Abstract
Pyramidal algorithms manipulate hierarchical representations of data and are used in many image processing applications, for example, in image segmentation and border extraction. We present a systolic array which performs pyramidal algorithms. The array is tow-dimensional with one processor per image pixel; the number of steps in its execution is independent of the size of the image. The derivation of the array is governed by a mechanical method whose input is a Pascal-like program. After a number of manual transformations that prepare the program for the method, correct and optimal parallelism is infused mechanically. A processor layout is selected, and the channel connections follow immediately.
Similar content being viewed by others
References
P.J. Burt, T.H. Hong and A. Rosenfeld, “Segmentation and Estimation of Image Region Properties through Cooperative Hierarchical Computation,”IEEE Trans. on Systems, Man and Cybernetics SMC-11, 12, 1981, pp. 802–809.
W.I. Grosky and R. Jain, “A Pyramid-Based Approach to Segmentation Applied to Region Matching,”IEEE Trans. on Pattern Analysis and Machine Intelligence PAMI-8, 5, 1986, pp. 639–650.
T.H. Hong, K.A. Narayanan, S. Peleg, and A. Rosenfeld, “Image Smoothing and Segmentation by Multiresolution Pixel Linking: Further Experiments and Extensions,”IEEE Transactions of Systems, Man and Cybernetics SMC-12, 5, 1982, pp. 611–622.
A. Rosenfeld, “Some Useful Properties of Pyramids,”Multiresolution Image Processing and Analysis, A. Rosenfeld (ed.), Series in Information Sciences, New York: Springer-Verlag, 1984, pp. 2–5.
S. Kasif and A. Rosenfeld, “Pyramid Linking is a Special Case of ISODATA,”IEEE Trans. on Systems, Man and Cybernetics SMC-13, 1, 1983, pp. 84–85.
T.H. Hong and A. Rosenfeld, “Compact Region Extraction Using Weighted Pixel Linking in a Pyramid,”IEEE Trans. Pattern Analysis and Machine Intelligence PAMI-6, 2, 1984, pp. 222–229.
H.T. Kung and C.E. Leiserson, “Algorithms for VLSI Processor Arrays,” inIntroduction to VLSI Systems, C. Mead and L. Conway (eds.), Reading, MA: Addison-Wesley, 1980, Sect. 8.3.
C.-H. Huang and C. Lengauer, “The Derivation of Systolic Implementations of Programs,”Acta Informatica 24, 6, 1987, pp. 595–632.
S.K. Rao and T. Kailath, “Regular Iterative Algorithms and their Implementations on Processor Arrays,”Proc. IEEE, 76, 2, 1988, pp. 259–282.
E.W. Dijkstra,A Discipline of Programming, Series in Automatic Computation, Englewood Cliffs, NJ: Prentice-Hall, 1976.
R.M. Karp, R.E. Miller and S. Winograd, “The Organization of Computations for Uniform Recurrence Equations,”J. ACM, 14, 3, 1967, pp. 563–590.
C. Lengauer, M. Barnett and D.G. Hudson, “Towards Systolizing Compilation,”Distributed Computing, 5, 1, 1991, pp. 7–24.
D. Gries, “The Multiple Assignment Statement,”IEEE Trans. on Software Engineering SE-4, 2, 1978, pp. 89–93.
P. Quinton and V. van Dongen, “The Mapping of Linear Recurrence Equations on Regular Arrays,”J. VLSI Signal Processing, 1, 1, 1989, pp. 95–113.
S.V. Rajopadhye, “Synthesizing Systolic Arrays with Control Signals from Recurrence Equations,”Distributed Computing, 3, 1989, pp. 88–105.
C. Lengauer, B. Sabata and F. Arman, “A Mechanically Derived Systolic Implementation of Pyramid Initialization,” Proc.Workshop on Hardware Specification, Verification and Synthesis: Mathematical Aspects, G. Brown and M. Leeser (eds.), Lecture Notes in Computer Science 408, New York: Springer-Verlag, 1990, pp. 90–105.
T. Kean and J. Gray, “Configurable Hardware: Two Case Studies of Micro-Grain Computation,”J. VLSI Signal Processing, 2, 1, 1990, pp. 9–16.
INMOS Ltd.,Transputer Reference Manual, Englewood Cliffs, NJ: Prentice-Hall, 1988.
C.-H. Huang and C. Lengauer, “An Incremental Mechanical Development of Systolic Solutions to the Algebraic Path Problem,”Acta Informatica 27, 2, 1989, pp. 97–124.
J. Cibulskis and C.R. Dyer, “Node Linking Strategies in Pyramids for Image Segmentation,” inMultiresolution Image Processing and Analysis, A. Rosenfeld (ed.), Series in Information Sciences, New York/Berlin: Springer-Verlag, 1984, pp. 109–120.
T. Ichikawa, “A Pyramid Representation of Images and its Feature Extraction Facility,”IEEE Trans. on Pattern Analysis and Machine Intelligence PAMI-3, 3, 1981, pp. 257–264.
B.P. Kjell and C.R. Dyer, “Segmentation of Textured Images by Pyarmid Linking,” inPyramidal Systems for Computer Vision, V. Cantoni and S. Levialdi (eds.), NATO ASI Series, vol. F-25, New York/Berlin: Springer-Verlag, 1986, pp. 273–288.
A. Rosenfeld, “Some Pyramid Techniques for Image Segmentation,” inPyramidal Systems for Computer Vision, V. Cantoni and S. Levialdi (eds.), NATO ASI Series, vol. F-25, New York: Springer-Verlag, 1986, pp. 261–271.
Author information
Authors and Affiliations
Additional information
Supported by an Overseas Research Students Award and a University of Edinburgh Postgraduate Fellowship.
An erratum to this article is available at http://dx.doi.org/10.1007/BF00930620.
Rights and permissions
About this article
Cite this article
Lengauer, C., Xue, J. A systolic array for pyramidal algorithms. J VLSI Sign Process Syst Sign Image Video Technol 3, 237–257 (1991). https://doi.org/10.1007/BF00925834
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/BF00925834