imaging

Shape description in medical imaging has become an increasingly important research field in recent years. Fast and high-resolution image acquisition methods like Magnetic Resonance (MR) imaging produce very detailed cross-sectional images of the human body - shape description is then a post-processing operation which abstracts quantitative descriptions of anatomically relevant object shapes. This task is usually performed by clinicians and other experts by first segmenting the shapes of interest, and then making volumetric and other quantitative measurements. High demand on expert time and inter- and intra-observer variability impose a clinical need of automating this process. Furthermore, recent studies in clinical neurology on the correspondence between disease status and degree of shape deformations necessitate the use of more sophisticated, higher-level shape description techniques. In this work a new hierarchical tool for shape description has been developed, combining two recently developed and powerful techniques in image processing: differential invariants in scale-space, and active contour models. This tool enables quantitative and qualitative shape studies at multiple levels of image detail, exploring the extra image scale degree of freedom. Using scale-space continuity, the global object shape can be detected at a coarse level of image detail, and finer shape characteristics can be found at higher levels of detail or scales. New methods for active shape evolution and focusing have been developed for the extraction of shapes at a large set of scales using an active contour model whose energy function is regularized with respect to scale and geometric differential image invariants. The resulting set of shapes is formulated as a multiscale shape stack which is analysed and described for each scale level with a large set of shape descriptors to obtain and analyse shape changes across scales. This shape stack leads naturally to several questions in regard to variable sampling and appropriate levels of detail to investigate an image. The relationship between active contour sampling precision and scale-space is addressed. After a thorough review of modem shape description, multi-scale image processing and active contour model techniques, the novel framework for multi-scale active shape description is presented and tested on synthetic images and medical images. An interesting result is the recovery of the fractal dimension of a known fractal boundary using this framework. Medical applications addressed are grey-matter deformations occurring for patients with epilepsy, spinal cord atrophy for patients with Multiple Sclerosis, and cortical impairment for neonates. Extensions to non-linear scale-spaces, comparisons to binary curve and curvature evolution schemes as well as other hierarchical shape descriptors are discussed

Towards an efficient haptic rendering using data-driven modeling

This thesis focuses on the optimisation of haptic rendering of interactions with deformable models. The research demonstrated that data-driven techniques can produce a real-time, accurate and complex simulation experience. Applications include, but not limited to, virtual training, rapid prototyping, virtual presence, and entertainment

Morphological Analysis for Object Recognition, Matching, and Applications

This thesis deals with the detection and classifcation of objects in visual images and with the analysis of shape changes between object instances. Whereas the task of object recognition focuses on learning models which describe common properties between instances of a specific category, the analysis of the specific differences between instances is also relevant to understand the objects and the categories themselves. This research is governed by the idea that important properties for the automatic perception and understanding of objects are transmitted through their geometry or shape. Therefore, models for object recognition and shape matching are devised which exploit the geometry and properties of the objects, using as little user supervision as possible. In order to learn object models for detection in a reliable manner, suitable object representations are required. The key idea in this work is to use a richer representation of the object shape within the object model in order to increase the description power and thus the performance of the whole system. For this purpose, we first investigate the integration of curvature information of shapes in the object model which is learned. Since natural objects intrinsically exhibit curved boundaries, an object is better described if this shape cue is integrated. This subject extends the widely used object representation based on gradient orientation histograms by incorporating a robust histogram-based description of curvature. We show that integrating this information substantially improves detection results over descriptors that solely rely upon histograms of orientated gradients. The impact of using richer shape representations for object recognition is further investigated through a novel method which goes beyond traditional bounding-box representations for objects. Visual recognition requires learning object models from training data. Commonly, training samples are annotated by marking only the bounding-box of objects since this appears to be the best trade-off between labeling information and effectiveness. However, objects are typically not box-shaped. Thus, the usual parametrization of objects using a bounding box seems inappropriate since such a box contains a significant amount of background clutter. Therefore, the presented approach learns object models for detection while simultaneously learning to segregate objects from clutter and extracting their overall shape, without however, requiring manual segmentation of the training samples. Shape equivalence is another interesting property related to shape. It refers to the ability of perceiving two distinct objects as having the same or similar shape. This thesis also explores the usage of this ability to detect objects in unsupervised scenarios, that is where no annotation of training data is available for learning a statistical model. For this purpose, a dataset of historical Chinese cartoons drawn during the Cultural Revolution and immediately thereafter is analyzed. Relevant objects in this dataset are emphasized through annuli of light rays. The idea of our method is to consider the different annuli as shape equivalent objects, that is, as objects sharing the same shape and devise a method to detect them. Thereafter, it is possible to indirectly infer the position, size and scale of the emphasized objects using the annuli detections. Not only commonalities among objects, but also the specific differences between them are perceived by a visual system. These differences can be understood through the analysis of how objects and their shape change. For this reason, this thesis also develops a novel methodology for analyzing the shape deformation between a single pair of images under missing correspondences. The key observation is that objects cannot deform arbitrarily, but rather the deformation itself follows the geometry and constraints imposed by the object itself. We describe the overall complex object deformation using a piecewise linear model. Thereby, we are able to identify each of the parts in the shape which share the same deformation. Thus, we are able to understand how an object and its parts were transformed. A remarkable property of the algorithm is the ability to automatically estimate the model complexity according to the overall complexity of the shape deformation. Specifically, the introduced methodology is used to analyze the deformation between original instances and reproductions of artworks. The nature of the analyzed alterations ranges from deliberate modifications by the artist to geometrical errors accumulated during the reproduction process of the image. The usage of this method within this application shows how productive the interaction between computer vision and the field of the humanities is. The goal is not to supplant human expertise, but to enhance and deepen connoisseurship about a given problem

