3D Object Super Resolution using Metric Tensor and Christoffel Symbols

Abstract

In this paper we address the problem of 3D super resolution. 3D super resolution is a process of generating high resolution point cloud, given a low resolution point cloud. We model 3D object as a set of Riemannian manifolds in continuous and discretized space. We propose to use Riemannian metric tensor and Christoffel symbols as a set of features to capture the inherent geometry of the 3D object. We propose a learning framework to decompose 3D object using metric tensor and Christoffel symbols into a set of basis functions to selectively super resolve the 3D object. We demonstrate the proposed algorithm on 3D objects and achieve better results than reported in literature.

Framework for 3D object hole filling

“…We aim to fill in the missing regions using a selective interpolation framework by considering metric tensor and Christoffel symbols as geometric features [9]. Inspired by the authors work in [10] where metric tensor and Christoffel symbols were used for 3D object super resolution, we extend these geometric features to address the problem of 3D object hole filling. Our proposed framework for hole filling is summarized and illustrated in Fig.…”

“…As stated in [12]: A Riemannian manifold is a real smooth differential manifold M equipped with an inner product g on tangent space at each point p. The Riemannian metric tensor g is computed at every point p locally by, where ds 2 is the geodesic distance between two neighboring points on the manifold and dx µ , dx ν are the contravariant tangent vectors between the neighboring points in the tangent plane of the manifold, computed as numerical differential line elements. The geodesic distance between neighborhood points in the region H neigh is computed as proposed in [10] and the contravariant tangent vectors dx µ , dx ν are computed as numerical differential line elements in the manifold.…”

Example-Based Super-Resolution for Point-Cloud Video

“…Mixed-resolution scenarios (interleaved low-and fullresolution frames) naturally emerge from this representation: a low-resolution error-protected base layer, for instance, can be enhanced from a previously decoded full-resolution frame [8,9]. The super-resolution technique was already explored when processing 3D signals, with works trying to increase data resolution in depth maps [10,11,12]. They usually explore geometric properties to improve the level of detail of a depth map.…”