The problem of subtracting the background in an image sequence is central to computer vision. The general idea is to model the values of each pixel as a random variable. This approach has proved to be efficient when treating slowly varying changes or changes that are fairly periodic. In this paper we propose a novel method for background and foreground estimation that efficiently handles changes that also occur with non periodicity and fast. Furthermore, the method makes only very mild assumptions about the scene making it able to operate in a wide variety of conditions. This is done by introducing a novel set of invariants that are independent to the over all intensity level in the images. By using these features instead of the raw pixel data we automatically obtain a background estimator that is insensitive to rapid changes in lighting conditions. Furthermore, the features can be computed very efficiently using the so called integral image. Inspired by the work in [17] we update the probability model over time to make it able to handle new objects entering the background, but here we work directly with the histogram which reduces the execution time considerably. Finally, we present test data that shows that the model works well in some outdoor scenes. In particular it is shown that it can handle difficult outdoor scenes with rapidly bypassing clouds. 1

In this paper we propose a novel method for recognizing handwritten symbols. The method relies on two fundamental ideas. The first is to treat the character as a parameterized curve and to associate geometric invariants to it, and the second is to use a so called proximity measure for comparing invariants. The use of invariants makes the recognition insensitive to a preselected class of deformations. The class of transformations can for example be the affine or the positive similarity transformations. Furthermore, the entire curve is used in the recognition process and is treated as one object. Experiments indicate that the proposed recognition system performs well and is robust to the writing variations that exist between persons and for a single person at different instances, thus being promising for user independent character recognition.

In this paper we present a theory for obtaining densities that are important for computer vision. As a result of the theory we compute the exact and novel density of the slope of a line fitted to image points. This density makes it possible to obtain confidence intervals for the slope or to make hypothesis testing about if two intersecting lines form a corner or not. The theory also lets us derive a novel technique for maximum likelihood estimation, that can be used for computing the fundamental matrix, conics, or any other constraint that can be expressed by polynomials of degree 2. We present exact and novel densities for the fundamental matrix and conic constraints, that are needed for the estimation. Experiments show how the results can be used in practise to compute maximum likelihood estimates of the fundamental matrix.

We present a novel method for finding the optimal affine transformation for matching of images. The method requires no feature points, does not rely on normalization of images and can be tuned to highlight interesting parts in the images. Furthermore, the method does not need any derivatives for obtaining the affine transformation and it has a computational cost proportional to n/sup 2/logn for n/spl times/n images. The problem of finding the optimal affine transformation is solved by an iterative algorithm. In each step a global optimization is performed by the use of FFT. This global characteristic helps the algorithm from getting trapped in a local optimum. Novel theoretical results are presented that show under what restrictions the algorithm can be expected to work properly. Its intended primary use is for reconstruction problems in computer vision. These rely heavily on the establishment of point correspondences in the images. Since the method makes no assumptions on the images it can be used when feature points are difficult to detect. Experiments on real images are included and it is shown that the algorithm is robust and performs well even in difficult situations, with occlusions.

In this paper we extend the notion of affine shape, introduced by Sparr (1995, 1996), from finite point sets to curves. The extension makes it possible to reconstruct 3D-curves up to projective transformations, from a number of their 2D-projections. We also extend the bundle adjustment technique from point features to curves. The first step of the curve reconstruction algorithm is based on affine shape, is independent of choice of coordinates, robust, does not rely on any preselected parameters and works for an arbitrary number of images. In particular this means that a solution is given to the aperture problem of finding point correspondences between curves. The second step takes advantage of any knowledge of measurement errors in the images. This is possible by extending the bundle adjustment technique to curves. Finally, experiments are performed on both synthetic and real data to show the performance and applicability of the algorithm.

We propose a method for maximising the affine correlation between images. The method is more global in its search than for example steepest descent based methods. In a first approximation, there is no need to compute any derivatives and it is shown that the results are very good. The method is based on certain changes of coordinates in the images and extensive use of the fast Fourier transformation (FFT). This makes the method very fast, when implemented on a computer.

In this paper, we propose an algorithm for doing reconstruction of general 3D-curves from a number of 2D-images taken by uncalibrated cameras. No point correspondences between the images are assumed. The curve and the view points are uniquely reconstructed, modulo common projective transformations and the point correspondence problem is solved. Furthermore, the algorithm is independent of the choice of coordinates, as it is based on orthogonal projections and aligning subspaces. The algorithm is based on an extension of affine shape of finite point configurations to more general objects.

A novel recursive method for estimating structure and motion from image sequences is presented. The novelty lies in the fact that the output of the algorithm is independent of the chosen coordinate systems in the images as well as the ordering of the points. It relies on subspace methods and is derived from both ordinary coordinate representations and camera matrices and from a so called depth and shape analysis. Furthermore, no initial phase is needed to start up the algorithm. It starts directly with the first two images and incorporates new images as soon as new corresponding points are obtained. The performance of the algorithm is shown on simulated data. Moreover, the two different approaches, one using camera matrices and the other using the concepts of affine shape and depth, are unified into a general theory of structure and motion from image sequences.