View Selection with Geometric Uncertainty Modeling

Estimating positions of world points from features observed in images is a key problem in 3D reconstruction, image mosaicking,simultaneous localization and mapping and structure from motion. We consider a special instance in which there is a dominant ground plane $\mathcal{G}$ viewed from a parallel viewing plane $\mathcal{S}$ above it. Such instances commonly arise, for example, in aerial photography. Consider a world point $g \in \mathcal{G}$ and its worst case reconstruction uncertainty $\varepsilon(g,\mathcal{S})$ obtained by merging \emph{all} possible views of $g$ chosen from $\mathcal{S}$. We first show that one can pick two views $s_p$ and $s_q$ such that the uncertainty $\varepsilon(g,\{s_p,s_q\})$ obtained using only these two views is almost as good as (i.e. within a small constant factor of) $\varepsilon(g,\mathcal{S})$. Next, we extend the result to the entire ground plane $\mathcal{G}$ and show that one can pick a small subset of $\mathcal{S'} \subseteq \mathcal{S}$ (which grows only linearly with the area of $\mathcal{G}$) and still obtain a constant factor approximation, for every point $g \in \mathcal{G}$, to the minimum worst case estimate obtained by merging all views in $\mathcal{S}$. Finally, we present a multi-resolution view selection method which extends our techniques to non-planar scenes. We show that the method can produce rich and accurate dense reconstructions with a small number of views. Our results provide a view selection mechanism with provable performance guarantees which can drastically increase the speed of scene reconstruction algorithms. In addition to theoretical results, we demonstrate their effectiveness in an application where aerial imagery is used for monitoring farms and orchards

Measurement of Charged Pion Production Yields off the NuMI Target

The fixed-target MIPP experiment, Fermilab E907, was designed to measure the production of hadrons from the collisions of hadrons of momenta ranging from 5 to 120 GeV/c on a variety of nuclei. These data will generally improve the simulation of particle detectors and predictions of particle beam fluxes at accelerators. The spectrometer momentum resolution is between 3 and 4%, and particle identification is performed for particles ranging between 0.3 and 80 GeV/c using $dE/dx$, time-of-flight and Cherenkov radiation measurements. MIPP collected $1.42 \times10^6$ events of 120 GeV Main Injector protons striking a target used in the NuMI facility at Fermilab. The data have been analyzed and we present here charged pion yields per proton-on-target determined in bins of longitudinal and transverse momentum between 0.5 and 80 GeV/c, with combined statistical and systematic relative uncertainties between 5 and 10%.Comment: 15 pages, 13 figure

Precise orbit determination for NASA's earth observing system using GPS (Global Positioning System)

An application of a precision orbit determination technique for NASA's Earth Observing System (EOS) using the Global Positioning System (GPS) is described. This technique allows the geometric information from measurements of GPS carrier phase and P-code pseudo-range to be exploited while minimizing requirements for precision dynamical modeling. The method combines geometric and dynamic information to determine the spacecraft trajectory; the weight on the dynamic information is controlled by adjusting fictitious spacecraft accelerations in three dimensions which are treated as first order exponentially time correlated stochastic processes. By varying the time correlation and uncertainty of the stochastic accelerations, the technique can range from purely geometric to purely dynamic. Performance estimates for this technique as applied to the orbit geometry planned for the EOS platforms indicate that decimeter accuracies for EOS orbit position may be obtainable. The sensitivity of the predicted orbit uncertainties to model errors for station locations, nongravitational platform accelerations, and Earth gravity is also presented

An optimal finite-dimensional modeling in heat conduction and diffusion equations with partially known eigenstructure

An optimal finite-dimensional modeling technique is presented for a standard class of distributed parameter systems for heat and diffusion equations. A finite-dimensional nominal model with minimum error bounds in frequency domain is established for spectral systems with partially known eigenvalues and eigenfunctions. The result is derived from a completely characterized geometric figure upon complex plane, of all the frequency responses of the systems that have (i) a finite number of given time constants T/sub i/'s and modal coefficients k/sub i/'s, (ii) an upper bound /spl rho/ to the infinite sum of the absolute values of all the modal coefficients k/sub i/'s, (iii) an upper bound T to the unknown T/sub i/'s, and (iv) a given dc gain G(0). Discussions are made on how each parameter mentioned above makes contribution to bounding error or uncertainty, and we stress that steady state analysis for dc input is used effectively in reduced order modeling and bounding errors. The feasibility of the presented scheme is demonstrated by a simple example of heat conduction in ideal copper rod. </p

3D ShapeNets: A Deep Representation for Volumetric Shapes

3D shape is a crucial but heavily underutilized cue in today's computer vision systems, mostly due to the lack of a good generic shape representation. With the recent availability of inexpensive 2.5D depth sensors (e.g. Microsoft Kinect), it is becoming increasingly important to have a powerful 3D shape representation in the loop. Apart from category recognition, recovering full 3D shapes from view-based 2.5D depth maps is also a critical part of visual understanding. To this end, we propose to represent a geometric 3D shape as a probability distribution of binary variables on a 3D voxel grid, using a Convolutional Deep Belief Network. Our model, 3D ShapeNets, learns the distribution of complex 3D shapes across different object categories and arbitrary poses from raw CAD data, and discovers hierarchical compositional part representations automatically. It naturally supports joint object recognition and shape completion from 2.5D depth maps, and it enables active object recognition through view planning. To train our 3D deep learning model, we construct ModelNet -- a large-scale 3D CAD model dataset. Extensive experiments show that our 3D deep representation enables significant performance improvement over the-state-of-the-arts in a variety of tasks.Comment: to be appeared in CVPR 201

"TNOs are Cool": A survey of the trans-Neptunian region VI. Herschel/PACS observations and thermal modeling of 19 classical Kuiper belt objects

Trans-Neptunian objects (TNO) represent the leftovers of the formation of the Solar System. Their physical properties provide constraints to the models of formation and evolution of the various dynamical classes of objects in the outer Solar System. Based on a sample of 19 classical TNOs we determine radiometric sizes, geometric albedos and beaming parameters. Our sample is composed of both dynamically hot and cold classicals. We study the correlations of diameter and albedo of these two subsamples with each other and with orbital parameters, spectral slopes and colors. We have done three-band photometric observations with Herschel/PACS and we use a consistent method for data reduction and aperture photometry of this sample to obtain monochromatic flux densities at 70.0, 100.0 and 160.0 \mu m. Additionally, we use Spitzer/MIPS flux densities at 23.68 and 71.42 \mu m when available, and we present new Spitzer flux densities of eight targets. We derive diameters and albedos with the near-Earth asteroid thermal model (NEATM). As auxiliary data we use reexamined absolute visual magnitudes from the literature and data bases, part of which have been obtained by ground based programs in support of our Herschel key program. We have determined for the first time radiometric sizes and albedos of eight classical TNOs, and refined previous size and albedo estimates or limits of 11 other classicals. The new size estimates of 2002 MS4 and 120347 Salacia indicate that they are among the 10 largest TNOs known. Our new results confirm the recent findings that there are very diverse albedos among the classical TNOs and that cold classicals possess a high average albedo (0.17 +/- 0.04). Diameters of classical TNOs strongly correlate with orbital inclination in our sample. We also determine the bulk densities of six binary TNOs.Comment: 21 pages, 9 figures, accepted for publication in Astronomy and Astrophysic