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Variational surface reconstruction

The demand for capturing 3D models of real world objects or scenes has steadily increased in the past. Today, there are numerous developments that indicate an even greater importance in the future: Computer generated special effects are extensively used and highly benefit from such data, 3D printing is starting to become more affordable, and the ability to conveniently include 3D content in websites has quite matured. Last but not least, augmented reality is on the rise and might find a way into everyday life in the near future through devices such as the HoloLens for example. This might open up various new applications that require knowledge about the geometry of real world objects or scenes. Thus 3D reconstruction has been and still is one of the most important research topics in the area of computer vision. Here, the reconstruction of a 3D model from a number of colour images with given camera poses is a common task known as multi-view stereo. We contribute to the two main steps that arise in popular strategies for solving this problem: The estimation of depth maps from multiple views and the integration of multiple depth maps into a single watertight surface. Concerning the former one, we generalise existing methods by introducing a parameterisation of depth. This allows to thoroughly analyse different choices and to theoretically and practically point out the benefits of an inverse depth parameterisation w.r.t. both the data and the smoothness term. Concerning the second step, we extend a popular volumetric approach by using anisotropic (direction-dependent) regularisation and relying on the Euclidean instead of the directional signed distance. Furthermore, we present an efficient parallel implementation on the GPU that uses a recently introduced cyclic solver named Fast Jacobi. While these two steps allow to obtain reconstructions in a multi-view stereo setting, we subsequently relax the constraint that the camera poses have to be known. To this end, we present a novel pipeline for 3D reconstruction from image sequences that solely relies on dense ideas. Each step minimises a suitable energy functional such that the modelling choices are transparent throughout the whole pipeline. This proves to be an interesting alternative to popular sparse approaches and leads to competitive results. When relying on sparse features, this only allows to estimate an oriented point cloud instead of a surface. Thus we finally propose a general higher order framework for the surface reconstruction from oriented points. This framework allows us to reach two goals: First, we can systematically understand and classify a number of existing methods. Second, it enables us to derive novel approaches to surface reconstruction from oriented points that are fairly simple and offer state-of-the-art performance.