Diffusion is All You Need for Learning on Surfaces

We introduce a new approach to deep learning on 3D surfaces such as meshes or point clouds. Our key insight is that a simple learned diffusion layer can spatially share data in a principled manner, replacing operations like convolution and pooling which are complicated and expensive on surfaces. The only other ingredients in our network are a spatial gradient operation, which uses dot-products of derivatives to encode tangent-invariant filters, and a multi-layer perceptron applied independently at each point. The resulting architecture, which we call DiffusionNet, is remarkably simple, efficient, and scalable. Continuously optimizing for spatial support avoids the need to pick neighborhood sizes or filter widths a priori, or worry about their impact on network size/training time. Furthermore, the principled, geometric nature of these networks makes them agnostic to the underlying representation and insensitive to discretization. In practice, this means significant robustness to mesh sampling, and even the ability to train on a mesh and evaluate on a point cloud. Our experiments demonstrate that these networks achieve state-of-the-art results for a variety of tasks on both meshes and point clouds, including surface classification, segmentation, and non-rigid correspondence

Feature preserving decimation of urban meshes

1 online resource (vii, 72 pages) : illustrations (chiefly colour), charts (chiefly colour)Includes abstract.Includes bibliographical references (pages 65-72).Commercial buildings as well as residential houses represent core structures of any modern day urban or semi-urban areas. Consequently, 3D models of urban buildings are of paramount importance to a majority of digital urban applications such as city planning, 3D mapping and navigation, video games and movies, among others. However, current studies suggest that existing 3D modeling approaches often involve high computational cost and large storage volumes for processing the geometric details of the buildings. Therefore, it is essential to generate concise digital representations of urban buildings from the 3D measurements or images, so that the acquired information can be efficiently utilized for various urban applications. Such concise representations, often referred to as “lightweight” models, strive to capture the details of the physical objects with less computational storage. Furthermore, lightweight models consume less bandwidth for online applications and facilitate accelerated visualizations. In this thesis, we provide an assessment study on state-of-the-art data structures for storing lightweight urban buildings. Then we propose a method to generate lightweight yet highly detailed 3D building models from LiDAR scans. The lightweight modeling pipeline comprises the following stages: mesh reconstruction, feature points detection and mesh decimation through gradient structure tensors. The gradient of each vertex of the reconstructed mesh is obtained by estimating the vertex confidence through eigen analysis and further encoded into a 3 X 3 structure tensor. We analyze the eigenvalues of structure tensor representing gradient variations and use it to classify vertices into various feature classes, e.g., edges, and corners. While decimating the mesh, fea ture points are preserved through a mean cost-based edge collapse operation. The experiments on different building facade models show that our method is effective in generating simplified models with a trade-off between simplification and accuracy

A Constrained Resampling Strategy for Mesh Improvement

In many geometry processing applications, it is required to improve an initial mesh in terms of multiple quality objectives. Despite the availability of several mesh generation algorithms with provable guarantees, such generated meshes may only satisfy a subset of the objectives. The conflicting nature of such objectives makes it challenging to establish similar guarantees for each combination, e.g., angle bounds and vertex count. In this paper, we describe a versatile strategy for mesh improvement by interpreting quality objectives as spatial constraints on resampling and develop a toolbox of local operators to improve the mesh while preserving desirable properties. Our strategy judiciously combines smoothing and transformation techniques allowing increased flexibility to practically achieve multiple objectives simultaneously.  We apply our strategy to both planar and surface meshes demonstrating how to simplify Delaunay meshes while preserving element quality, eliminate all obtuse angles in a complex mesh, and maximize the shortest edge length in a Voronoi tessellation far better than the state-of-the-art

Device-based decision-making for adaptation of three-dimensional content

The goal of this research was the creation of an adaptation mechanism for the delivery of three-dimensional content. The adaptation of content, for various network and terminal capabilities - as well as for different user preferences, is a key feature that needs to be investigated. Current state-of-the art research of the adaptation shows promising results for specific tasks and limited types of content, but is still not well-suited for massive heterogeneous environments. In this research, we present a method for transmitting adapted three-dimensional content to multiple target devices. This paper presents some theoretical and practical methods for adapting three-dimensional content, which includes shapes and animation. We also discuss practical details of the integration of our methods into MPEG-21 and MPEG-4 architecture

Optimization of 3D Immunofluorescence Analysis and Visualization Using IMARIS and MeshLab.

The precision of colocalization analysis is enhanced by 3D and is potentially more accurate than 2D. Even though 3D improves the visualization of colocalization analysis, rendering a colocalization model may generate a model with numerous polygons. We developed a 3D colocalization model of FtMt/LC3 followed by simplification. Double immunofluorescence staining of FtMt and LC3 was conducted, and stacked images were acquired. We used IMARIS to render the 3D colocalization model of FtMt/LC3 and further processed it with MeshLab to decimate and generate a less complex colocalization model. We examined the available simplification algorithm using MeshLab in detail and evaluated the feasibility of each procedure in generating a model with less complexity. The quality of the simplified model was subsequently assessed. MeshLab\u27s available shaders were scrutinized to facilitate the spatial colocalization determination. Finally, we showed that QECD was the most effective method for reducing the polygonal complexity of the colocalization model without compromising its quality. In addition, we would recommend implementing the x-ray shader, which we found useful for visualizing colocalization. As 3D was found to be more accurate in quantifying colocalization, our study provides a novel and dependable method for rendering 3D models for colocalization analysis

