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This paper is concerned with model fitting in the presence of noise and outliers. Previously it has been shown that the number of outliers can be minimized with polynomial complexity in the number of measurements. This paper improves on these results in two ways. First, it is shown that for a large class of problems, the statistically more desirable truncated L-2-norm can be optimized with the sam
The problem of fitting models to measured data has been studied extensively, not least in the field of computer vision. A central problem in this field is the difficulty in reliably find corresponding structures and points in different images, resulting in outlier data. This thesis presents theoretical results improving the understanding of the connection between model parameter estimation and pos
This work presents a study of sensor network calibration from time-difference-of-arrival (TDOA) measurements for cases when the dimensions spanned by the receivers and the transmitters differ. This could for example be if receivers are restricted to a line or plane or if the transmitting objects are moving linearly in space. Such calibration arises in several applications such as calibration of (a
The ability to quickly acquire 3D models is an essential capability needed in many disciplines including robotics, computer vision, geodesy, and architecture. In this paper we present a novel method for real-time camera tracking and 3D reconstruction of static indoor environments using an RGB-D sensor. We show that by representing the geometry with a signed distance function (SDF), the camera pose
The estimation of three-dimensional position information from two-dimensional images in computer vision systems can be formulated as a state estimation problem for a nonlinear perspective dynamic system. The multi-output state estimation problem has been treated by several authors using methods for nonlinear observer design. This paper shows that a perspective system can be transformed to two obse
This thesis concerns ego-motion and pose estimation of a single camera under the assumptions of planar motion and constant internal camera parameters. Planar motion is common for cameras mounted onto mobile robots, particularly in indoor scenarios, as they remain at a constant height above the ground plane. In Paper A, a parametrisation of the camera motion and pose is presented, along with an ite
Is the real problem in finding the relative orientation of two viewpoints the correspondence problem? We argue that this is only one difficulty. Even with known correspondences, popular methods like the eight point algorithm and minimal solvers may break down due to planar scenes or small relative motions. In this paper, we derive a simple, brute-force algorithm which is both robust to outliers an
Recent work on geometric vision problems has exploited convexity properties in order to obtain globally optimal solutions. In this paper we give an overview of these developments and show the tight connections between different types of convexity and optimality conditions for a large class of multiview geometry problems. We also show how the convexity properties are closely linked to different typ
Graph cuts methods are at the core of many state-of-the-art algorithms in computer vision due to their efficiency in computing globally optimal solutions. In this paper, we solve the maximum flow/minimum cut problem in parallel by splitting the graph into multiple parts and hence, further increase the computational efficacy of graph cuts. Optimality of the solution is guaranteed by dual decomposit
When robots are working in dynamic environments, close to humans lacking extensive knowledge of robotics, there is a strong need to simplify the user interaction and make the system execute as autonomously as possible. For industrial robots working side-by-side with humans in manufacturing industry, AI systems are necessary to lower the demand on programming time and expertise. We are convinced th
Abstract in UndeterminedReference attribute grammars (RAGs) provide a practical declarative means to implement programming language compilers and other tools. RAGs have previously been extended to support both circular attributes and context-dependent declarative rewrites of the abstract syntax tree. In this previous work, dependencies between circular attributes and rewrites are not considered. I
Terrestrial ecosystem models are employed to calculate the sources and sinks of carbon dioxide between land and atmosphere. These models may be heavily parameterised. Where reliable estimates are unavailable for a parameter, it remains highly uncertain; uncertainty of parameters can substantially contribute to overall model output uncertainty. This paper builds on the work of the terrestrial Carbo
In experimental design and 3D reconstruction it is desirable to minimize the number of observations required to reach a prescribed estimation accuracy. Many approaches in the literature attempt to find the next best view from which to measure, and iterate this procedure. This paper discusses a continuous optimization method for finding a whole set of future imaging locations which minimize the rec
Automated object detection is perhaps the most central task of computer vision and arguably the most difficult one. This paper extends previous work on part-based models by using accurate geometric models both in the learning phase and at detection. In the learning phase manual annotations are used to reduce perspective distortion before learning the part-based models. That training is performed o
The problem of finding a low rank approximation of a given measurement matrix is of key interest in computer vision. If all the elements of the measurement matrix are available, the problem can be solved using factorization. However, in the case of missing data no satisfactory solution exists. Recent approaches replace the rank term with the weaker (but convex) nuclear norm. In this paper we show
Fast algorithms for unequally spaced discrete Laplace transforms are presented. The algorithms are approximate up to a prescribed choice of computational precision, and they employ modified versions of algorithms for unequally spaced fast Fourier transforms using Gaussians. Various configurations of sums with equally and unequally spaced points can be dealt with. In contrast to previously presente
In this paper, we describe a novel approach to create 3D miniatures of persons using a Kinect sensor and a 3D color printer. To achieve this, we acquire color and depth images while the person is rotating on a swivel chair. We represent the model with a signed distance function which is updated and visualized as the images are captured for immediate feedback. Our approach automatically fills small
We introduce a multi-region model for simultaneous segmentation of medical images. In contrast to many other models, geometric constraints such as inclusion and exclusion between the regions are enforced, which makes it possible to correctly segment different regions even if the intensity distributions are identical. We efficiently optimize the model using a combination of graph cuts and Lagrangia
Underdrawings and pentimenti-typically revealed through x-ray imaging and infrared reflectography-comprise important evidence about the intermediate states of an artwork and thus the working methods of its creator.(1) To this end, Shahram, Stork and Donoho introduced the De-pict algorithm, which recovers layers of brush strokes in paintings with open brush work where several layers are partially v
