Parametric Fourier image characterization toolkit

ABSTRACT

A suite of APL programs is described for characterization of bounded images for on-line process control or for artificial intelligence recognition functions. Beginning with an acquired threshold and edge enhanced image, the programs: detect the edges and close all bounded areas in the image produce arrays with the (x,y) locations of the boundaries of each object (bounded area) in the field, allowing for touching, segmented, perforated, embedded objects (all reported as separate arrays of sequenced coordinate pairs) compress the image using a quad tree procedure for archival or legal purposes fit parametric polynomial, conventional Fourier or inner product-outer product - matrix inversion Fourier equations to the object boundaries, to any desired number of coefficient terms or number of boundary pixel points. displays results and analyses of degree of fit in a windowed environment performs accept-reject-identify checks by comparison of the calculated Fourier coefficients from “perfect” objects or from a CAD system database. The system is written in 500 lines of IBM APL/PC Version 2 for a PC/AT with 80287 co-processor, and it is presently being interfaced to Data Translation image grabber hardware and software, with 512x512 acquisition resolution. Parameterization fitting accuracy is increased by considering not pixel center coordinates but intersection of boundary regression lines with pixel boundaries. The user interface makes the suite of programs manageable by a competent technical user without programming or APL knowledge.

REFERENCES

• 1: Alonso, J.R.F., Vilsten, V.T., and Kotaridis, S., "Parametric Fourier Method Application to Image Acquisition, Compression, Storage and Comparison. Array Processing Oriented Formulation." Proceedings AUSGRAPH 85 Third Australasian Conference on Computer Graphics, Brisbane, 12-16 August 1985.
• 2: Alonso, J.R.F., Tava. V., and Verhoosel, P., "Array Formulation of General Image Analysis Problem." Proceedings International Conference in Modelling and Simulation, Melbourne, 14-16 October, 1987.
• 3: Alonso, J.R.F., "Application of Image Analysis Algorithms and Equipment to the Solution of Integro-Differential Equations." Society of Manufacturing Engineers Journal, Melbourne, Vol. 8, No.5, Page 18-23, 1987.

INDEX TERMS

Primary Classification:
  J. Computer Applications
  J.7 COMPUTERS IN OTHER SYSTEMS
      Subjects: Process control

Additional Classification:
  D. Software
  D.2 SOFTWARE ENGINEERING
      D.2.2 Design Tools and Techniques
          Subjects: User interfaces

  G. Mathematics of Computing
  G.1 NUMERICAL ANALYSIS
      G.1.3 Numerical Linear Algebra
          Subjects: Matrix inversion
  G.2 DISCRETE MATHEMATICS
      G.2.2 Graph Theory
          Subjects: Trees

  I. Computing Methodologies
  I.2 ARTIFICIAL INTELLIGENCE
  I.3 COMPUTER GRAPHICS
      I.3.4 Graphics Utilities
          Subjects: Graphics packages

  K. Computing Milieux
  K.8 PERSONAL COMPUTING

      Nouns: IBM PC

General Terms:
Algorithms, Human Factors, Theory