937 research outputs found
Orthogonally Decoupled Variational Gaussian Processes
Gaussian processes (GPs) provide a powerful non-parametric framework for
reasoning over functions. Despite appealing theory, its superlinear
computational and memory complexities have presented a long-standing challenge.
State-of-the-art sparse variational inference methods trade modeling accuracy
against complexity. However, the complexities of these methods still scale
superlinearly in the number of basis functions, implying that that sparse GP
methods are able to learn from large datasets only when a small model is used.
Recently, a decoupled approach was proposed that removes the unnecessary
coupling between the complexities of modeling the mean and the covariance
functions of a GP. It achieves a linear complexity in the number of mean
parameters, so an expressive posterior mean function can be modeled. While
promising, this approach suffers from optimization difficulties due to
ill-conditioning and non-convexity. In this work, we propose an alternative
decoupled parametrization. It adopts an orthogonal basis in the mean function
to model the residues that cannot be learned by the standard coupled approach.
Therefore, our method extends, rather than replaces, the coupled approach to
achieve strictly better performance. This construction admits a straightforward
natural gradient update rule, so the structure of the information manifold that
is lost during decoupling can be leveraged to speed up learning. Empirically,
our algorithm demonstrates significantly faster convergence in multiple
experiments.Comment: Appearing NIPS 201
Purposive three-dimensional reconstruction by means of a controlled environment
Retrieving 3D data using imaging devices is a relevant task for many applications in medical imaging, surveillance, industrial quality control, and others. As soon as we gain procedural control over parameters of the imaging device, we encounter the necessity of well-defined reconstruction goals and we need methods to achieve them. Hence, we enter next-best-view planning. In this work, we present a formalization of the abstract view planning problem and deal with different planning aspects, whereat we focus on using an intensity camera without active illumination. As one aspect of view planning, employing a controlled environment also provides the planning and reconstruction methods with additional information. We incorporate the additional knowledge of camera parameters into the Kanade-Lucas-Tomasi method used for feature tracking. The resulting Guided KLT tracking method benefits from a constrained optimization space and yields improved accuracy while regarding the uncertainty of the additional input. Serving other planning tasks dealing with known objects, we propose a method for coarse registration of 3D surface triangulations. By the means of exact surface moments of surface triangulations we establish invariant surface descriptors based on moment invariants. These descriptors allow to tackle tasks of surface registration, classification, retrieval, and clustering, which are also relevant to view planning. In the main part of this work, we present a modular, online approach to view planning for 3D reconstruction. Based on the outcome of the Guided KLT tracking, we design a planning module for accuracy optimization with respect to an extended E-criterion. Further planning modules endow non-discrete surface estimation and visibility analysis. The modular nature of the proposed planning system allows to address a wide range of specific instances of view planning. The theoretical findings in this work are underlined by experiments evaluating the relevant terms
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