Probability Distributions.- Linear Models for Regression.- Linear Models for Classification.- Neural Networks.- Kernel Methods.- Sparse Kernel Machines.- Graphical Models.- Mixture Models and EM.- Approximate Inference.- Sampling Methods.- Continuous Latent Variables.- Sequential Data.- Combining Models.

Pattern Recognition and Machine Learning

Statistics for Spatial Data.

We show that surface reconstruction from oriented points can be cast as a spatial Poisson problem. This Poisson formulation considers all the points at once, without resorting to heuristic spatial partitioning or blending, and is therefore highly resilient to data noise. Unlike radial basis function schemes, our Poisson approach allows a hierarchy of locally supported basis functions, and therefore the solution reduces to a well conditioned sparse linear system. We describe a spatially adaptive multiscale algorithm whose time and space complexities are proportional to the size of the reconstructed model. Experimenting with publicly available scan data, we demonstrate reconstruction of surfaces with greater detail than previously achievable.

Poisson surface reconstruction

A novel method is proposed for performing multilabel, interactive image segmentation. Given a small number of pixels with user-defined (or predefined) labels, one can analytically and quickly determine the probability that a random walker starting at each unlabeled pixel will first reach one of the prelabeled pixels. By assigning each pixel to the label for which the greatest probability is calculated, a high-quality image segmentation may be obtained. Theoretical properties of this algorithm are developed along with the corresponding connections to discrete potential theory and electrical circuits. This algorithm is formulated in discrete space (i.e., on a graph) using combinatorial analogues of standard operators and principles from continuous potential theory, allowing it to be applied in arbitrary dimension on arbitrary graphs

/pdf/random-walks-for-image-segmentation-4ppfcpqq4u.pdf

Random Walks for Image Segmentation

Monthly Notices is one of the three largest general primary astronomical research publications. It is an international journal, published by the Royal Astronomical Society. This article 1 describes its publication policy and practice.

Monthly Notices of the Royal Astronomical Society

In this work, the emphasis is on the development of strategies to realize techniques of numerical computing on the graphics chip. In particular, the focus is on the acceleration of techniques for solving sets of algebraic equations as they occur in numerical simulation. We introduce a framework for the implementation of linear algebra operators on programmable graphics processors (GPUs), thus providing the building blocks for the design of more complex numerical algorithms. In particular, we propose a stream model for arithmetic operations on vectors and matrices that exploits the intrinsic parallelism and efficient communication on modern GPUs. Besides performance gains due to improved numerical computations, graphics algorithms benefit from this model in that the transfer of computation results to the graphics processor for display is avoided. We demonstrate the effectiveness of our approach by implementing direct solvers for sparse matrices, and by applying these solvers to multi-dimensional finite difference equations, i.e. the 2D wave equation and the incompressible Navier-Stokes equations.

https://www.cc.gatech.edu/~jarek/graphics/papers/15GPUsimulationKruger.pdf

Linear algebra operators for GPU implementation of numerical algorithms

OpenGLand its extensionsprovide accessto advancedper-pixel operationsavailable in the rasterizationstageand in the frame buffer hardware of modern graphicsworkstations. With these mechanisms, completelynew renderingalgorithmscanbedesigned andimplementedin a very particularway. In this paperwe extend theideaof extensi vely usinggraphicshardwarefor therenderingof volumetricdatasetsin variousways. First, we introducethe conceptof clipping geometriesby meansof stencilbuffer operations, and we exploit pixel texturesfor the mappingof volume datato sphericaldomains.We show waysto use3D texturesfor the renderingof lightedandshadediso-surfacesin real-timewithout extractingany polygonalrepresentation. Second,wedemonstratethat even for volumedataon unstructuredgrids, whereonly software solutionsexist up to now, bothmethods,iso-surfaceextractionand directvolumerendering,canbeacceleratedto new ratesof interactivity by simplepolygondrawing andframebuffer operations. CR Categories: I.3.7 [ComputerGraphics]:Three-Dimensional GraphicsandRealism—Graphics Hardware, 3D Textures, Volume Rendering, Unstructured Grids

Efficiently using graphics hardware in volume rendering applications

Porous structures such as trabecular bone are widely seen in nature. These structures are lightweight and exhibit strong mechanical properties. In this paper, we present a method to generate bone-like porous structures as lightweight infill for additive manufacturing. Our method builds upon and extends voxel-wise topology optimization. In particular, for the purpose of generating sparse yet stable structures distributed in the interior of a given shape, we propose upper bounds on the localized material volume in the proximity of each voxel in the design domain. We then aggregate the local per-voxel constraints by their p -norm into an equivalent global constraint, in order to facilitate an efficient optimization process. Implemented on a high-resolution topology optimization framework, our results demonstrate mechanically optimized, detailed porous structures which mimic those found in nature. We further show variants of the optimized structures subject to different design specifications, and we analyze the optimality and robustness of the obtained structures.

/pdf/infill-optimization-for-additive-manufacturing-approaching-51ckd7qa67.pdf

Infill Optimization for Additive Manufacturing—Approaching Bone-Like Porous Structures

We present a system for real-time animation and rendering of large particle sets using GPU computation and memory objects in OpenGL. Memory objects can be used both as containers for geometry data stored on the graphics card and as render targets, providing an effective means for the manipulation and rendering of particle data on the GPU.To fully take advantage of this mechanism, efficient GPU realizations of algorithms used to perform particle manipulation are essential. Our system implements a versatile particle engine, including inter-particle collisions and visibility sorting. By combining memory objects with floating-point fragment programs, we have implemented a particle engine that entirely avoids the transfer of particle data at run-time. Our system can be seen as a forerunner of a new class of graphics algorithms, exploiting memory objects or similar concepts on upcoming graphics hardware to avoid bus bandwidth becoming the major performance bottleneck.

/pdf/uberflow-a-gpu-based-particle-engine-d63k9qltzl.pdf

UberFlow: a GPU-based particle engine

Interactive, efficient, methods of foreground extraction and alpha-matting are of increasing practical importance for digital image editing. Although several new approaches to this problem have recently been developed, many challenges remain. We propose a new technique based on random walks that has the following advantages: First, by leveraging a recent technique from manifold learning theory, we effectively use RGB values to set boundaries for the random walker, even in fuzzy or low-contrast images. Second, the algorithm is straightforward to implement, requires specification of only a single free parameter (set the same for all images), and performs the segmentation and alpha-matting in a single step. Third, the user may locally fine tune the results by interactively manipulating the foreground/background maps. Finally, the algorithm has an inherit parallelism that leads to a particularly efficient implementation via the graphics processing unit (GPU). Our method processes a 1024× 1024 image at the interactive speed of 0.5 seconds and, most importantly, produces highquality results. We show that our algorithm can generate good segmentation and matting results at an interactive rate with minimal user interaction.

Rüdiger Westermann

Papers

Linear algebra operators for GPU implementation of numerical algorithms

Efficiently using graphics hardware in volume rendering applications

Infill Optimization for Additive Manufacturing—Approaching Bone-Like Porous Structures

UberFlow: a GPU-based particle engine

Random walks for interactive alpha-matting