3 research outputs found

    Stereographic Visualization of 5-Dimensional Regular Polytopes

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    Regular polytopes (RPs) are an extension of 2D (two-dimensional) regular polygons and 3D regular polyhedra in n-dimensional (n≥4) space. The high abstraction and perfect symmetry are their most prominent features. The traditional projections only show vertex and edge information. Although such projections can preserve the highest degree of symmetry of the RPs, they can not transmit their metric or topological information. Based on the generalized stereographic projection, this paper establishes visualization methods for 5D RPs, which can preserve symmetries and convey general metric and topological data. It is a general strategy that can be extended to visualize n-dimensional RPs (n>5)

    Dense real-time 3D reconstruction from multiple images

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    The rapid increase in computer graphics and acquisition technologies has led to the widespread use of 3D models. Techniques for 3D reconstruction from multiple views aim to recover the structure of a scene and the position and orientation (motion) of the camera using only the geometrical constraints in 2D images. This problem, known as Structure from Motion (SfM) has been the focus of a great deal of research effort in recent years; however, the automatic, dense, real-time and accurate reconstruction of a scene is still a major research challenge. This thesis presents work that targets the development of efficient algorithms to produce high quality and accurate reconstructions, introducing new computer vision techniques for camera motion calibration, dense SfM reconstruction and dense real-time 3D reconstruction. In SfM, a second challenge is to build an effective reconstruction framework that provides dense and high quality surface modelling. This thesis develops a complete, automatic and flexible system with a simple user-interface of `raw images to 3D surface representation'. As part of the proposed image reconstruction approach, this thesis introduces an accurate and reliable region-growing algorithm to propagate the dense matching points from the sparse key points among all stereo pairs. This dense 3D reconstruction proposal addresses the deficiencies of existing SfM systems built on sparsely distributed 3D point clouds which are insufficient for reconstructing a complete 3D model of a scene. The existing SfM reconstruction methods perform a bundle adjustment optimization of the global geometry in order to obtain an accurate model. Such an optimization is very computational expensive and cannot be implemented in a real-time application. Extended Kalman Filter (EKF) Simultaneous Localization and Mapping (SLAM) considers the problem of concurrently estimating in real-time the structure of the surrounding world, perceived by moving sensors (cameras), simultaneously localizing in it. However, standard EKF-SLAM techniques are susceptible to errors introduced during the state prediction and measurement prediction linearization.

    27th Annual European Symposium on Algorithms: ESA 2019, September 9-11, 2019, Munich/Garching, Germany

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