This paper tackles the problem of data abstraction in the context of 3D point sets. Our method classifies points into different geometric primitives, such as planes and cones, leading to a compact representation of the data. Being based on a semi-global Hough voting scheme, the method does not need initialization and is robust, accurate, and efficient. We use a local, low-dimensional parameterization of primitives to determine type, shape and pose of the object that a point belongs to. This makes our algorithm suitable to run on devices with low computational power, as often required in robotics applications. The evaluation shows that our method outperforms state-of-the-art methods both in terms of accuracy and robustness.

In computer vision, many problems can be formulated as finding a low rank approximation of a given matrix. Ideally, if all elements of the measurement matrix are available, this is easily solved in the L2-norm using factorization. However, in practice this is rarely the case. Lately, this problem has been addressed using different approaches, one is to replace the rank term by the convex nuclear norm, another is to derive the convex envelope of the rank term plus a data term. In the latter case, matrices are divided into sub-matrices and the envelope is computed for each subblock individually. In this paper a new convex envelope is derived which takes all sub-matrices into account simultaneously. This leads to a simpler formulation, using only one parameter to control the trade-of between rank and data fit, for applications where one seeks low rank approximations of multiple matrices with the same rank. We show in this paper how our general framework can be used for manifold denoising of several images at once, as well as just denoising one image. Experimental comparisons show that our method achieves results similar to state-of-the-art approaches while being applicable for other problems such as linear shape model estimation.

Online 3D reconstruction has been an active research area for a long time. Since the release of the Microsoft Kinect Camera and publication of KinectFusion [11] attention has been drawn how to acquire dense models in real-time. In this paper we present a method to make online 3D reconstruction which increases robustness for scenes with little structure information and little texture information. It is shown empirically that our proposed method also increases robustness when the distance between the camera positions becomes larger than what is commonly assumed. Quantitative and qualitative results suggest that this approach can handle situations where other well-known methods fail. This is important in, for example, robotics applications like when the camera position and the 3D model must be created online in real-time.

One of the major research areas in computer vision is scene reconstruction from image streams. The advent of RGB-D cameras, such as the Microsoft Kinect, has lead to new possibilities for performing accurate and dense 3D reconstruction. There are already well-working algorithms to acquire 3D models from depth sensors, both for large and small scale scenes. However, these methods often break down when the scene geometry is not so informative, for example, in the case of planar surfaces. Similarly, standard image-based methods fail for texture-less scenes. We combine both color and depth measurements from an RGB-D sensor to simultaneously reconstruct both the camera motion and the scene geometry in a robust manner. Experiments on real data show that we can accurately reconstruct large-scale 3D scenes despite many planar surfaces.