Many change detection algorithms work by calculating the probability of change on a pixel-wise basis. This is a disadvantage since one is usually looking for regions of change, and such information is not used in pixel-wise classification - per definition. This issue becomes apparent in the face of noise, implying that the pixel-wise classifier is also noisy. There is thus a need for incorporating local homogeneity constraints into such a change detection framework. For this modelling task Markov Random Fields are suitable. Markov Random Fields have, however, previously been plagued by lack of efficient optimization methods or numerical solvers. We here address the issue of efficient incorporation of local homogeneity constraints into change detection algorithms. We do this by exploiting recent advances in graph based algorithms for Markov Random Fields. This is combined with an IR-MAD change detector, and demonstrated on real data with good results.

A method for locating distorted grid structures in images is presented. The method is based on the theories of template matching and Bayesian image restoration. The grid is modeled as a deformable template. Prior knowledge of the grid is described through a Markov random field (MRF) model which represents the spatial coordinates of the grid nodes. Knowledge of how grid nodes are depicted in the observed image is described through the observation model. The prior consists of a node prior and an arc (edge) prior, both modeled as Gaussian MRFs. The node prior models variations in the positions of grid nodes and the arc prior models variations in row and column spacing across the grid. Grid matching is done by placing an initial rough grid over the image and applying an ensemble annealing scheme to maximize the posterior distribution of the grid. The method can be applied to noisy images with missing grid nodes and grid-node artifacts and the method accommodates a wide range of grid distortions including: large-scale warping, varying row/column spacing, as well as nonrigid random fluctuations of the grid nodes. The methodology is demonstrated in two case studies concerning (1) localization of DNA signals in hybridization filters and (2) localization of knit units in textile samples.

Factorization algorithms for recovering structure and motion from an image stream have many advantages, but they usually require a set of well-tracked features. Such a set is in generally not available in practical applications. There is thus a need for making factorization algorithms deal effectively with errors in the tracked features. We propose a new and computationally efficient algorithm for applying an arbitrary error function in the factorization scheme. This algorithm enables the use of robust statistical techniques and arbitrary noise models for the individual features. These techniques and models enable the factorization scheme to deal effectively with mismatched features, missing features, and noise on the individual features. The proposed approach further includes a new method for Euclidean reconstruction that significantly improves convergence of the factorization algorithms. The proposed algorithm has been implemented as a modification of the Christy-Horaud factorization scheme, which yields a perspective reconstruction. Based on this implementation, a considerable increase in error tolerance is demonstrated on real and synthetic data. The proposed scheme can, however, be applied to most other factorization algorithms.

Synthetic aperture radar (SAR) images acquired by radar satellites at different times can be combined into interferograms that reveal information about the change in range from ground to satellite, wrapped into phase fringes corresponding to half the radar wavelength. We describe a methodology that uses Markov random field (MRF) regularization and simulated annealing optimization to unwrap such differential interferograms. Often, repeated Global Positioning System (GPS) geodetic measurements are available in an area covered by interferograms. Here, such repeated GPS observations are used to provide a complementary measurement of the unwrapped change in range at sparse locations. The process of unwrapping interferograms can be initialized and guided with such sparsely located "correct" values. Both interferograms and GPS observations may include several error factors, which are reduced before combining the two observations. GPS-measured range change is used to eliminate residual orbital error. In the unwrapping procedure, a vectorized lowpass filter is used to gain temporarily increased smoother variation of the phase. For the purposes of initializing the unwrapping process, virtual unwrapped interferograms are created by ordinary kriging of GPS-measured range change. The initial interferograms are then optimized further by using MRF regularization that incorporate the assumption of a smoothly varying displacement field and the relationship of the unwrapped images to the GPS observations. A simulated annealing optimization algorithm is used to find an optimal solution of the MRF regularization. The smoothed unwrapped interferograms are then used to construct unwrapped versions of the unfiltered input interferogram. Several additional image analyses methods are used in the optimization process to make the unwrapping more efficient and faster. The unwrapping technique is applied to unwrap interferograms from the Reykjanes Peninsula, in southwest Iceland.

General deformable models have reduced the need for hand crafting new models for every new problem, but still most of the general models rely on manual interaction by an expert, when applied to a new problem, e.g. for selecting parameters and initialization. We propose a full and unified scheme for applying the general deformable template model proposed by (Grenander et al., 1991) to a new problem with minimal manual interaction, beside supplying a training set, which can be done by a non-expert user. The main contributions compared to previous work are a supervised learning scheme for the model parameters, a very fast general initialization algorithm and an adaptive likelihood model based on local means. The model parameters are trained by a combination of a 2D shape learning algorithm and a maximum likelihood based criteria. The fast initialization algorithm is based on a search approach using a filter interpretation of the likelihood model.

Deformable templates have been intensively studied in image analysis through the last decade, but despite its significance the estimation of model parameters has received little attention. We present a method for supervised and unsupervised model parameter estimation using a general Bayesian formulation of deformable templates. In the supervised estimation the parameters are estimated using a likelihood and a least squares criterion given a training set. For most deformable template models the supervised estimation provides the opportunity for simulation of the prior model. The unsupervised method is based on a modified version of the EM algorithm. Experimental results for a deformable template used for textile inspection are presented.