High-Quality Simplification and Repair of Polygonal Models

Because of the rapid evolution of 3D acquisition and modelling methods, highly complex and detailed polygonal models with constantly increasing polygon count are used as three-dimensional geometric representations of objects in computer graphics and engineering applications. The fact that this particular representation is arguably the most widespread one is due to its simplicity, flexibility and rendering support by 3D graphics hardware. Polygonal models are used for rendering of objects in a broad range of disciplines like medical imaging, scientific visualization, computer aided design, film industry, etc. The handling of huge scenes composed of these high-resolution models rapidly approaches the computational capabilities of any graphics accelerator. In order to be able to cope with the complexity and to build level-of-detail representations, concentrated efforts were dedicated in the recent years to the development of new mesh simplification methods that produce high-quality approximations of complex models by reducing the number of polygons used in the surface while keeping the overall shape, volume and boundaries preserved as much as possible. Many well-established methods and applications require "well-behaved" models as input. Degenerate or incorectly oriented faces, T-joints, cracks and holes are just a few of the possible degenaracies that are often disallowed by various algorithms. Unfortunately, it is all too common to find polygonal models that contain, due to incorrect modelling or acquisition, such artefacts. Applications that may require "clean" models include finite element analysis, surface smoothing, model simplification, stereo lithography. Mesh repair is the task of removing artefacts from a polygonal model in order to produce an output model that is suitable for further processing by methods and applications that have certain quality requirements on their input. This thesis introduces a set of new algorithms that address several particular aspects of mesh repair and mesh simplification. One of the two mesh repair methods is dealing with the inconsistency of normal orientation, while another one, removes the inconsistency of vertex connectivity. Of the three mesh simplification approaches presented here, the first one attempts to simplify polygonal models with the highest possible quality, the second, applies the developed technique to out-of-core simplification, and the third, prevents self-intersections of the model surface that can occur during mesh simplification

LOD Generation for Urban Scenes

International audienceWe introduce a novel approach that reconstructs 3D urban scenes in the form of levels of detail (LODs). Starting from raw data sets such as surface meshes generated by multi-view stereo systems, our algorithm proceeds in three main steps: classification, abstraction and reconstruction. From geometric attributes and a set of semantic rules combined with a Markov random field, we classify the scene into four meaningful classes. The abstraction step detects and regularizes planar structures on buildings, fits icons on trees, roofs and facades, and performs filtering and simplification for LOD generation. The abstracted data are then provided as input to the reconstruction step which generates watertight buildings through a min-cut formula-tion on a set of 3D arrangements. Our experiments on complex buildings and large scale urban scenes show that our approach generates meaningful LODs while being robust and scalable. By combining semantic segmentation and abstraction it also outperforms general mesh approximation ap-proaches at preserving urban structures

Visual attention models and applications to 3D computer graphics

Ankara : The Department of Computer Engineering and the Graduate School of Engineering and Science of Bilkent University, 2012.Thesis (Ph. D.) -- Bilkent University, 2012.Includes bibliographical refences.3D computer graphics, with the increasing technological and computational opportunities, have advanced to very high levels that it is possible to generate very realistic computer-generated scenes in real-time for games and other interactive environments. However, we cannot claim that computer graphics research has reached to its limits. Rendering photo-realistic scenes still cannot be achieved in real-time; and improving visual quality and decreasing computational costs are still research areas of great interest. Recent e orts in computer graphics have been directed towards exploiting principles of human visual perception to increase visual quality of rendering. This is natural since in computer graphics, the main source of evaluation is the judgment of people, which is based on their perception. In this thesis, our aim is to extend the use of perceptual principles in computer graphics. Our contribution is two-fold: First, we present several models to determine the visually important, salient, regions in a 3D scene. Secondly, we contribute to use of de nition of saliency metrics in computer graphics. Human visual attention is composed of two components, the rst component is the stimuli-oriented, bottom-up, visual attention; and the second component is task-oriented, top-down visual attention. The main di erence between these components is the role of the user. In the top-down component, viewer's intention and task a ect perception of the visual scene as opposed to the bottom-up component. We mostly investigate the bottom-up component where saliency resides. We de ne saliency computation metrics for two types of graphical contents. Our rst metric is applicable to 3D mesh models that are possibly animating, and it extracts saliency values for each vertex of the mesh models. The second metric we propose is applicable to animating objects and nds visually important objects due to their motion behaviours. In a third model, we present how to adapt the second metric for the animated 3D meshes. Along with the metrics of saliency, we also present possible application areas and a perceptual method to accelerate stereoscopic rendering, which is based on binocular vision principles and makes use of saliency information in a stereoscopic rendering scene. Each of the proposed models are evaluated with formal experiments. The proposed saliency metrics are evaluated via eye-tracker based experiments and the computationally salient regions are found to attract more attention in practice too. For the stereoscopic optimization part, we have performed a detailed experiment and veri ed our model of optimization. In conclusion, this thesis extends the use of human visual system principles in 3D computer graphics, especially in terms of saliency.Bülbül, Muhammed AbdullahPh.D