High Performance Issues in Image Processing and Computer Vision

Typical image processing and computer vision tasks found in industrial, medical, and military applications require real-time solutions. These requirements have motivated the design of many parallel architectures and algorithms. Recently, a new architecture called the reconfigurable mesh has been proposed. This thesis addresses a number of problems in image processing and computer vision on reconfigurable meshes. We first show that a number of low-level descriptors of a digitized image such as the perimeter, area, histogram and median row can be reduced to computing the sum of all the integers in a matrix, which in turn can be reduced to computing the prefix sums of a binary sequence and the prefix sums of an integer sequence. We then propose a new computational paradigm for reconfigurable meshes, that is, identifying an entity by a bus and performing computations on the bus to obtain properties of the entity. Using the new paradigm, we solve a number of mid-level vision tasks including the Hough transform and component labeling. Finally, a VLSI-optimal constant time algorithm for computing the convex hull of a set of planar points is presented based on a VLSI-optimal constant time sorting algorithm. As by-products, two basic data movement techniques, computing the prefix sums of a binary sequence and computing the prefix maxima of a sequence of real numbers, and a VLSI-optimal constant time sorting algorithm have been developed. These by-products are interesting in their own right. In addition, they can be exploited to obtain efficient algorithms for a number of computational problems

A constant time parallel algorithm for the triangularization of a sparse matrix using CD-PARBS

An algorithm for the triangularization of a matrix whose graph is a directed acyclic graph, popularly known as dag, is presented. One of the algorithms for obtaining this special form has been given by Sargent and Westerberg. Their approach is practically good but sequential in nature and cannot be parallelised easily. In this work we present a parallel algorithm which is based on the observation that, if we find the transitive closure matrix of a directed acyclic graph, count the number of entries in each row, sort them in the ascending order of their values and rank them accordingly, we get a lower triangular matrix. We show that all these operations can be done using 3-d CD- PARBS(Complete Directed PARBS) in constant time. The same approach can be used for the block cases, producing the same relabelling as produced by Tarjan’s algorithm, in constant time. To the best of our knowledge, it is the first approach to solve such problems using directed PARBS

An efficient parallel algorithm for the all pairs shortest path problem using processor arrays with reconfigurable bus systems

The all pairs shortest path problem is a class of the algebraic path problem. Many parallel algorithms for the solution of this problem appear in the literature. One of the efficient parallel algorithms on W-RAM model is given by Kucera [17]. Though efficient, algorithms written for the W-RAM model of parallel computation are too idealistic to be implemented on the current hardware. In this report we present an efficient parallel algorithm for the solution of this problem using a relatively new model of parallel computing, Processor Arrays with Reconfigurable Bus Systems. The parallel time complexity of this algorithm is O(log2 n) and processors complexity is n2 × n × n

A fast parallel algorithm for special linear systems of equations using processor arrays with reconfigurable bus systems

A parallel algorithm using Processor Arrays with Reconfigurable Bus Systems has been designed to solve dense Symmetric Positive Definite (SPD) systems of equations Ax = b. The key content of this report is the parallelisation of the algorithm by Delosme & Ipson [8]. In order to design a parallel algorithm for PARBS, many procedures involved in [8] are handled in a slightly different way. The parallel time and processor’s complexity of each step of the algorithm is calculated. The parallel time complexity is O(n) using 2n × 2n × 5n number of Processing Elements

Mesh Connected Computers With Multiple Fixed Buses: Packet Routing, Sorting and Selection

Mesh connected computers have become attractive models of computing because of their varied special features. In this paper we consider two variations of the mesh model: 1) a mesh with fixed buses, and 2) a mesh with reconfigurable buses. Both these models have been the subject matter of extensive previous research. We solve numerous important problems related to packet routing, sorting, and selection on these models. In particular, we provide lower bounds and very nearly matching upper bounds for the following problems on both these models: 1) Routing on a linear array; and 2) k-k routing, k-k sorting, and cut through routing on a 2D mesh for any k ≥ 12. We provide an improved algorithm for 1-1 routing and a matching sorting algorithm. In addition we present greedy algorithms for 1-1 routing, k-k routing, cut through routing, and k-k sorting that are better on average and supply matching lower bounds. We also show that sorting can be performed in logarithmic time on a mesh with fixed buses. As a consequence we present an optimal randomized selection algorithm. In addition we provide a selection algorithm for the mesh with reconfigurable buses whose time bound is significantly better than the existing ones. Our algorithms have considerably better time bounds than many existing best known algorithms

