Hostname: page-component-586b7cd67f-l7hp2 Total loading time: 0 Render date: 2024-11-24T12:00:45.718Z Has data issue: false hasContentIssue false

Inference on binary images from binary data

Published online by Cambridge University Press:  01 July 2016

C. A. Glasbey*
Affiliation:
University of Edinburgh
*
Postal address: Biomathematics and Statistics Scotland, The University of Edinburgh, James Clerk Maxwell Building, King's Buildings, Edinburgh, EH9 3JZ, UK.

Abstract

The problem addressed is to reverse the degradation which occurs when images are digitised: they are blurred, subjected to noise and rounding error, and sampled only at a lattice of points. Inference is considered for the fundamental case of binary scenes, binary data and isotropic blur. The inferential process is separable into two stages: first from the lattice points to a binary image in continuous space and then the reversal of thresholding and blur. Methods are motivated by, and illustrated using, an electron micrograph of an immunogold-labelled section of tulip virus.

Type
Stochastic Geometry and Statistical Applications
Copyright
Copyright © Applied Probability Trust 1996 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Ambartzumian, R. V. (1981) Combinatorial Integral Geometry: with Applications to Mathematical Stereology . Wiley, Chichester.Google Scholar
Aykroyd, R. G. and Green, P. J. (1991) Global and local priors, and the location of lesions using gamma-camera imagery. Phil. Trans. R. Soc. A 337, 323342.Google Scholar
Bleher, P. M., Cheng, Z. M., Dyson, F. J. and Lebowitz, J. L. (1993) Distribution of the error term for the number of lattice points inside a shifted circle. Commun. Math. Phys. 154, 433469.Google Scholar
Boult, T. E. and Wolberg, G. (1993) Local image-reconstruction and subpixel restoration algorithms. CVGIP: Graph. Models Image Processing 55, 6377.Google Scholar
Bruckstein, A. M. (1987) On optimal image digitization. IEEE Trans. Acoustics, Speech Signal Processing 35, 553555.Google Scholar
Davies, E. R. (1990) Machine Vision. Academic Press, New York.Google Scholar
Dorst, L. and Duin, R. P. W. (1984) Spirograph theory: a framework for calculations of digitized straight lines. IEEE Trans on Pattern Anal. Machine Intelligence 6, 632639.CrossRefGoogle ScholarPubMed
Fu, C. C., Yang, T. S. and Stone, D. R. (1991) Enhancement of lithographic patterns by using serif features. IEEE Trans. Electron Devices 38, 25992603.CrossRefGoogle Scholar
Gilliland, D. C. (1962) Integral of the bivariate normal distribution over an offset circle. J. Amer. Statist. Assoc. 57, 758768.CrossRefGoogle Scholar
Grenander, U. (1976) Pattern Synthesis: Lectures in Pattern Theory , Vol. 1. Springer, New York.Google Scholar
Havelock, D. I. (1989) Geometric precision in noise-free digital images. IEEE Trans. Pattern Anal. Machine Intelligence 11, 10651075.CrossRefGoogle Scholar
Havelock, D. I. (1991) The topology of locales and its effects on position uncertainty. IEEE Trans. Pattern Anal. Machine Intelligence 13, 380386.CrossRefGoogle Scholar
Hitchcock, D. and Glasbey, C. A. (1995) Binary image restoration at sub-pixel resolution from multi-level data. BioSS internal report. .Google Scholar
Holgate, P. (1990) Lattice points in a random parallelogram. Adv. Appl. Prob. 22, 484485.Google Scholar
Jennison, C. and Jubb, M. (1991) Aggregation and refinement in binary image restoration. Spatial Statistics and Imaging (IMS Lecture Notes). Hayward . pp. 150162.Google Scholar
Kendall, D. G. (1948) On the number of lattice points inside a random oval. Quart. J. Math. 19, 126.CrossRefGoogle Scholar
Kendall, D. G. and Moran, P. A. P. (1962) Geometrical Probability. Griffin, London.Google Scholar
Kiryati, N. and Bruckstein, A. M. (1991) Gray levels can improve the performance of binary image digitizers. CVGIP: Graph. Models Image Processing 53, 3139.Google Scholar
Koplowitz, J. and Raj, A. P. S. (1987) A robust filtering algorithm for subpixel reconstruction of chain coded line drawings. IEEE Trans. Pattern Anal. Machine Intelligence 9, 451457.Google Scholar
Korostelev, A. P. and Tsybakov, A. B. (1993) Minimax Theory of Image Reconstruction. Springer, New York.CrossRefGoogle Scholar
Nakamura, A. and Aizawa, K. (1984) Digital circles. Comput. Vision, Graph. Image Processing 26, 242255.Google Scholar
Nielsen, L., Astrom, K. J. and Jury, E. I. (1984) Optimal digitization of 2-D images. IEEE Trans. Acoustics, Speech Signal Processing 32, 12471249.Google Scholar
Patel, J. K. and Read, C. B. (1982) Handbook of the Normal Distribution. Marcel Dekker, New York.Google Scholar
Pavlidis, T. (1981) Algorithms for Graphics and Image Processing. Computer Science Press, Rockville, MD.Google Scholar
Ripley, B. D. (1991) The use of spatial models as image priors. Spatial Statistics and Imaging (IMS Lecture Notes). Hayward. pp. 309340.Google Scholar
Roberts, I. M. (1994) Factors affecting the efficiency of immunogold labelling of plant virus antigens in thin sections. J. Virological Meth. 50, 155166.Google Scholar
Rosenfeld, A. and Kak, A. C. (1982) Digital Picture Processing. 2nd edn. Academic Press, San Diego.Google Scholar
Rudemo, M. and Stryhn, H. (1994) Approximating the distribution of maximum likelihood contour estimators in two-region images. Scand. J. Statist. 21, 4455.Google Scholar
Saleh, B. E. A. (1987) Image synthesis: discovery instead of recovery. In Image Recovery: Theory and Application. ed. Stark, H.. Academic Press, Orlando. pp. 463498.Google Scholar
Serra, J. (1982) Image Analysis and Mathematical Morphology . Academic Press, London.Google Scholar
Serra, J. (1988) Image Analysis and Mathematical Morphology. Vol. 2: Theoretical Advances. Academic Press, London.Google Scholar
Solomon, H. (1978) Geometric Probability. SIAM, Philadelphia.Google Scholar
Sriraman, R., Koplowitz, J. and Mohan, S. (1989) Tree searched chain coding for subpixel reconstruction of planar curves. IEEE Trans. Pattern Anal. Machine Intelligence 11, 95103.Google Scholar