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NASA NTRS2013

Building a 2.5D Digital Elevation Model from 2D Imagery

When projecting imagery into a georeferenced coordinate frame, one needs to have some model of the geographical region that is being projected to. This model can sometimes be a simple geometrical curve, such as an ellipse or even a plane. However, to obtain accurate projections, one needs to have a more sophisticated model that encodes the undulations in the terrain including things like mountains, valleys, and even manmade structures. The product that is often used for this purpose is a Digital Elevation Model (DEM). The technology presented here generates a high-quality DEM from a collection of 2D images taken from multiple viewpoints, plus pose data for each of the images and a camera model for the sensor. The technology assumes that the images are all of the same region of the environment. The pose data for each image is used as an initial estimate of the geometric relationship between the images, but the pose data is often noisy and not of sufficient quality to build a high-quality DEM. Therefore, the source imagery is passed through a feature-tracking algorithm and multi-plane-homography algorithm, which refine the geometric transforms between images. The images and their refined poses are then passed to a stereo algorithm, which generates dense 3D data for each image in the sequence. The 3D data from each image is then placed into a consistent coordinate frame and passed to a routine that divides the coordinate frame into a number of cells. The 3D points that fall into each cell are collected, and basic statistics are applied to determine the elevation of that cell. The result of this step is a DEM that is in an arbitrary coordinate frame. This DEM is then filtered and smoothed in order to remove small artifacts. The final step in the algorithm is to take the initial DEM and rotate and translate it to be in the world coordinate frame [such as UTM (Universal Transverse Mercator), MGRS (Military Grid Reference System), or geodetic] such that it can be saved in a standard DEM format and used for projection.

Padgett, Curtis W.↗

NASA NTRS2017

Harmonized Landsat/Sentinel-2 Reflectance Products for Land Monitoring (Invited)

Many land applications require more frequent observations than can be obtained from a single 'Landsat class' sensor. Agricultural monitoring, inland water quality assessment, stand-scale phenology, and numerous other applications all require near-daily imagery at better than 1ha resolution. Thus the land science community has begun expressing a desire for a '30-meter MODIS' global monitoring capability. One cost-effective way to achieve this goal is via merging data from multiple, international observatories into a single virtual constellation. The Harmonized Landsat/Sentinel-2 (HLS) project has been working to generate a seamless surface reflectance product by combining observations from USGS/NASA Landsat-8 and ESA Sentinel-2. Harmonization in this context requires a series of radiometric and geometric transforms to create a single surface reflectance time series agnostic to sensor origin. Radiometric corrections include a common atmospheric correction using the Landsat-8 LaSRC/6S approach, a simple BRDF adjustment to constant solar and nadir view angle, and spectral bandpass adjustments to fit the Landsat-8 OLI reference. Data are then resampled to a consistent 30m UTM grid, using the Sentinel-2 global tile system. Cloud and shadow masking are also implemented. Quality assurance (QA) involves comparison of the output 30m HLS products with near-simultaneous MODIS nadir-adjusted observations. Prototoype HLS products have been processed for approximately 7% of the global land area using the NASA Earth Exchange (NEX) compute environment at NASA Ames, and can be downloaded from the HLS web site (https://hls.gsfc.nasa.gov). A wall-to-wall North America data set is being prepared for 2018. This talk will review the objectives and status of the HLS project, and illustrate applications of high-density optical time series data for agriculture and ecology. We also discuss lessons learned from HLS in the general context of implementing virtual constellations.

Reflectance↗

NASA NTRS1984

Geometric interpretations of the Discrete Fourier Transform (DFT)

One, two, and three dimensional Discrete Fourier Transforms (DFT) and geometric interpretations of their periodicities are presented. These operators are examined for their relationship with the two sided, continuous Fourier transform. Discrete or continuous transforms of real functions have certain symmetry properties. The symmetries are examined for the one, two, and three dimensional cases. Extension to higher dimension is straight forward.

Campbell, C. W.↗

NASA NTRS1995

Thin-Film Power Transformers

Transformer core made of thin layers of insulating material interspersed with thin layers of ferromagnetic material. Flux-linking conductors made of thinner nonferromagnetic-conductor/insulator multilayers wrapped around core. Transformers have geometric features finer than those of transformers made in customary way by machining and mechanical pressing. In addition, some thin-film materials exhibit magnetic-flux-carrying capabilities superior to those of customary bulk transformer materials. Suitable for low-cost, high-yield mass production.

