Fast algorithms for clipping lines and line segments in E2

E ² are presented. The suggested algorithms are based on a technique of coding the line direction together with the end points of the clipped line segment. They solve all cases more effectively. The algorithms are convenient for clippings lines or line segments by rectangle. Theoretical considerations and experimental results are also presented.     

An algorithm for the asynchronous Write-All problem based on process collision

Summary. The problem of using P processes to write a given value to all positions of a shared array of size N is called the Write-All problem. We present and analyze an asynchronous algorithm with work complexity , where (assuming and ). Our algorithm is a generalization of the naive two-processor algorithm where the two processes each start at one side of the array and walk towards each other until they collide. Received: October 1999 / Accepted: September 2000     

An adaptive collect algorithm with applications

Summary. In a shared-memory distributed system, n independent asynchronous processes communicate by reading and writing to shared variables. An algorithm is adaptive (to total contention) if its step complexity depends only on the actual number, k, of active processes in the execution; this number is unknown in advance and may change in different executions of the algorithm. Adaptive algorithms are inherently wait-free, providing fault-tolerance in the presence of an arbitrary number of crash failures and different processes' speed. A wait-free adaptive collect algorithm with O(k) step complexity is presented, together with its applications in wait-free adaptive alg orithms for atomic snapshots, immediate snapshots and renaming. Received: August 1999 / Accepted: August 2001     

Towards cognitive evaluation of computer-drawn sketches

This paper seeks to raise visual comparisons beyond subjective opinions into evidence-based visual reasoning. It provides an informal deductive analysis of the marks in sketches derived with two competing line-filtering algorithms. This prompted the novel speculation that the visual system might be placing some types of anomalies in the foreground of mental 3D space, where they can be ignored. A brief survey is provided to encourage informed debate. Although the proposed cognitive computation was not automated, it justified the rejection of the Douglas–Peucker algorithm in favour of Visvalingam's algorithm in subsequent research within the Cartographic Information Systems Research Group (CISRG).     

An Efficient Algorithm for Line Clipping by Convex and Non-convex Polyhedra in E3

A new algorithm for clipping lines against convex polyhedron with O(N) complexity is given with modification for non-convex polyhedron. The suggested algorithm is faster for higher number of facets of the given polyhedron than the traditional Cyrus-Beck's algorithm. Some principal results of comparison of all algorithms are shown and give some ideas how the proposed algorithm could be used effectively.     

On the magic of SLIDE

Subspace-based line detection (SLIDE) is a novel approach for straight line fitting that has recently been suggested by Aghajan and Kailath. It is based on an analogy made between a straight line in an image and a planar propagating wavefront impinging on an array of sensors. Efficient sensor array processing algorithms are used to detect the parameters of the line. SLIDE is computationally cheaper than the Hough transform, but it has not been clear whether or not this is a magical free bonus. In particular, it has not been known how the breakpoints of SLIDE relate to those of the Hough transform. We compare the failure modes and limitations of the two algorithms and demonstrate that SLIDE is significantly less robust than the Hough transform.     

Dynamic sculpting and animation of free-form subdivision solids

Published online: 15 March 2002     

Real-time CAM-based Hough transform algorithm and its performance evaluation

Abstract. This paper proposes a highly parallel Hough transform algorithm for real-time straight-line extraction and its hardware implementation on a content-addressable memory (CAM). To achieve high-speed processing, incrementation for voting, which composes the Hough transform, and calculations for coordinate updating are carried out for the every scan line, not every edge pixel, and extracting maxima in Hough space is executed by parallel comparing. Moreover, variously weighted voting achieves more accurate line extraction in spite of the quantization error and noise in the image space. In the implementation, the CAM acts as a PE (processing-element) array that effectively performs highly parallel processing for the Hough transform and also as a memory for two-dimensional Hough space, and both voting and peak extraction are directly executed by the CAM. Evaluations of CAM hardware size, processing time and the accuracy of line extraction show that a real-time and high-resolution Hough transform for a 256256 picture can be achieved using a single CAM chip with current VLSI technology. This CAM-based Hough transform algorithm promises to be an important step towards the realization of a real-time and compact image-understanding system. Received: 15 August 1998 / Accepted: 15 March 2000     

