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

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

We present efficient implementations of two primitives for datamapping and distribution on the massively multithreaded architec-ture of the GPUs in this paper. Thesplitprimitive distributes el-ements of a list according to their category. Split is an importantoperation for data mapping and is used to build data structures,distribute work load, etc., in a massively parallel environment.Thegather/scatterprimitive performs fast, distributed data move-ment. Efficient data movement is critical to high performance onthe GPUs as suboptimal memory accesses can pay heavy penalties.The split we implement is a generalization of the binary split [Blel-loch 1990] and is implemented using the shared memory and theatomic operations available on them. The split performance scaleslogarithmically with the number of categories, linearly with the listlength, and linearly with the number of cores on the GPU. Thismakes it useful for applications that deal with large data sets. Wealso present a variant of split that partitions the indexes of records.This facilitates the use of the GPU as a coprocessor for split or sort,with the actual data movement handled separately. We can computethe split indexes for a list of 32 million records in 180 millisecondsfor a 32-bit key and in 800 ms for a 96-bit key. The instantaneouslocality of memory references play a critical role in data movementon the current GPU memory architectures. For scatter and gatherinvolving large records, we use collective data movement in whichmultiple threads cooperate on individual records to improve the in-stantaneous locality. The split, gather, and their combinations findmany applications and expect our primitives will be used by fu-ture GPU programmers. We show sorting of 16 million 128-byterecords in 379 milliseconds with 4-byte keys and in 556 ms with8-byte keys

Abstract

The Graphics Processing Units (GPUs) provide highcomputation power at a low cost and is an important computeaccelerator with a massively multithreaded architecture. Inthis paper, we present fast implementations of common graphoperations like breadth-first search, st-connectivity, single-sourceshortest path, all-pairs shortest path, minimum spanning tree,and maximum flow for undirected graphs on the GPU using theCUDA programming model. Our implementations exhibit highperformance, especially on large graphs. We use two data-parallelprogramming methodologies for these algorithms. One is aniterative, mask-based approach that processes valid data elementslike vertices and edges using independent threads for each.The other is a divide-and-conquer approach that reduces theproblem into smaller problems that are handled later using thesame approach. Parallel algorithms for such problems have beenreported in the literature before, especially on supercomputers.The massively multithreaded model of the GPU makes it possibleto adopt the data-parallel approach even to irregular algorithmslike graph algorithms, usingO(V)orO(E)simultaneous threads.The algorithms and the underlying techniques presented in thispaper are likely to be applicable to many irregular algorithms.We show the impact of our implementations on random, scale-free, and real-life graphs of up to millions of vertices on high-end and low-end GPUs. The availability and spread of GPUs todesktops and laptops make them ideal candidates to accelerategraph operations over the CPU-only implementations. Practicalimplementations of basic operations go a long way in realizingtheir potential.

Abstract

As large quantity of document images is getting archived by the digital libraries, there is a need for an efficient search strategies to make them available as per users information need. In this paper, we propose an effective word image matching scheme that achieves high performance in the presence of script variability, printing variation, degradation and word-form variants. A novel partial matching algorithm is designed for morphological matching of word form variants in a language. We formulate feature extraction scheme that extracts local features by scanning vertical strips of the word image and combining them automatically based on their discriminatory potential. We present detailed performance analysis of the proposed approach on English, Amharic and Hindi documents.

Abstract

This paper presents an edge-directed super-resolution algorithm for document images without using any training set. This technique creates an image with smooth regions in both the foreground and the background, while allowing sharp discontinuities across and smoothness along the edges. Our method preserves sharp corners in text images by using the local edge direction, which is computed first by evaluating the gradient field and then taking its tangent. Super-resolution of document images is characterized by bimodality, smoothness along the edges as well as subsampling consistency. These characteristics are enforced in a Markov Random Field (MRF) framework by defining an appropriate energy function. In our method, subsampling of super-resolution image will return the original lowresolution one, proving the correctness of the method. The super-resolution image, is generated by iteratively reducing this energy function. Experimental results on a variety of input images, demonstrate the effectiveness of our method for document image super-resolution.

Abstract

We present a method for finding paths for multiple unmanned air vehicles (UAVs) such that the sum over their lengths is minimum as they cover a 3D terrain (represented as height fields). The paths are constrained to lie beneath an exposure surface to ensure stealth from enemy outposts. The exposure surface is also computed as a height field. The algorithm greedily clusters the terrain such that gain in visibility per distance would be higher for intra-cluster points than points across clusters. Paths generated on clusters formed by such a per distance visibility metric are reduced by more than 25% over other related decoupled methods. The method is extended to cover terrains with partial visibilities. The advantage of the coupled metric extends under constrained visibility also. We again show performance gain by comparing with an existing decoupled algorithm that solves a similar problem of minimum distance terrain coverage with constrained visibility. The paper reveals that decomposing the terrain based on visibility first and then distance is always better than the other way round to cover the terrain in shorter distances.

Abstract

In environments which possess relatively few features that enable a robot to unambiguously determine its location, global localization algorithms can result in multiple hypotheses locations of a robot. In such a scenario the robot, for effective localization, has to be actively guided to those locations where there is a maximum chance of eliminating most of the ambiguous states - which is often referred to as dasiaactive localizationpsila. When extended to multi robotic scenarios where all robots possess more than one hypothesis of their position, there is the opportunity to do better by using robots apart from obstacles as dasiahypotheses resolving agentspsila. The paper presents a unified framework accounting for the map structure as well as measurement amongst robots while guiding a set of robots to locations where they can singularize to a unique state. The appropriateness of our approach is demonstrated empirically in both simulation & real-time (on Amigobots) and its efficacy verified. Extensive comparative analysis portrays the advantage of the current method over others that do not perform active localization in a multi-robotic sense.

Abstract

This paper presents a novel real-time algorithm to sequentially solve the triangulation problem. The problem addressed is estimation of 3D point coordinates given its images and the matrices of the respective cameras used in the imaging process. The algorithm has direct application to real time systems like visual SLAM. This article demonstrates the application of the proposed algorithm to the mapping problem in visual SLAM. Experiments have been carried out for the general triangulation problem as well as the application to visual SLAM. Results show that the application of the proposed method to mapping in visual SLAM outperforms the state of the art mapping methods.

Abstract

To improve the mobility of wheeled robots traversing on and uneven terrain having slopes in all three orthogonal directions is the primary focus of our research. Past research on ‘all terrain vehicles’,[1],[2], was focused on developing mechanical suspension systems which could improve terrain adaptability and locomotion. Consequently control algorithms were developed for posture stability of the vehicle [3],[4]. Shrimp robots [1] and Rocky rovers [2] are terrain vehicles with passive suspension systems which have excellent terrain adaptability and ability to negotiate terrains having discontinuities that are higher than the wheel radius. But mobility and stability of such vehicles is not guaranteed. Thus for such conditions Sreenivasan and Waldron [4] developed vehicles called Wheeled and Actively Articulated Vehicles