General Dynamic Surface Reconstruction: Application to the 3D Segmentation of the Left Ventricle

Aquesta tesi descriu la nostra contribució a la reconstrucció tridimensional de les superfícies interna i externa del ventricle esquerre humà. La reconstrucció és un primer procés dins d'una aplicació global de Realitat Virtual dissenyada com una important eina de diagnòstic per a hospitals. L'aplicació parteix de la reconstrucció de les superfícies i proveeix a l'expert de manipulació interactiva del model en temps real, a més de càlculs de volums i de altres paràmetres d'interès. El procés de recuperació de les superfícies es caracteritza per la seva velocitat de convergència, la suavitat a les malles finals i la precisió respecte de les dades recuperades. Donat que el diagnòstic de patologies cardíaques requereix d'experiència, temps i molt coneixement professional, la simulació és un procés clau que millora la eficiència.Els nostres algorismes i implementacions han estat aplicats a dades sintètiques i reals amb diferències relatives a la quantitat de dades inexistents, casuístiques presents a casos patològics i anormals. Els conjunts de dades inclouen adquisicions d'instants concrets i de cicles cardíacs complets. La bondat del sistema de reconstrucció ha estat avaluada mitjançant paràmetres mèdics per a poder comparar els nostres resultats finals amb aquells derivats a partir de programari típic utilitzat pels professionals de la medicina.A més de l'aplicació directa al diagnòstic mèdic, la nostra metodologia permet reconstruccions de tipus genèric en el camp dels Gràfics 3D per ordinador. Les nostres reconstruccions permeten generar models tridimensionals amb un baix cost en quant a la interacció manual necessària i a la càrrega computacional associada. Altrament, el nostre mètode pot entendre's com un robust algorisme de triangularització que construeix superfícies partint de núvols de punts que poden obtenir-se d'escàners làser o sensors magnètics, per exemple.Esta tesis describe nuestra contribución a la reconstrucción tridimensional de las superficies interna y externa del ventrículo izquierdo humano. La reconstrucción es un primer proceso que forma parte de una aplicación global de Realidad Virtual diseñada como una importante herramienta de diagnóstico para hospitales. La aplicación parte de la reconstrucción de las superficies y provee al experto de manipulación interactiva del modelo en tiempo real, además de cálculos de volúmenes y de otros parámetros de interés. El proceso de recuperación de las superficies se caracteriza por su velocidad de convergencia, la suavidad en las mallas finales y la precisión respecto de los datos recuperados. Dado que el diagnóstico de patologías cardíacas requiere experiencia, tiempo y mucho conocimiento profesional, la simulación es un proceso clave que mejora la eficiencia.Nuestros algoritmos e implementaciones han sido aplicados a datos sintéticos y reales con diferencias en cuanto a la cantidad de datos inexistentes, casuística presente en casos patológicos y anormales. Los conjuntos de datos incluyen adquisiciones de instantes concretos y de ciclos cardíacos completos. La bondad del sistema de reconstrucción ha sido evaluada mediante parámetros médicos para poder comparar nuestros resultados finales con aquellos derivados a partir de programario típico utilizado por los profesionales de la medicina.Además de la aplicación directa al diagnóstico médico, nuestra metodología permite reconstrucciones de tipo genérico en el campo de los Gráficos 3D por ordenador. Nuestras reconstrucciones permiten generar modelos tridimensionales con un bajo coste en cuanto a la interacción manual necesaria y a la carga computacional asociada. Por otra parte, nuestro método puede entenderse como un robusto algoritmo de triangularización que construye superficies a partir de nubes de puntos que pueden obtenerse a partir de escáneres láser o sensores magnéticos, por ejemplo.This thesis describes a contribution to the three-dimensional reconstruction of the internal and external surfaces of the human's left ventricle. The reconstruction is a first process fitting in a complete VR application that will serve as an important diagnosis tool for hospitals. Beginning with the surfaces reconstruction, the application will provide volume and interactive real-time manipulation to the model. We focus on speed, precision and smoothness for the final surfaces. As long as heart diseases diagnosis requires experience, time and professional knowledge, simulation is a key-process that enlarges efficiency.The algorithms and implementations have been applied to both synthetic and real datasets with differences regarding missing data, present in cases where pathologies and abnormalities arise. The datasets include single acquisitions and complete cardiac cycles. The goodness of the reconstructions has been evaluated with medical parameters in order to compare our results with those retrieved by typical software used by physicians.Besides the direct application to medicine diagnosis, our methodology is suitable for generic reconstructions in the field of computer graphics. Our reconstructions can serve for getting 3D models at low cost, in terms of manual interaction and CPU computation overhead. Furthermore, our method is a robust tessellation algorithm that builds surfaces from clouds of points that can be retrieved from laser scanners or magnetic sensors, among other available hardware