Magnus Oskarsson

Branch-and-Bound Methods for Euclidean Registration Problems

In this paper, we propose a practical and efficient method for finding the globally optimal solution to the problem of determining the pose of an object. We present a framework that allows us to use point-to-point, point-to-line, and point-to-plane correspondences for solving various types of pose and registration problems involving euclidean (or similarity) transformations. Traditional methods such as the iterative closest point algorithm or bundle adjustment methods for camera pose may get trapped in local minima due to the nonconvexity of the corresponding optimization problem. Our approach of solving the mathematical optimization problems guarantees global optimality. The optimization scheme is based on ideas from global optimization theory, in particular convex underestimators in combination with branch-and-bound methods. We provide a provably optimal algorithm and demonstrate good performance on both synthetic and real data. We also give examples of where traditional methods fail due to the local minima problem.

Adaptive enhancement and noise reduction in very low light-level video

A general methodology for noise reduction and contrast enhancement in very noisy image data with low dynamic range is presented. Video footage recorded in very dim light is especially targeted. Smoothing kernels that automatically adapt to the local spatio-temporal intensity structure in the image sequences are constructed in order to preserve and enhance fine spatial detail and prevent motion blur. In color image data, the chromaticity is restored and demosaicing of raw RGB input data is performed simultaneously with the noise reduction. The method is very general, contains few user-defined parameters and has been developed for efficient parallel computation using a GPU. The technique has been applied to image sequences with various degrees of darkness and noise levels, and results from some of these tests, and comparisons to other methods, are presented. The present work has been inspired by research on vision in nocturnal animals, particularly the spatial and temporal visual summation that allows these animals to see in dim light.

Box Jellyfish Use Terrestrial Visual Cues for Navigation

Box jellyfish have an impressive set of 24 eyes of four different types, including eyes structurally similar to those of vertebrates and cephalopods [1, 2]. However, the known visual responses are restricted to simple phototaxis, shadow responses, and object avoidance responses [3-8], and it has been a puzzle why they need such a complex set of eyes. Here we report that medusae of the box jellyfish Tripedalia cystophora are capable of visually guided navigation in mangrove swamps using terrestrial structures seen through the water surface. They detect the mangrove canopy by an eye type that is specialized to peer up through the water surface and that is suspended such that it is constantly looking straight up, irrespective of the orientation of the jellyfish. The visual information is used to navigate to the preferred habitat at the edge of mangrove lagoons.

Solutions and Ambiguities of the Structure and Motion Problem for 1DRetinal Vision

In this paper we investigate the geometry and algebra of multiple one-dimensional projections of a two-dimensional environment. This is relevant for one-dimensional cameras, e.g. as used in certain autonomous guided vehicles. It is also relevant for understanding the projection of lines in ordinary vision. A third application is on ordinary vision of vehicles undergoing so called planar motion. The structure and motion problem for such cameras is studied and the two possible minimal cases is solved. The technique of solving these questions reveal interesting ambiguities. It is shown that for each solution with three images there is an ambiguous solution. It is also shown that for each solution for four points there is an ambiguous solution. The connection between these two different types of ambiguities is also given. Although the paper deals with calibrated cameras, it is shown that similar results exist for uncalibrated cameras.

The Registration Problem Revisited: Optimal Solutions From Points, Lines and Planes

In this paper we propose a practical and efficient method for finding the globally optimal solution to the problem of pose estimation of a known object. We present a framework that allows us to use both point-to-point, point-to-line and point-to-plane correspondences in the optimization algorithm. Traditional methods such as the iterative closest point algorithm may get trapped in local minima due to the non-convexity of the problem, however, our approach guarantees global optimality. The approach is based on ideas from global optimization theory, in particular, convex under-estimators in combination with branch and bound. We provide a provably optimal algorithm and demonstrate good performance on both synthetic and real data.

Accurate Localization and Pose Estimation for Large 3D Models

We consider the problem of localizing a novel image in a large 3D model. In principle, this is just an instance of camera pose estimation, but the scale introduces some challenging problems. For one, it makes the correspondence problem very difficult and it is likely that there will be a significant rate of outliers to handle. In this paper we use recent theoretical as well as technical advances to tackle these problems. Many modern cameras and phones have gravitational sensors that allow us to reduce the search space. Further, there are new techniques to efficiently and reliably deal with extreme rates of outliers. We extend these methods to camera pose estimation by using accurate approximations and fast polynomial solvers. Experimental results are given demonstrating that it is possible to reliably estimate the camera pose despite more than 99% of outlier correspondences.

A Convex Approach to Low Rank Matrix Approximation with Missing Data

Many computer vision problems can be formulated as low rank bilinear minimization problems. One reason for the success of these problems is that they can be efficiently solved using singular value decomposition. However this approach fails if the measurement matrix contains missing data. In this paper we propose a new method for estimating missing data. Our approach is similar to that of L 1 approximation schemes that have been successfully used for recovering sparse solutions of under-determined linear systems. We use the nuclear norm to formulate a convex approximation of the missing data problem. The method has been tested on real and synthetic images with promising results.

Structure and motion from lines under affine projections

In this paper we investigate the geometry and algebra of multiple projections of lines with affine cameras. Previously, the case of seven lines in three images has been studied. It was thought that this was the minimal data necessary for recovering affine structure and motion and that there are in general two solutions. It was also thought that these two solutions persist with more than seven lines. In this paper it is shown that the minimal cases are six lines in three images and five lines in four images. These cases are solved and it is shown that there are in general four solutions in both problems. Two almost minimal cases (seven lines in three images and six lines in four images) are solved using linear methods. Furthermore, it is shown that the solution is in general unique in these almost minimal cases. Finally, experiments are conducted on both simulated and real data in order to show the applicability of the theory.

Optimal Estimation of Perspective Camera Pose

In this paper we propose a practical and efficient method for finding the globally optimal solution to the problem of camera pose estimation for calibrated cameras. While traditional methods may get trapped in local minima, due to the non-convexity of the problem, we have developed an approach that guarantees global optimality. The scheme is based on ideas from global optimization theory, in particular, convex under-estimators in combination with branch and bound. We provide a provably optimal algorithm and demonstrate good performance on both synthetic and real data

City-Scale Localization for Cameras with Known Vertical Direction

We consider the problem of localizing a novel image in a large 3D model, given that the gravitational vector is known. In principle, this is just an instance of camera pose estimation, but the scale of the problem introduces some interesting challenges. Most importantly, it makes the correspondence problem very difficult so there will often be a significant number of outliers to handle. To tackle this problem, we use recent theoretical as well as technical advances. Many modern cameras and phones have gravitational sensors that allow us to reduce the search space. Further, there are new techniques to efficiently and reliably deal with extreme rates of outliers. We extend these methods to camera pose estimation by using accurate approximations and fast polynomial solvers. Experimental results are given demonstrating that it is possible to reliably estimate the camera pose despite cases with more than 99 percent outlier correspondences in city-scale models with several millions of 3D points.