On the power of shared object types to implement one-resilient Consensus

Abstract. In this paper we study the ability of shared object types to implement Consensus in asynchronous shared-memory systems where at most one process may crash. More specifically, we consider the following question: Let and be a set of object types that can be used to solve one-resilient Consensus among n processes. Can always be used to solve one-resilient Consensus among n - 1 processes? We prove that for n = 3 the answer is negative, even if consists only ofdeterministic types. (This strengthens an earlier result by the first author proving the same fact for nondeterministic types.) We also prove that, in contrast, for the answer to the above question is affirmative. Received: July 1997 / Accepted: May 2000     

An empirical measure of the performance of a document image segmentation algorithm

Document image segmentation is the first step in document image analysis and understanding. One major problem centres on the performance analysis of the evolving segmentation algorithms. The use of a standard document database maintained at the Universities/Research Laboratories helps to solve the problem of getting authentic data sources and other information, but some methodologies have to be used for performance analysis of the segmentation. We describe a new document model in terms of a bounding box representation of its constituent parts and suggest an empirical measure of performance of a segmentation algorithm based on this new graph-like model of the document. Besides the global error measures, the proposed method also produces segment-wise details of common segmentation problems such as horizontal and vertical split and merge as well as invalid and mismatched regions. Received July 14, 2000 / Revised June 12, 2001[-1mm]     

Optimistic parallel Delaunay triangulation

The paper describes a new parallel algorithm of Delaunay triangulation based on randomized incremental insertion. The algorithm is practical, simple and can be modified also for constrained triangulation or tetrahedralization. It was developed for architectures with a lower degree of parallelism, such as several-processor workstations, and tested on up to 8 processors. Published online: November 20, 2002 This work was supported by the Ministry of Education of The Czech Republic, project MSM 235 200 005     

Verification of the randomized consensus algorithm of Aspnes and Herlihy: a case study

Summary. The Probabilistic I/O Automaton model of [31] is used as the basis for a formal presentation and proof of the randomized consensus algorithm of Aspnes and Herlihy. The algorithm guarantees termination within expected polynomial time. The Aspnes-Herlihy algorithm is a rather complex algorithm. Processes move through a succession of asynchronous rounds, attempting to agree at each round. At each round, the agreement attempt involves a distributed random walk. The algorithm is hard to analyze because of its use of nontrivial results of probability theory (specifically, random walk theory which is based on infinitely many coin flips rather than on finitely many coin flips), because of its complex setting, including asynchrony and both nondeterministic and probabilistic choice, and because of the interplay among several different sub-protocols. We formalize the Aspnes-Herlihy algorithm using probabilistic I/O automata. In doing so, we decompose it formally into three subprotocols: one to carry out the agreement attempts, one to conduct the random walks, and one to implement a shared counter needed by the random walks. Properties of all three subprotocols are proved separately, and combined using general results about automaton composition. It turns out that most of the work involves proving non-probabilistic properties (invariants, simulation mappings, non-probabilistic progress properties, etc.). The probabilistic reasoning is isolated to a few small sections of the proof. The task of carrying out this proof has led us to develop several general proof techniques for probabilistic I/O automata. These include ways to combine expectations for different complexity measures, to compose expected complexity properties, to convert probabilistic claims to deterministic claims, to use abstraction mappings to prove probabilistic properties, and to apply random walk theory in a distributed computational setting. We apply all of these techniques to analyze the expected complexity of the algorithm. Received: February 1999 / Accepted: March 2000     

