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ABSTRACT: The problem of mapping a general iterative algorithm with nonunit increment/decrement steps of the loop indices onto a systolic array using space-time transformation is studied. Necessary and sufficient conditions for the existence of such a space-time mapping are presented. The latency of a systolic computation is characterised in terms of the spa-time mapping and the increment/decrement step size of the iterative algorithm. Formulas for the latency of linear and 2D systolic arrays are derived. An efficient space-time mapping using restricted row operations which guarantees unit latency, thereby maximising the utilisation of the processors, is also proposed. Necessary and sufficient conditions under which column operations can be used to derive a legitimate space-time mapping are presented. A theory relating concurrent error detection and space-time mapping in systolic arrays is proposed. Based on this theory, existing (ad hoc) concurrent error detection approaches can be explained.
Computers and Digital Techniques, IEE Proceedings E. 02/1993;
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ABSTRACT: A shape matching technique based on the straight line Hough transform (SLHT) is presented. In the θ-ρ space, the transform can be expressed as the sum of the translation term and the intrinsic term. This formulation allows the translation, rotation, and intrinsic parameters of the curve to be easily decoupled. A shape signature, called the scalable translation invariant rotation-to-shifting (STIRS) signature, is obtained from the θ-ρ space by computing the distances between pairs of points having the same θ value. This signature is invariant to translation and can be easily normalized, and rotation in the image space corresponds to circular shifting of the signature. Matching two signatures only amounts to computing a 1D correlation. The height and location of a peak (if it exists) indicate the similarity and orientation of the test object with respect to the reference object. The location of the test object is obtained, once the orientation is known, by an inverse transform (voting) from the θ-ρ space to the x - y plane
IEEE Transactions on Pattern Analysis and Machine Intelligence 12/1992; 14(11):1076-1089. · 4.91 Impact Factor
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ABSTRACT: A novel approach for the detection of parametric curves using the
straight-line Hough transform is presented. The transform function of a
curve can be expressed as the sum of two terms, namely, the intrinsic
term and the translation term. This representation allows a natural
decomposition of the high-dimensional parameter space into three
subspaces: the intrinsic curve parameters, translation, and rotation. By
eliminating either the translation term or the intrinsic term, one can
easily determine the parameters of the remaining term. The complexity of
this method depends mainly on the angular resolution, which is
relatively independent of the arc length of the curve. The computational
complexity of this approach compares favorably with that of other
approaches based on the Hough transform
Pattern Recognition, 1990. Proceedings., 10th International Conference on; 07/1990
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ABSTRACT: Presents a critical study of two approaches, the classical RC-cut
approach and H.T. Kung and M.S. Lam's (Proc. 1984 MIT Conf. Advanced
Res. VLSI p.74-83, 1984) RCS-cut approach, for reconfiguring faulty
systolic arrays. The amount of cell (processing element) redundancy
needed to ensure successful reconfiguration into an
n × n array is considered. It is shown that no
polynomial bounded redundancy is sufficient for the classical approach,
whereas O( n <sup>2</sup>log n ) redundancy is sufficient
for the Kung and Lams approach. The number of faulty cells that can be
tolerated in a given array regardless of their locations is
characterized and derived. It is shown that, for both approaches, in
almost all cases a square array has better fault tolerance than a
rectangular array having the same number of cells. A minimal fault
pattern in a 2 n ×2 n array with 3 n +1
faults that is not reconfigurable into an n × n
array using either of the two approaches is established
IEEE Transactions on Computers 07/1989; · 1.10 Impact Factor
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ABSTRACT: The problem of restructuring systolic arrays with faulty cells is
considered. An approach to derive the required data-flow paths and
computational sites is proposed. The data skewing requirement, which
must be satisfied to find an input schedule, is also discussed.
Algorithms to restructure systolic arrays for three different
architectures of processing elements are presented. A systematic method
to retime the restructured array using additional programmable delays so
that the retimed array satisfies the data skewing requirements is
developed
IEEE Transactions on Computers 03/1989; · 1.10 Impact Factor
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ABSTRACT: Bit-serial systolic sorting in very large scale integration (VLSI) is considered. Lower bounds on the area, computation time, and flush time for such a sorter are derived for three different input formats, namely the bitwise, the wordwise and the unconstrained formats. The logic design and CMOS circuit design of an optimal bit-serial wordwise systolic sorter are presented. The performance characteristics of the designed chip are discussed.
Computers and Digital Techniques, IEE Proceedings E. 06/1987;
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ABSTRACT: Hough Transformation (HT) is an efficient method to detect straight lines in digital pictures. In the conventional HT, pixel contiguity is not taken into account, and this leads to the following drawbacks: (1) actual length of line segments cannot be computed; (2) colinear line segments cannot be distinguished; and (3) very often, false lines are detected and short lines go undetected. This paper proposes a modified Hough Transformation which performs contiguity check in a simple and efficient way. A systolic architecture that implements this modified transform is presented. The systolic array takes the bit-map of the binary picture as input and processes one row/column of pixels concurrently. The area-time complexity of the proposed architecture is shown to be superior to the conventional sequential algorithm. Preliminary simulation results are presented.
Pattern Recognition.
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ABSTRACT: Hough transform is a well-known method for detecting parametric curves in binary images. One major drawback of the method is that the transform requires time and memory space exponential in the number of parameters of the curves. An effective approach to reduce both the time and space requirement is the parameter space decomposition. In this paper, we present two methods for the detection of ellipses based on the straight line Hough transform (SLHT).The SLHT of a curve in the θ-π space can be expressed as the sum of two terms, namely, the translation term, and the intrinsic term. One useful property of this representation is that it allows the translation, rotation and intrinsic parametersof the curve be separated easily. Timing performance of the proposed methods compares favorably with the other Hough-based methods.
Pattern Recognition Letters.
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ABSTRACT: A notion of systolicity based on embeddability of processing structures is introduced. This notion characterizes the systolic structures that can be extended to solve problems of larger size, without a corresponding increase in processing time. A mathematical model for specifying such extendable structures is developed. The extensions of these structures are specified by extension rules using wavefronts and interconnection functions. An approach to deriving the algorithm schema corresponding to the computation performed by extendable structures is discussed. A simple necessary and sufficient condition for the systolicity of these structures is finally established.
Journal of Parallel and Distributed Computing 3(3):373-397. · 0.86 Impact Factor
