Stochastic background models incorporating spatial correlations can be used to enhance the detection of targets in natural terrain imagery, but are generally difficult to apply when the statistics are non-Gaussian. Chapple and Bertilone (see Opt. Commun., vol.150, p.71-76, 1998) proposed a simple stochastic model for images of natural backgrounds based on the pointwise nonlinear transformation of Gaussian random fields, and demonstrated its effectiveness and computational efficiency in modeling the textures found in natural terrain imagery acquired from airborne IR sensors. In this paper, we show how this model can be used to design algorithms that detect small targets (up to several pixels in size) in natural imagery by identifying anomalous regions of the image where the statistics differ significantly from the rest of the background. All of the model-based algorithms described here involve nonlinear spatial processing prior to the final decision threshold. Monte Carlo testing reveals that the model-based algorithms generally perform better than both the adaptive threshold filter and the generalized matched filter for detecting low-contrast targets, despite the fact that they do not require the target statistics needed for constructing the matched filter.

Orthogonal distance regression (ODR) is widely used to fit a curve through scattered points in the plane. It generally produces good fits, but intuition and practice suggest it can give biased results when fitting closed convex curves or corners. ODR gives the maximum likelihood estimate of the best curve under a straightforward stochastic model for data generation. The paper proposes an extension of this model to include a reasonable partial prior for the distribution of samples along the curve. Although the associated optimisation problem for the maximum likelihood estimator under the extended model no longer has a simple form, it lends itself naturally to asymptotic approximation. The first order approximation is essentially ODR: the second order approximation has an extra contribution involving the local curvature. Finally the results are applied to the illustrative problem of fitting a circle through scattered data: ODR is shown to indeed give a biased estimate of the true radius, and this bias is reduced under the second order estimator.

Detecting background changes in scenes containing significant numbers of moving objects has several applications in video surveillance. One important example is the detection of suspicious packages left in busy airport terminals or train stations. The paper outlines a statistical approach to automatically detecting long term changes to the stationary component of a scene, and describes a prototype system which has been used to successfully demonstrate the feasibility of this approach.

Sea surface simulations are needed to generate realistic glitter in Monte-Carlo testing of automatic target detection in electro-optical imagery of sea scenes. Glitter is determined by the sea surface's height and slope. At present sea surfaces are generally modelled as correlated random fields. Current algorithms for generating large realizations of random fields generally produce correlated Gaussian fields, but the available empirical statistics on sea surfaces show a non-Gaussian distribution of point slope values. The paper introduces a class of non-Gaussian random fields with specified correlation functions and point distributions of slopes generated by pointwise transformation of Gaussian fields. This definition allows generation of large scale simulations of such fields through simple pointwise transformation of simulations of the associated Gaussians.>

We present a new approach to analysing the continuous Gabor transform and two critically sampled discretizations of it: the periodic finite-discrete and non-periodic finite-discrete versions. In particular, we distinguish between the analysis and synthesis forms of the transform, and introduce an intermediate operation that decomposes both transforms to collections of independent Toeplitz operators. In the continuous and the periodic finite-discrete case this decomposition allows us to show that for appropriate window functions the analysis and synthesis transforms are inverses of each other. In the nonperiodic finite-discrete case this relation no longer holds, but we are still able to use the decomposition and results on Toeplitz matrices to show that both transforms and their inverses are computable in O(PlogP) operations (after a setup cost of O(Plog/sup 2/P)) for P discrete samples. Moreover the decomposition also facilitates analysis of the conditioning of finite versions of the transform.>

Dembo et al. (see ibid., vol. 35, pp. 1206-1212, 1989) showed that an N/spl times/N positive definite Toeplitz matrix T could be embedded in a 2M/spl times/2M nonnegative definite circulant matrix S with M=O[/spl kappa/(T)N/sup 2/]. This paper shows that the size of the embedding can be reduced to M=O[/spl kappa/(T)/sup 1/2/N/sup 5/4/] and that this is best possible for the technique presented by Dembo et al.>