Heuristic and randomized optimization for the join ordering problem

Recent developments in database technology, such as deductive database systems, have given rise to the demand for new, cost-effective optimization techniques for join expressions. In this paper many different algorithms that compute approximate solutions for optimizing join orders are studied since traditional dynamic programming techniques are not appropriate for complex problems. Two possible solution spaces, the space of left-deep and bushy processing trees, are evaluated from a statistical point of view. The result is that the common limitation to left-deep processing trees is only advisable for certain join graph types. Basically, optimizers from three classes are analysed: heuristic, randomized and genetic algorithms. Each one is extensively scrutinized with respect to its working principle and its fitness for the desired application. It turns out that randomized and genetic algorithms are well suited for optimizing join expressions. They generate solutions of high quality within a reasonable running time. The benefits of heuristic optimizers, namely the short running time, are often outweighed by merely moderate optimization performance.     

SymGeons: A Prototype Model of Visual Complexity with Implications For Visual Control Tasks

The way in which humans perceive and react to visual complexity is an important issue in many areas of research and application, particularly because simplification of complex matter can lead to better understanding of both human behaviour in visual control tasks as well as the visual environment itself. One area of interest is how people perceive their world in terms of complexity and how this can be modelled mathematically and/or computationally. A prototype model of complexity has been derived using subcomponents called ‘SymGeons’ (Symmetrical Geometric Icons) based on Biederman’s original Geon Model for human perception. The SymGeons are primitive shapes which constitute foreground objects. This paper outlines the derivation and ongoing development of the ‘SymGeon’ model and how it compares to human perception of visual complexity. The application of the model to understanding complex human-in-the-loop problems associated with visual remote control operations, e.g. control of remotely operated vehicles, is discussed.     

Multicriteria-optimized triangulations

Published online: 2 August 2001     

Direct manipulation of FFD: efficient explicit solutions and decomposible multiple point constraints

Published online: 25 July 2001     

The BG distributed simulation algorithm

We present a shared memory algorithm that allows a set of f+1 processes to wait-free “simulate” a larger system of n processes, that may also exhibit up to f stopping failures. Applying this simulation algorithm to the k-set-agreement problem enables conversion of an arbitrary k-fault-tolerant{\it n}-process solution for the k-set-agreement problem into a wait-free k+1-process solution for the same problem. Since the k+1-processk-set-agreement problem has been shown to have no wait-free solution [5,18,26], this transformation implies that there is no k-fault-tolerant solution to the n-process k-set-agreement problem, for any n. More generally, the algorithm satisfies the requirements of a fault-tolerant distributed simulation.\/ The distributed simulation implements a notion of fault-tolerant reducibility\/ between decision problems. This paper defines these notions and gives examples of their application to fundamental distributed computing problems. The algorithm is presented and verified in terms of I/O automata. The presentation has a great deal of interesting modularity, expressed by I/O automaton composition and both forward and backward simulation relations. Composition is used to include a safe agreement\/ module as a subroutine. Forward and backward simulation relations are used to view the algorithm as implementing a multi-try snapshot\/ strategy. The main algorithm works in snapshot shared memory systems; a simple modification of the algorithm that works in read/write shared memory systems is also presented. Received: February 2001 / Accepted: February 2001     

An algorithm for blob hierarchy layout

Published online: 15 March 2002     

THRED: a two-handed design system

This paper describes a computer-aided design system for sketching free-form polygonal surfaces such as terrains and other natural objects. The user manipulates two 3D position and orientation trackers with three buttons, one for each hand. Each hand has a distinct role to play, with the dominant hand being responsible for picking and manipulation, and the less dominant hand being responsible for context setting of various kinds. The less dominant hand holds the workpiece, sets which refinement level that can be picked by the dominant hand, sets the constraint mode and the reshape operator, and generally acts as a counterpoint to the dominant hand. In this paper, the architecture of the system is outlined, the interaction techniques are presented, and a simple surface is shown.