Katti, Romney R.↗

NASA NTRS1980

Three dimensional spline-generated coordinate transformations for grids around wing-body configurations

A direct algebraic method was developed and applied to generate three dimensional grids around wing-body configurations. The method used is a generalized transfinite interpolation method which generates the desired coordinate transformation using geometric data only on the boundaries of the domain of interest. The geometric data that can be specified includes not only coordinates on the boundaries but also out-of-surface parametric derivatives that give a very precise control over the transformation in the vicinity of the surface. In addition to this, the method gives good control over the stretching of the mesh between different boundaries.

Eriksson, L. E.↗

DOE OSTI2018

Computation at a coordinate singularity

Coordinate singularities are sometimes encountered in computational problems. An important example involves global atmospheric models used for climate and weather prediction. Classical spherical coordinates can be used to parameterize the manifold – that is, generate a grid for the computational spherical shell domain. This particular parameterization offers significant benefits such as orthogonality and exact representation of curvature and connection (Christoffel) coefficients. But it also exhibits two polar singularities and at or near these points typical continuity/integral constraints on dependent fields and their derivatives are generally inadequate and lead to poor model performance and erroneous results. Other parameterizations have been developed that eliminate polar singularities, but problems of weaker singularities and enhanced grid noise compared to spherical coordinates (away from the poles) persist. Here, in this study reparameterization invariance of geometric objects (scalars, vectors and the forms generated by their covariant derivatives) is utilized to generate asymptotic forms for dependent fields of interest valid in the neighborhood of a pole. The central concept is that such objects cannot be altered by the metric structure of a parameterization. The new boundary conditions enforce symmetries that are required for transformations of geometric objects. They are implemented in an implicit polar filter of a structured grid, nonhydrostatic global atmospheric model that is simulating idealized Held–Suarez flows. A series of test simulations using different configurations of the asymptotic boundary conditions are made, along with control simulations that use the default model numerics with no absorber, at three different grid sizes. Typically the test simulations are ~ 20% faster in wall clock time than the control—resulting from a decrease in noise at the poles in all cases. In the control simulations adverse numerical effects from the polar singularity are observed to increase with grid resolution. In contrast, test simulations demonstrate robust polar behavior independent of grid resolution.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2023

Geometric Event-Based Quantum Mechanics

In this work, we propose a special relativistic framework for quantum mechanics. It is based on introducing a Hilbert space for events. Events are taken as primitive notions (as customary in relativity), whereas quantum systems (e.g. fields and particles) are emergent in the form of joint probability amplitudes for position and time of events. Textbook relativistic quantum mechanics and quantum field theory can be recovered by dividing the event Hilbert spaces into space and time (a foliation) and then conditioning the event states onto the time part. Our theory satisfies the full Lorentz symmetry as a ‘geometric’ unitary transformation, and possesses relativistic observables for space (location of an event) and time (position in time of an event).

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2018

Cylindrical Damped Solitary Propagation in Superthermal Plasmas

Wave properties of damped solitons in a collisional unmagnetized four-components dusty fluid plasma system contains superthermal distributed electrons, mobile ions, and negative-positive dusty grains have been examined. To study dissipative DIA mode properties, a reductive perturbation (RP) analysis is used under convenient geometrical coordinate transformation, three-dimensional damped Kadomtsev–Petviashvili (3D-CDKP) equation in cylindrical coordinates is obtained. Effects of collisional parameters on damped soliton pulse structures are studied. More specifically, the impact of axial, radial, and polar coordinates with the time on solitary propagation are examined. This investigation may be viable in plasma of the Earth’s mesosphere.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

NASA NTRS1973

An investigation of the SNS Josephson junction as a three-terminal device

A particular phenomenon of the SNS Josephson junction was investigated; i.e., control by a current entering the normal region and leaving through one of the superconducting regions. The effect of the control current on the junction was found to be dependent upon the ration of the resistances of the two halves of the N layer. A low frequency, lumped, nonlinear model was proposed to describe the electrical characteristics of the device, and a method was developed to plot the dynamic junction resistance as a function of junction current. The effective thermal noise temperature of the sample was determined. Small signal linearized analysis of the device suggests its use as an impedance transformer, although geometric limitations must be overcome. Linear approximation indicates that it is reciprocal and no power gain is possible. It is felt that, with suitable metallurgical and geometrical improvements, the device has promise to become a superconducting transistor.

