Probabilistic RGB-D Odometry based on Points, Lines and Planes Under Depth Uncertainty

This work proposes a robust visual odometry method for structured environments that combines point features with line and plane segments, extracted through an RGB-D camera. Noisy depth maps are processed by a probabilistic depth fusion framework based on Mixtures of Gaussians to denoise and derive the depth uncertainty, which is then propagated throughout the visual odometry pipeline. Probabilistic 3D plane and line fitting solutions are used to model the uncertainties of the feature parameters and pose is estimated by combining the three types of primitives based on their uncertainties. Performance evaluation on RGB-D sequences collected in this work and two public RGB-D datasets: TUM and ICL-NUIM show the benefit of using the proposed depth fusion framework and combining the three feature-types, particularly in scenes with low-textured surfaces, dynamic objects and missing depth measurements.Comment: Major update: more results, depth filter released as opensource, 34 page

Covariant constraints for generic massive gravity and analysis of its characteristics

We perform a covariant constraint analysis of massive gravity valid for its entire parameter space, demonstrating that the model generically propagates five degrees of freedom; this is also verified by a new and streamlined Hamiltonian description. The constraint's covariant expression permits computation of the model's caustics. Although new features such as the dynamical Riemann tensor appear in the characteristic matrix, the model still exhibits the pathologies uncovered in earlier work: superluminality and likely acausalities.Comment: 26 pages LaTeX, references added, version to appear in Phys. Rev.

Regularized Newton Methods for X-ray Phase Contrast and General Imaging Problems

Like many other advanced imaging methods, x-ray phase contrast imaging and tomography require mathematical inversion of the observed data to obtain real-space information. While an accurate forward model describing the generally nonlinear image formation from a given object to the observations is often available, explicit inversion formulas are typically not known. Moreover, the measured data might be insufficient for stable image reconstruction, in which case it has to be complemented by suitable a priori information. In this work, regularized Newton methods are presented as a general framework for the solution of such ill-posed nonlinear imaging problems. For a proof of principle, the approach is applied to x-ray phase contrast imaging in the near-field propagation regime. Simultaneous recovery of the phase- and amplitude from a single near-field diffraction pattern without homogeneity constraints is demonstrated for the first time. The presented methods further permit all-at-once phase contrast tomography, i.e. simultaneous phase retrieval and tomographic inversion. We demonstrate the potential of this approach by three-dimensional imaging of a colloidal crystal at 95 nm isotropic resolution.Comment: (C)2016 Optical Society of America. One print or electronic copy may be made for personal use only. Systematic reproduction and distribution, duplication of any material in this paper for a fee or for commercial purposes, or modifications of the content of this paper are prohibite

Shape-from-shading using the heat equation

This paper offers two new directions to shape-from-shading, namely the use of the heat equation to smooth the field of surface normals and the recovery of surface height using a low-dimensional embedding. Turning our attention to the first of these contributions, we pose the problem of surface normal recovery as that of solving the steady state heat equation subject to the hard constraint that Lambert's law is satisfied. We perform our analysis on a plane perpendicular to the light source direction, where the z component of the surface normal is equal to the normalized image brightness. The x - y or azimuthal component of the surface normal is found by computing the gradient of a scalar field that evolves with time subject to the heat equation. We solve the heat equation for the scalar potential and, hence, recover the azimuthal component of the surface normal from the average image brightness, making use of a simple finite difference method. The second contribution is to pose the problem of recovering the surface height function as that of embedding the field of surface normals on a manifold so as to preserve the pattern of surface height differences and the lattice footprint of the surface normals. We experiment with the resulting method on a variety of real-world image data, where it produces qualitatively good reconstructed surfaces

3D scanning of cultural heritage with consumer depth cameras

Three dimensional reconstruction of cultural heritage objects is an expensive and time-consuming process. Recent consumer real-time depth acquisition devices, like Microsoft Kinect, allow very fast and simple acquisition of 3D views. However 3D scanning with such devices is a challenging task due to the limited accuracy and reliability of the acquired data. This paper introduces a 3D reconstruction pipeline suited to use consumer depth cameras as hand-held scanners for cultural heritage objects. Several new contributions have been made to achieve this result. They include an ad-hoc filtering scheme that exploits the model of the error on the acquired data and a novel algorithm for the extraction of salient points exploiting both depth and color data. Then the salient points are used within a modified version of the ICP algorithm that exploits both geometry and color distances to precisely align the views even when geometry information is not sufficient to constrain the registration. The proposed method, although applicable to generic scenes, has been tuned to the acquisition of sculptures and in this connection its performance is rather interesting as the experimental results indicate