Kent, John T.; Mardia, Kanti V.; Walder, Alistair N. Conditional cyclic Markov random fields. (English) Zbl 0874.60045 Adv. Appl. Probab. 28, No. 1, 1-12 (1996). The authors consider cyclic Gaussian Markov random fields (MRF) as models for the digital image of closed contours in the plane. Some of these models were initiated by U. Grenander, Y. Chow and D. M. Keenan [“Hands: A pattern theoretic study of biological shapes” (1990; Zbl 0808.68018)]. The covariance matrices of the MRF describing the vertices of the contour are compared with those describing the edges. Moreover, the authors determine the limiting behaviour of the MRF when the vertices are closely spaced. They show that the quadratic form of the residuals (weighted by the covariance matrix) behaves like their quadratic variation when the number of vertices grows to infinity. The relationship to the theory of “snakes” is given by Kass et al. [Internat. J. Comp. Vis. 1, 321-331 (1987)]. The article ends with a discussion of possible applications of these models to object detection. Reviewer: M.Dozzi (Nancy) Cited in 1 ReviewCited in 2 Documents MSC: 60G60 Random fields 60F05 Central limit and other weak theorems Keywords:deformable templates; cyclic stationarity; limiting behaviour; snakes; cyclic Gaussian Markov random fields Citations:Zbl 0808.68018 PDFBibTeX XMLCite \textit{J. T. Kent} et al., Adv. Appl. Probab. 28, No. 1, 1--12 (1996; Zbl 0874.60045) Full Text: DOI