Meissner, H.↗

NASA NTRS1981

Recent developments with the ORSER system

Additions to the ORSER remote sensing data processing package are described. The ORSER package consists of about 35 individual programs that are grouped into preprocessing, data analysis, and display subsystems. Additional data formats and data management, data transformation, and geometric correlation programs were supplemented to the preprocessing subsystem. Enhancements to the data analysis techniques include a maximum likelihood classifier (MAXCLASS) and a new version of the STATS program which makes delineation of training areas easier and allows for detection of outlier points. Ongoing developments are also described.

Baumer, G. M.↗

NASA NTRS1982

Image processing via VLSI: A concept paper

Implementing specific image processing algorithms via very large scale integrated systems offers a potent solution to the problem of handling high data rates. Two algorithms stand out as being particularly critical -- geometric map transformation and filtering or correlation. These two functions form the basis for data calibration, registration and mosaicking. VLSI presents itself as an inexpensive ancillary function to be added to almost any general purpose computer and if the geometry and filter algorithms are implemented in VLSI, the processing rate bottleneck would be significantly relieved. A set of image processing functions that limit present systems to deal with future throughput needs, translates these functions to algorithms, implements via VLSI technology and interfaces the hardware to a general purpose digital computer is developed.

Nathan, R.↗

NASA NTRS1988

Digital and optical shape representation and pattern recognition; Proceedings of the Meeting, Orlando, FL, Apr. 4-6, 1988

The present conference discusses topics in pattern-recognition correlator architectures, digital stereo systems, geometric image transformations and their applications, topics in pattern recognition, filter algorithms, object detection and classification, shape representation techniques, and model-based object recognition methods. Attention is given to edge-enhancement preprocessing using liquid crystal TVs, massively-parallel optical data base management, three-dimensional sensing with polar exponential sensor arrays, the optical processing of imaging spectrometer data, hybrid associative memories and metric data models, the representation of shape primitives in neural networks, and the Monte Carlo estimation of moment invariants for pattern recognition.

Juday, Richard D.↗

NASA NTRS1990

Polar exponential sensor arrays unify iconic and Hough space representation

The log-polar coordinate system, inherent in both polar exponential sensor arrays and log-polar remapped video imagery, is identical to the coordinate system of its corresponding Hough transform parameter space. The resulting unification of iconic and Hough domains simplifies computation for line recognition and eliminates the slope quantization problems inherent in the classical Cartesian Hough transform. The geometric organization of the algorithm is more amenable to massively parallel architectures than that of the Cartesian version. The neural architecture of the human visual cortex meets the geometric requirements to execute 'in-place' log-Hough algorithms of the kind described here.

Weiman, Carl F. R.↗

NASA NTRS2000

GeoSAR: A Radar Terrain Mapping System for the New Millennium

GeoSAR Geographic Synthetic Aperture Radar) is a new 3 year effort to build a unique, dual-frequency, airborne Interferometric SAR for mapping of terrain. This is being pursued via a Consortium of the Jet Propulsion Laboratory (JPL), Calgis, Inc., and the California Department of Conservation. The airborne portion of this system will operate on a Calgis Gulfstream-II aircraft outfitted with P- and X-band Interferometric SARs. The ground portions of this system will be a suite of Flight Planning Software, an IFSAR Processor and a Radar-GIS Workstation. The airborne P-band and X-band radars will be constructed by JPL with the goal of obtaining foliage penetration at the longer P-band wavelengths. The P-band and X-band radar will operate at frequencies of 350 Mhz and 9.71 Ghz with bandwidths of either 80 or 160 Mhz. The airborne radars will be complemented with airborne laser system for measuring antenna positions. Aircraft flight lines and radar operating instructions will be computed with the Flight Planning Software The ground processing will be a two-step step process. First, the raw radar data will be processed into radar images and interferometer derived Digital Elevation Models (DEMs). Second, these radar images and DEMs will be processed with a Radar GIS Workstation which performs processes such as Projection Transformations, Registration, Geometric Adjustment, Mosaicking, Merging and Database Management. JPL will construct the IFSAR Processor and Calgis, Inc. will construct the Radar GIS Workstation. The GeoSAR Project was underway in November 1996 with a goal of having the radars and laser systems fully integrated onto the Calgis Gulfstream-II aircraft in early 1999. Then, Engineering Checkout and Calibration-Characterization Flights will be conducted through November 1999. The system will be completed at the end of 1999 and ready for routine operations in the year 2000.