Routing with locality in partitioned-bus meshes

We show that adding partitioned-buses (as opposed to long buses that span an entire row or column) to ordinary meshes can reduce the routing time by approximately one-third for permutation routing with locality. A matching time lower bound is also proved. The result can be generalized to multi-packet routing.published_or_final_versio

Randomized Routing and Sorting on the Reconfigurable Mesh

In this paper we demonstrate the power of reconfiguration by presenting efficient randomized algorithms for both packet routing and sorting on a reconfigurable mesh connected computer (referred to simply as the mesh from hereon). The run times of these algorithms are better than the best achievable time bounds on a conventional mesh. In particular, we show that permutation routing problem can be solved on a linear array of size n in 3/4n steps, whereas n-1 is the best possible run time without reconfiguration. We also show that permutation routing on an n x n reconfigurable mesh can be done in time n + o(n)using a randomized algorithm or in time 1.25n + o(n) deterministically. In contrast, 2n-2 is the diameter of a conventional mesh and hence routing and sorting will need at least 2n-2 steps on a conventional mesh. In addition we show that the problem of sorting can be solved in time n+ o(n). All these time bounds hold with high probability. The bisection lower bound for both sorting and routing on the mesh is n/2, and hence our algorithms have nearly optimal time bounds

Visibility-Related Problems on Parallel Computational Models

Visibility-related problems find applications in seemingly unrelated and diverse fields such as computer graphics, scene analysis, robotics and VLSI design. While there are common threads running through these problems, most existing solutions do not exploit these commonalities. With this in mind, this thesis identifies these common threads and provides a unified approach to solve these problems and develops solutions that can be viewed as template algorithms for an abstract computational model. A template algorithm provides an architecture independent solution for a problem, from which solutions can be generated for diverse computational models. In particular, the template algorithms presented in this work lead to optimal solutions to various visibility-related problems on fine-grain mesh connected computers such as meshes with multiple broadcasting and reconfigurable meshes, and also on coarse-grain multicomputers. Visibility-related problems studied in this thesis can be broadly classified into Object Visibility and Triangulation problems. To demonstrate the practical relevance of these algorithms, two of the fundamental template algorithms identified as powerful tools in almost every algorithm designed in this work were implemented on an IBM-SP2. The code was developed in the C language, using MPI, and can easily be ported to many commercially available parallel computers

High-Performance Bus-Based Architectures - Guest Editorial

(First paragrapg) This special issue of VLSI Design presents a collection of seven papers selected out of more than 35 submissions received following the Call for Papers. Each submission was sent to three referees, all of them experts in the area of bus-based architectures. The result is impressive. The papers featured in this Special Issue cover a wide range of topics from sorting to string matching, to load balancing, to simulation, matrix operations, to robotics, to the design of high-performance scalable architectures

Geometric modeling for computer aided design

The primary goal of this grant has been the design and implementation of software to be used in the conceptual design of aerospace vehicles particularly focused on the elements of geometric design, graphical user interfaces, and the interaction of the multitude of software typically used in this engineering environment. This has resulted in the development of several analysis packages and design studies. These include two major software systems currently used in the conceptual level design of aerospace vehicles. These tools are SMART, the Solid Modeling Aerospace Research Tool, and EASIE, the Environment for Software Integration and Execution. Additional software tools were designed and implemented to address the needs of the engineer working in the conceptual design environment. SMART provides conceptual designers with a rapid prototyping capability and several engineering analysis capabilities. In addition, SMART has a carefully engineered user interface that makes it easy to learn and use. Finally, a number of specialty characteristics have been built into SMART which allow it to be used efficiently as a front end geometry processor for other analysis packages. EASIE provides a set of interactive utilities that simplify the task of building and executing computer aided design systems consisting of diverse, stand-alone, analysis codes. Resulting in a streamlining of the exchange of data between programs reducing errors and improving the efficiency. EASIE provides both a methodology and a collection of software tools to ease the task of coordinating engineering design and analysis codes