Abstract

Compact representation of geometry using a suitable procedural or mathematical model and a ray-tracing mode ofrendering fit the programmable graphics processor units (GPUs) well. Several such representations including parametric andsubdivision surfaces have been explored in recent research. The important and widely applicable category of the general implicitsurface has received less attention. In this paper, we present a ray-tracing procedure to render general implicit surfaces efficiently onthe GPU. Though only the fourth or lower order surfaces can be rendered using analytical roots, ouradaptive marching pointsalgorithm can ray trace arbitrary implicit surfaces without multiple roots, by sampling the ray at selected points till a root is found.Adapting the sampling step size based on a proximity measure and a horizon measure delivers high speed. The sign test can handleany surface without multiple roots. The Taylor test that uses ideas from interval analysis can ray trace many surfaces with complexroots. Overall, a simple algorithm that fits the SIMD architecture of the GPU results in high performance. We demonstrate the raytracing of algebraic surfaces up to order 50 and nonalgebraic surfaces including a Blinn’s blobby with 75 spheres at better thaninteractive frame rates.

Abstract

Linear algebra algorithms are fundamental to many com-puting applications. Modern GPUs are suited for manygeneral purpose processing tasks and have emerged asinexpensive high performance co-processors due to theirtremendous computing power. In this paper, we present theimplementation of singular value decomposition (SVD) of adense matrix on GPU using the CUDA programming model.SVD is implemented using the twin steps of bidiagonalizationfollowed by diagonalization. It has not been implemented onthe GPU before. Bidiagonalization is implemented using aseries of Householder transformations which map well toBLAS operations. Diagonalization is performed by applyingthe implicitly shifted QR algorithm. Our complete SVDimplementation outperforms the MATLAB and IntelR©MathKernel Library (MKL) LAPACK implementation significantlyon the CPU. We show a speedup of upto60over theMATLAB implementation and upto8over the Intel MKLimplementation on a Intel Dual Core2.66GHz PC onNVIDIA GTX280for large matrices. We also give resultsfor very large matrices on NVIDIA Tesla S1070.

Abstract

Graphics Processor Units are used for many general purpose pro-cessing due to high compute power available on them. Regular,data-parallel algorithms map well to the SIMD architecture of cur-rent GPU. Irregular algorithms on discrete structures like graphs areharder to map to them. Efficient data-mapping primitives can playcrucial role in mapping such algorithms onto the GPU. In this paper,we present a minimum spanning tree algorithm on Nvidia GPUsunder CUDA, as a recursive formulation of Bor ̊uvka’s approach forundirected graphs. We implement it using scalable primitives suchas scan, segmented scan and split. The irregular steps of superver-tex formation and recursive graph construction are mapped to prim-itives like split to categories involving vertex ids and edge weights.We obtain30to50times speedup over the CPU implementationon most graphs and3to10times speedup over our previous GPUimplementation. We construct the minimum spanning tree on a5million node and30million edge graph in under1second on onequarter of the Tesla S1070GPU.

Abstract

Many vision problems map to the minimization of an energyfunction over a discrete MRF. Fast performance is needed if the energyminimization is one step in a control loop. In this paper, we presentthe incrementalα-expansion algorithm for high-performance multilabelMRF optimization on the GPU. Our algorithm utilizes the gridstruc-ture of the MRFs for good parallelism on the GPU. We improve the basicpush-relabel implementation of graph cuts using the atomicoperationsof the GPU and by processing blocks stochastically. We also reuse theflow using reparametrization of the graph from cycle to cycleand itera-tion to iteration for fast performance. We show results on various visionproblems on standard datasets. Our approach takes 950 milliseconds onthe GPU for stereo correspondence on Tsukuba image with 16 labelscompared to 5.4 seconds on the CPU.

