GASP : Geometric Association with Surface Patches

A fundamental challenge to sensory processing tasks in perception and robotics is the problem of obtaining data associations across views. We present a robust solution for ascertaining potentially dense surface patch (superpixel) associations, requiring just range information. Our approach involves decomposition of a view into regularized surface patches. We represent them as sequences expressing geometry invariantly over their superpixel neighborhoods, as uniquely consistent partial orderings. We match these representations through an optimal sequence comparison metric based on the Damerau-Levenshtein distance - enabling robust association with quadratic complexity (in contrast to hitherto employed joint matching formulations which are NP-complete). The approach is able to perform under wide baselines, heavy rotations, partial overlaps, significant occlusions and sensor noise. The technique does not require any priors -- motion or otherwise, and does not make restrictive assumptions on scene structure and sensor movement. It does not require appearance -- is hence more widely applicable than appearance reliant methods, and invulnerable to related ambiguities such as textureless or aliased content. We present promising qualitative and quantitative results under diverse settings, along with comparatives with popular approaches based on range as well as RGB-D data.Comment: International Conference on 3D Vision, 201

The Argyris isogeometric space on unstructured multi-patch planar domains

Multi-patch spline parametrizations are used in geometric design and isogeometric analysis to represent complex domains. We deal with a particular class of $C^0$ planar multi-patch spline parametrizations called analysis-suitable $G^1$ (AS-$G^{1}$) multi-patch parametrizations (Collin, Sangalli, Takacs; CAGD, 2016). This class of parametrizations has to satisfy specific geometric continuity constraints, and is of importance since it allows to construct, on the multi-patch domain, $C^1$ isogeometric spaces with optimal approximation properties. It was demonstrated in (Kapl, Sangalli, Takacs; CAD, 2018) that AS-$G^1$ multi-patch parametrizations are suitable for modeling complex planar multi-patch domains. In this work, we construct a basis, and an associated dual basis, for a specific $C^1$ isogeometric spline space $\mathcal{W}$ over a given AS-$G^1$ multi-patch parametrization. We call the space $\mathcal{W}$ the Argyris isogeometric space, since it is $C^1$ across interfaces and $C^2$ at all vertices and generalizes the idea of Argyris finite elements to tensor-product splines. The considered space $\mathcal{W}$ is a subspace of the entire $C^1$ isogeometric space $\mathcal{V}^{1}$, which maintains the reproduction properties of traces and normal derivatives along the interfaces. Moreover, it reproduces all derivatives up to second order at the vertices. In contrast to $\mathcal{V}^{1}$, the dimension of $\mathcal{W}$ does not depend on the domain parametrization, and $\mathcal{W}$ admits a basis and dual basis which possess a simple explicit representation and local support. We conclude the paper with some numerical experiments, which exhibit the optimal approximation order of the Argyris isogeometric space $\mathcal{W}$ and demonstrate the applicability of our approach for isogeometric analysis