Volume 34 (2015)

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Browsing Volume 34 (2015) by Subject "and object representations"

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    Object Completion using k-Sparse Optimization
    (The Eurographics Association and John Wiley & Sons Ltd., 2015) Mavridis, Pavlos; Sipiran, Ivan; Andreadis, Anthousis; Papaioannou, Georgios; Stam, Jos and Mitra, Niloy J. and Xu, Kun
    We present a new method for the completion of partial globally-symmetric 3D objects, based on the detection of partial and approximate symmetries in the incomplete input dataset. In our approach, symmetry detection is formulated as a constrained sparsity maximization problem, which is solved efficiently using a robust RANSACbased optimizer. The detected partial symmetries are then reused iteratively, in order to complete the missing parts of the object. A global error relaxation method minimizes the accumulated alignment errors and a nonrigid registration approach applies local deformations in order to properly handle approximate symmetry. Unlike previous approaches, our method does not rely on the computation of features, it uniformly handles translational, rotational and reflectional symmetries and can provide plausible object completion results, even on challenging cases, where more than half of the target object is missing. We demonstrate our algorithm in the completion of 3D scans with varying levels of partiality and we show the applicability of our approach in the repair and completion of heavily eroded or incomplete cultural heritage objects.
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    Quaternion Julia Set Shape Optimization
    (The Eurographics Association and John Wiley & Sons Ltd., 2015) Kim, Theodore; Mirela Ben-Chen and Ligang Liu
    We present the first 3D algorithm capable of answering the question: what would a Mandelbrot-like set in the shape of a bunny look like? More concretely, can we find an iterated quaternion rational map whose potential field contains an isocontour with a desired shape? We show that it is possible to answer this question by casting it as a shape optimization that discovers novel, highly complex shapes. The problem can be written as an energy minimization, the optimization can be made practical by using an efficient method for gradient evaluation, and convergence can be accelerated by using a variety of multi-resolution strategies. The resulting shapes are not invariant under common operations such as translation, and instead undergo intricate, non-linear transformations.