Abstract

In this paper, we present the design and construction of a simple andinexpensive 3D display made up of polygonal elements. We use aper-pixel transformation of image and depth to produce accuratepicture and depth map on an arbitrary planar display facet fromany viewpoint. Though the facets are rendered independently, theimage and depth for rays from the eye-point through the facet pixelsis produced by our method. Thus, there are no artifacts on a facet orat facet boundaries. Our method can be extended to any polygonaldisplay surface as demonstrated using synthetic setups. We alsoshow a real display constructed using off-the-shelf LCD panels andcomputers. The display uses a simple calibration procedure and canbe setup in minutes. Frame-sequential and anaglyphic stereo modescan be supported for any eye-orientation and at high resolutions.

Abstract

Multicore processors are a shift of paradigm in computer architecture that promises dramatic increase in performance. But they also bring complexity in algorithmic design. In this paper we describe the challenges and design issues involved in parallelizing two dimensional convex hull on both CUDA and Cell Brodband Engine (Cell BE). We have parallelized the quickhull algorithm for two dimensional convex hull. The major advantage of this algorithm is that interprocessor communication cost is highly reduced.

Abstract

GPGPU has received lot of attention in the past few years mainly because of the performance gain GPUs offer at a low price. Recently, researchers have identified hybrid multi-core computing as a better solution compared to accelerator based computing for several prob-lems. In this paper, we evaluate two regular problems in image processing, bilateral filtering and convolution, on a hybrid multi-core platform. We provide a detailed analysis of these algorithms by comparing their performance on three platforms 1)CPU+GPU hybrid, 2) pure GPU and3)pure CPU. We show that performance gains as hig has 30-40%can be obtained by using basic techniques like data decomposition and overlapped execution, when a hybrid computing model is used. Finally, we conclude by discussing some future prospects in the area of hybrid computing

Abstract

General purpose programming on the graphics processing units (GPGPU) has received a lot of attention in the parallel computing community as it promises to offer the highest performance per dollar. The GPUs have been used extensively on regular problems that can be easily parallelized. In this paper, we describe two implementations of List Ranking, a traditional irregular algorithm that is difficult to parallelize on such massively multi-threaded hardware. We first present an implementation of Wyllie's algorithm based on pointer jumping. This technique does not scale well to large lists due to the suboptimal work done. We then present a GPU-optimized, Recursive Helman-JaJa (RHJ) algorithm. Our RHJ implementation can rank a random list of 32 million elements in about a second and achieves a speedup of about 8-9 over a CPU implementation as well as a speedup of 3-4 over the best reported implementation on the Cell Broadband engine. We also discuss the practical issues relating to the implementation of irregular algorithms on massively multi-threaded architectures like that of the GPU. Regular or coalesced memory accesses pattern and balanced load are critical to achieve good performance on the GPU.

Abstract

The significant growth in computational power of modern Graphics Processing Units (GPUs) coupled with the advent of general purpose programming environments like NVIDIA's CUDA, has seen GPUs emerging as a very popular parallel computing platform. Till recently, there has not been a performance model for GPGPUs. The absence of such a model makes it difficult to definitively assess the suitability of the GPU for solving a particular problem and is a significant impediment to the mainstream adoption of GPUs as a massively parallel (super)computing platform. In this paper we present a performance prediction model for the CUDA GPGPU platform. This model encompasses the various facets of the GPU architecture like scheduling, memory hierarchy, and pipelining among others. We also perform experiments that demonstrate the effects of various memory access strategies. The proposed model can be used to analyze pseudo code for a CUDA kernel to obtain a performance estimate, in a way that is similar to performing asymptotic analysis. We illustrate the usage of our model and its accuracy with three case studies: matrix multiplication, list ranking, and histogram generation.

Abstract

Depth movies provide 2-D representations of a time-varying 3D scene. Multistream depth movies arise in many structure-capturing setups and have been used for image based rendering. They are bulky and carry redundant information. We propose a proxy-based compression scheme for multistream depth movies of a scene involving dynamic human actors. The input to our system is depth movies from different viewpoints and the calibration parameters to relate depths to 3D points. We use an articulated human model as a proxy to represent the common structure of the scene. The proxy is parametrized by various bone angles.