Regular Grids: An Irregular Approach to the 3D Modelling Pipeline

The 3D modelling pipeline covers the process by which a physical object is scanned to create a set of points that lay on its surface. These data are then cleaned to remove outliers or noise, and the points are reconstructed into a digital representation of the original object. The aim of this thesis is to present novel grid-based methods and provide several case studies of areas in the 3D modelling pipeline in which they may be effectively put to use. The first is a demonstration of how using a grid can allow a significant reduction in memory required to perform the reconstruction. The second is the detection of surface features (ridges, peaks, troughs, etc.) during the surface reconstruction process. The third contribution is the alignment of two meshes with zero prior knowledge. This is particularly suited to aligning two related, but not identical, models. The final contribution is the comparison of two similar meshes with support for both qualitative and quantitative outputs

Online surface reconstruction from unorganized point clouds with integrated texture mapping

Surface-reconstructing growing neural gas (Sgng) konstruiert iterativ aus Sample-Punkten von einer Objektoberfläche ein Dreiecksnetz, das diese Oberfläche repräsentiert: Zunächst wird eine Approximation erstellt, die nach und nach verfeinert wird. Sgng berücksichtigt dabei jegliche Änderungen an den Eingabedaten während der Ausführung. Wenn geeignete Bilder vorliegen, weist Sgng diese automatisch den Dreiecken als Texturen zu. Dabei wird die Anzahl der wahrnehmbaren Verdeckungsfehler auf ein Minimum reduziert, indem Sgng Sichtbarkeitsinformationen aus den Eingabedaten lernt. Sgng basiert auf einer Familie eng verwandter neuronaler Netze, die mittels Pseudocode und Beispielen detailliert vorgestellt werden. Sgng wird anhand von Erkenntnissen aus einer genauen Analyse früherer Ansätze hergeleitet. Die Ergebnisse ausgiebiger Evaluationen legen nahe, dass Sgng signifikant bessere Ergebnisse liefert als frühere Ansätze und es sich mit State-of-the-Art-Verfahren messen kann.Surface-reconstructing growing neural gas (sgng) takes a set of sample points lying on an object’s surface as an input and iteratively constructs a triangle mesh representing the original object’s surface. It starts with an initial approximation that gets continuously refined. At any time, sgng instantly incorporates any modifications of the input data into the reconstruction. If registered images are available, sgng assigns suitable textures to the constructed triangles. The number of noticeable occlusion artifacts is reduced to a minimum by learning visibility from the input data. Sgng is based on a family of closely related artificial neural networks that are presented in detail and illustrated by pseudocode and examples. Sgng is derived according to a careful analysis of these prior approaches. Results of an extensive evaluation indicate that sgng improves significantly upon its predecessors and that it can compete with other state-of-the-art reconstruction algorithm

A regularization approach for reconstruction and visualization of 3-D data

Esta tesis trata sobre reconstrucción de superficies a partir de imágenes de rango utilizando algunas extensiones de la Regularización de Tikhonov, que produce Splines aplicables a datos en n dimensiones. La idea central es que estos splines se pueden obtener mediante la teoría de regularización, utilizando un equilibrio entre la suavidad y la fidelidad a los datos, por tanto, serán aplicables tanto en la interpolación como en la aproximación de datos exactos o ruidosos. En esta tesis proponemos un enfoque variacional que incluye los datos e información a priori acerca de la solución, dada en forma de funcionales. Solucionamos problemas de optimización que resultan ser una extensión de la teoría de Tikhonov, con el propósito de incluir funcionales con propiedades locales y globales que pueden ser ajustadas mediante parámetros de regularización. El a priori es analizado en términos de las propiedades físicas y geométricas de los funcionales para luego ser agregados a la formulación variacional. Los resultados obtenidos se prueban con datos para reconstrucción de superficies, mostrando notables propiedades de reproducción y aproximación. En particular, utilizamos la reconstrucción de superficies para ilustrar las aplicaciones prácticas, pero nuestro enfoque tiene muchas más aplicaciones. En el centro de nuestra propuesta esta la teoría general de problemas inversos y las aplicaciones de algunas ideas provenientes del análisis funcional. Los splines que obtenemos son combinaciones lineales de las soluciones fundamentales de ciertos operadores en derivadas parciales, frecuentes en la teoría de la elasticidad y no se hace ninguna suposición previa sobre el modelo estadístico de los datos de entrada, de manera que se pueden tomar en términos de una inferencia estadística no paramétrica. Estos splines son implementables en una forma muy estable y se pueden aplicar en problemas de interpolación y suavizado. / Abstract: This thesis is about surface reconstruction from range images using some extensions of Tikhonov regularization that produces splines applicable on n-dimensional data. The central idea is that these splines can be obtained by regularization theory, using a trade-off between fidelity to data and smoothness properties; as a consequence, they are applicable both in interpolation and approximation of exact or noisy data. We propose a variational framework that includes data and a priori information about the solution, given in the form of functionals. We solve optimization problems which are extensions of Tikhonov theory, in order to include functionals with local and global features that can be tuned by regularization parameters. The a priori is thought in terms of geometric and physical properties of functionals and then added to the variational formulation. The results obtained are tested on data for surface reconstruction, showing remarkable reproducing and approximating properties. In this case we use surface reconstruction to illustrate practical applications; nevertheless, our approach has many other applications. In the core of our approach is the general theory of inverse problems and the application of some abstract ideas from functional analysis. The splines obtained are linear combinations of certain fundamental solutions of partial differential operators from elasticity theory and no prior assumption is made on a statistical model for the input data, so it can be thought in terms of nonparametric statistical inference. They are implementable in a very stable form and can be applied for both interpolation and smoothing problems.Doctorad

Neural mesh ensembles

This paper proposes the use of neural network ensembles to boost the performance of a neural network based surface reconstruction algorithm. Ensemble is a very popular and powerful statistical technique based on the idea of averaging several outputs of a probabilistic algorithm. In the context of surface reconstruction, two main problems arise. The first is finding an efficient way to average meshes with different connectivity, and the second is tuning the parameters for surface reconstruction to maximize the performance of the ensemble. We solve the first problem by voxelizing all the meshes on the same regular grid and taking majority vote on each voxel. We tune the parameters experimentally, borrowing ideas from weak learning methods

Neural Mesh Ensembles

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