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

Implicit meshes:unifying implicit and explicit surface representations for 3D reconstruction and tracking

This thesis proposes novel ways both to represent the static surfaces, and to parameterize their deformations. This can be used both by automated algorithms for efficient 3–D shape reconstruction, and by graphics designers for editing and animation. Deformable 3–D models can be represented either as traditional explicit surfaces, such as triangulated meshes, or as implicit surfaces. Explicit surfaces are widely accepted because they are simple to deform and render, however fitting them involves minimizing a non-differentiable distance function. By contrast, implicit surfaces allow fitting by minimizing a differentiable algebraic distance, but they are harder to meaningfully deform and render. Here we propose a method that combines the strength of both representations to avoid their drawbacks, and in this way build robust surface representation, called implicit mesh, suitable for automated shape recovery from video sequences. This surface representation lets us automatically detect and exploit silhouette constraints in uncontrolled environments that may involve occlusions and changing or cluttered backgrounds, which limit the applicability of most silhouette based methods. We advocate the use of Dirichlet Free Form Deformation (DFFD) as generic surface deformation technique that can be used to parameterize objects of arbitrary geometry defined as explicit meshes. It is based on the small set of control points and the generalized interpolant. Control points become model parameters and their change causes model's shape modification. Using such parameterization the problem dimensionality can be dramatically reduced, which is desirable property for most optimization algorithms, thus makes DFFD good tool for automated fitting. Combining DFFD as a generic parameterization method for explicit surfaces and implicit meshes as a generic surface representation we obtained a powerfull tool for automated shape recovery from images. However, we also argue that any other avaliable surface parameterization can be used. We demonstrate the applicability of our technique to 3–D reconstruction of the human upper-body including – face, neck and shoulders, and the human ear, from noisy stereo and silhouette data. We also reconstruct the shape of a high resolution human faces parametrized in terms of a Principal Component Analysis model from interest points and automatically detected silhouettes. Tracking of deformable objects using implicit meshes from silhouettes and interest points in monocular sequences is shown in following two examples: Modeling the deformations of a piece of paper represented by an ordinary triangulated mesh; tracking a person's shoulders whose deformations are expressed in terms of Dirichlet Free Form Deformations

Computerized Analysis of Magnetic Resonance Images to Study Cerebral Anatomy in Developing Neonates

The study of cerebral anatomy in developing neonates is of great importance for the understanding of brain development during the early period of life. This dissertation therefore focuses on three challenges in the modelling of cerebral anatomy in neonates during brain development. The methods that have been developed all use Magnetic Resonance Images (MRI) as source data. To facilitate study of vascular development in the neonatal period, a set of image analysis algorithms are developed to automatically extract and model cerebral vessel trees. The whole process consists of cerebral vessel tracking from automatically placed seed points, vessel tree generation, and vasculature registration and matching. These algorithms have been tested on clinical Time-of- Flight (TOF) MR angiographic datasets. To facilitate study of the neonatal cortex a complete cerebral cortex segmentation and reconstruction pipeline has been developed. Segmentation of the neonatal cortex is not effectively done by existing algorithms designed for the adult brain because the contrast between grey and white matter is reversed. This causes pixels containing tissue mixtures to be incorrectly labelled by conventional methods. The neonatal cortical segmentation method that has been developed is based on a novel expectation-maximization (EM) method with explicit correction for mislabelled partial volume voxels. Based on the resulting cortical segmentation, an implicit surface evolution technique is adopted for the reconstruction of the cortex in neonates. The performance of the method is investigated by performing a detailed landmark study. To facilitate study of cortical development, a cortical surface registration algorithm for aligning the cortical surface is developed. The method first inflates extracted cortical surfaces and then performs a non-rigid surface registration using free-form deformations (FFDs) to remove residual alignment. Validation experiments using data labelled by an expert observer demonstrate that the method can capture local changes and follow the growth of specific sulcus

Cortical Surface Reconstruction from High-Resolution MR Brain Images

Reconstruction of the cerebral cortex from magnetic resonance (MR) images is an important step in quantitative analysis of the human brain structure, for example, in sulcal morphometry and in studies of cortical thickness. Existing cortical reconstruction approaches are typically optimized for standard resolution (~1 mm) data and are not directly applicable to higher resolution images. A new PDE-based method is presented for the automated cortical reconstruction that is computationally efficient and scales well with grid resolution, and thus is particularly suitable for high-resolution MR images with submillimeter voxel size. The method uses a mathematical model of a field in an inhomogeneous dielectric. This field mapping, similarly to a Laplacian mapping, has nice laminar properties in the cortical layer, and helps to identify the unresolved boundaries between cortical banks in narrow sulci. The pial cortical surface is reconstructed by advection along the field gradient as a geometric deformable model constrained by topology-preserving level set approach. The method's performance is illustrated on exvivo images with 0.25–0.35 mm isotropic voxels. The method is further evaluated by cross-comparison with results of the FreeSurfer software on standard resolution data sets from the OASIS database featuring pairs of repeated scans for 20 healthy young subjects

Implicit Meshes for Effective Silhouette Handling

Using silhouettes in uncontrolled environments typically requires handling occlusions as well as changing or cluttered backgrounds, which limits the applicability of most silhouette based methods. For the purpose of 3-D shape modeling, we show that representing generic 3-D surfaces as implicit surfaces lets us effectively address these issues. This desirable behavior is completely independent from the way the surface deformations are parame-trized. To show this, we demonstrate our technique in three very different cases: Modeling the deformations of a piece of paper represented by an ordinary triangulated mesh; reconstruction and tracking a person's shoulders whose deformations are expressed in terms of Dirichlet Free Form Deformations; reconstructing the shape of a human face parametrized in terms of a Principal Component Analysis mode