Thompson, Thomas↗

NASA NTRS2009

Testing First-Order Logic Axioms in AutoCert

AutoCert [2] is a formal verification tool for machine generated code in safety critical domains, such as aerospace control code generated from MathWorks Real-Time Workshop. AutoCert uses Automated Theorem Provers (ATPs) [5] based on First-Order Logic (FOL) to formally verify safety and functional correctness properties of the code. These ATPs try to build proofs based on user provided domain-specific axioms, which can be arbitrary First-Order Formulas (FOFs). These axioms are the most crucial part of the trusted base, since proofs can be submitted to a proof checker removing the need to trust the prover and AutoCert itself plays the part of checking the code generator. However, formulating axioms correctly (i.e. precisely as the user had really intended) is non-trivial in practice. The challenge of axiomatization arise from several dimensions. First, the domain knowledge has its own complexity. AutoCert has been used to verify mathematical requirements on navigation software that carries out various geometric coordinate transformations involving matrices and quaternions. Axiomatic theories for such constructs are complex enough that mistakes are not uncommon. Second, adjusting axioms for ATPs can add even more complexity. The axioms frequently need to be modified in order to have them in a form suitable for use with ATPs. Such modifications tend to obscure the axioms further. Thirdly, speculating validity of the axioms from the output of existing ATPs is very hard since theorem provers typically do not give any examples or counterexamples.

Ahn, Ki Yung↗

NASA NTRS2021

A Physical Model for a Slim Convective Dusty Disk in AGN

An accretion disk in an Active Galactic Nucleus (AGN) harbors and shields dust from external illumination. Our model shows that at the mid-plane of the disk around a MBH = 107M black hole, dust can exist at 0:1pc from the black hole, compared to 0.5pc outside of the disk where such self-shielding is constrained. We construct a physical model of a disk region approximately located between the radius of dust sublimation at the disk mid-plane and the radius at which dust sublimes at the disk surface. Our main conclusion is that for a wide range of model parameters such as local accretion rate and/or opacity, the accretion disk’s own radiation pressure on dust significantly influences its vertical structure. In this region convection plays important role in the vertical transport of energy. When the local accretion rate exceeds 2:5M yr the 10􀀀2pc-scale disk is super-critical with respect to dust opacity. Such a disk puffs up and transforms from geometrically thin to slim. Our model fits into the narrative of a "failed wind" scenario of Czerny & Hryniewicz (2011) and the "compact torus" model of Baskin & Laor (2018), incorporating them as variations of the radiative dusty disk model.

A Dorodnitsyn↗

DOE OSTI2020

Canonical Transformation of Potential Model Hamiltonian Mechanics to Geometrical Form I

Using the methods of symplectic geometry, we establish the existence of a canonical transformation from potential model Hamiltonians of standard form in a Euclidean space to an equivalent geometrical form on a manifold, where the corresponding motions are along geodesic curves. The advantage of this representation is that it admits the computation of geodesic deviation as a test for local stability, shown in recent previous studies to be a very effective criterion for the stability of the orbits generated by the potential model Hamiltonian. We describe here an algorithm for finding the generating function for the canonical transformation and describe some of the properties of this mapping under local diffeomorphisms. We give a convergence proof for this algorithm for the one-dimensional case, and provide a precise geometric formulation of geodesic deviation which relates the stability of the motion in the geometric form to that of the Hamiltonian standard form. We apply our methods to a simple one-dimensional harmonic oscillator and conclude with a discussion of the relation of bounded domains in the two representations for which Morse theory would be applicable.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2023

Geometrical control of topological charge transfer in Shakti-Cairo colloidal ice

Lattice transformations that preserve the system topology, but not its geometry, are common in condensed matter systems. However, how geometric constrains influence the topological properties of the lattices is still unclear. Here we show that a geometric transformation between two mixed coordination lattices, from Shakti to Cairo in an artificial colloidal ice, leads to a breakdown of the ice rule in all but one specific geometry. We observe a transfer of topological charge among sublattices which can be controlled in sign and intensity, vanishing at the ice-rule point. These unusual topological effects are absent in magnetic spin ices and they are due to collective, non-local geometric frustration in the particle ice. By merging numerical simulations, theory and experiments, we demonstrate how the charge transfer occurs in the Cairo geometry. The broader implication of our results is that we demonstrate how geometric constraints can control the topological properties of a mesoscopic colloidal system.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