Compression for Smooth Shape Analysis

Most 3D shape analysis methods use triangular meshes to discretize both the shape and functions on it as piecewise linear functions. With this representation, shape analysis requires fine meshes to represent smooth shapes and geometric operators like normals, curvatures, or Laplace-Beltrami eigenfunctions at large computational and memory costs. We avoid this bottleneck with a compression technique that represents a smooth shape as subdivision surfaces and exploits the subdivision scheme to parametrize smooth functions on that shape with a few control parameters. This compression does not affect the accuracy of the Laplace-Beltrami operator and its eigenfunctions and allow us to compute shape descriptors and shape matchings at an accuracy comparable to triangular meshes but a fraction of the computational cost. Our framework can also compress surfaces represented by point clouds to do shape analysis of 3D scanning data

How smooth are particle trajectories in a Λ\LambdaCDM Universe?

It is shown here that in a flat, cold dark matter (CDM) dominated Universe with positive cosmological constant ($\Lambda$), modelled in terms of a Newtonian and collisionless fluid, particle trajectories are analytical in time (representable by a convergent Taylor series) until at least a finite time after decoupling. The time variable used for this statement is the cosmic scale factor, i.e., the "$a$-time", and not the cosmic time. For this, a Lagrangian-coordinates formulation of the Euler-Poisson equations is employed, originally used by Cauchy for 3-D incompressible flow. Temporal analyticity for $\Lambda$CDM is found to be a consequence of novel explicit all-order recursion relations for the $a$-time Taylor coefficients of the Lagrangian displacement field, from which we derive the convergence of the $a$-time Taylor series. A lower bound for the $a$-time where analyticity is guaranteed and shell-crossing is ruled out is obtained, whose value depends only on $\Lambda$ and on the initial spatial smoothness of the density field. The largest time interval is achieved when $\Lambda$ vanishes, i.e., for an Einstein-de Sitter universe. Analyticity holds also if, instead of the $a$-time, one uses the linear structure growth $D$-time, but no simple recursion relations are then obtained. The analyticity result also holds when a curvature term is included in the Friedmann equation for the background, but inclusion of a radiation term arising from the primordial era spoils analyticity.Comment: 16 pages, 4 figures, published in MNRAS, this paper introduces a convergent formulation of Lagrangian perturbation theory for LCD

Mesh-based 3D Textured Urban Mapping

In the era of autonomous driving, urban mapping represents a core step to let vehicles interact with the urban context. Successful mapping algorithms have been proposed in the last decade building the map leveraging on data from a single sensor. The focus of the system presented in this paper is twofold: the joint estimation of a 3D map from lidar data and images, based on a 3D mesh, and its texturing. Indeed, even if most surveying vehicles for mapping are endowed by cameras and lidar, existing mapping algorithms usually rely on either images or lidar data; moreover both image-based and lidar-based systems often represent the map as a point cloud, while a continuous textured mesh representation would be useful for visualization and navigation purposes. In the proposed framework, we join the accuracy of the 3D lidar data, and the dense information and appearance carried by the images, in estimating a visibility consistent map upon the lidar measurements, and refining it photometrically through the acquired images. We evaluate the proposed framework against the KITTI dataset and we show the performance improvement with respect to two state of the art urban mapping algorithms, and two widely used surface reconstruction algorithms in Computer Graphics.Comment: accepted at iros 201

3D Object Reconstruction from Hand-Object Interactions

Recent advances have enabled 3d object reconstruction approaches using a single off-the-shelf RGB-D camera. Although these approaches are successful for a wide range of object classes, they rely on stable and distinctive geometric or texture features. Many objects like mechanical parts, toys, household or decorative articles, however, are textureless and characterized by minimalistic shapes that are simple and symmetric. Existing in-hand scanning systems and 3d reconstruction techniques fail for such symmetric objects in the absence of highly distinctive features. In this work, we show that extracting 3d hand motion for in-hand scanning effectively facilitates the reconstruction of even featureless and highly symmetric objects and we present an approach that fuses the rich additional information of hands into a 3d reconstruction pipeline, significantly contributing to the state-of-the-art of in-hand scanning.Comment: International Conference on Computer Vision (ICCV) 2015, http://files.is.tue.mpg.de/dtzionas/In-Hand-Scannin