Tychonis: A model-based approach to define and search for geometric events in space
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M. Llopis↗
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Results for “geometric search”
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Unstructured mesh methods for CFD
Mesh generation methods for Computational Fluid Dynamics (CFD) are outlined. Geometric modeling is discussed. An advancing front method is described. Flow past a two engine Falcon aeroplane is studied. An algorithm and associated data structure called the alternating digital tree, which efficiently solves the geometric searching problem is described. The computation of an initial approximation to the steady state solution of a given poblem is described. Mesh generation for transient flows is described.
Peraire, J.↗
Integrating the Science Opportunity Analyzer with a Reusable Opportunity Search Framework
In our interactions with the Science Opportunity Analyzer (SOA) software, we recognized how its ability to search for geometric events in space is a need for robotic space missions in general. To satisfy this need, we propose the Tychonis framework, which is built upon the principles of: (1) separations of concerns, (2) extensibility, (3) reusability, and (4) independent verification and validation. Tychonis’ separation of concerns results in the availability of different constructs to model geometric events and search for them. These constructs can be extended by users as needed and reused across missions without changes. Given the low coupling between concerns, and the fact Tychonis can be augmented in isolation, its constructs can be validated independently from other pieces of software. This paper elaborates on these topics and presents an integration case study between Tychonis and SOA that relies on the concept of dynamic integration. Dynamic integration entails that augmentations of the framework are reflected automatically in the host application without any changes to the host application’s code. The SOA-Tychonis integration case study can be extrapolated to other tools that need to search for geometric events as the pattern repeats across implementations: (i) the manipulation of a user interface to model opportunities, (ii) the execution of algorithms to search for opportunities, and (iii) the presentation of search results to users. Overall, Tychonis’ is a story about how the application of proven software principles and good design choices can reduce risk and cost to space missions
Soria, Manel↗
WebGeocalc: Web Interface to SPICE
The WebGeocalc tool (WGC) provides a web-based graphical user interface to many of the observation geometry calculations available from the “SPICE” system. WGC is based on client-server architecture. A user selects calculation parameters using GUI widgets in a Web browser. The request is sent to a WGC geometry server that performs the calculation and sends results back to the client. WGC can compute various geometric parameters such as positions, orientations, and surface intercept coordinates for a series of times; perform geometric event searches for time intervals when a geometric condition is met; and perform time conversions. WGC offers many features such as plotting and downloading results. Currently only the NAIF group at JPL operates a WGC server that has access to all data on the NAIF web site but WGC can be deployed on any computer that has Java, Apache Tomcat server, MySQL Community Server, and SPICE data.
Semenov, Boris↗
WebGeocalc: Web Interface to SPICE
The WebGeocalc tool (WGC) provides a web-based graphical user interface to many of the observation geometry calculations available from the “SPICE” system. WGC is based on client-server architecture. A user selects calculation parameters using GUI widgets in a Web browser. The request is sent to a WGC geometry server that performs the calculation and sends results back to the client. WGC can compute various geometric parameters such as positions, orientations, and surface intercept coordinates for a series of times; perform geometric event searches for time intervals when a geometric condition is met; and perform time conversions. WGC offers many features such as plotting and downloading results. Currently only the NAIF group at JPL operates a WGC server that has access to all data on the NAIF web site but WGC can be deployed on any computer that has Java, Apache Tomcat server, MySQL Community Server, and SPICE data.
Semenov, Boris↗
Parallel algorithm for dominant points correspondences in robot binocular stereo vision
This paper presents an algorithm to find the correspondences of points representing dominant feature in robot stereo vision. The algorithm consists of two main steps: dominant point extraction and dominant point matching. In the feature extraction phase, the algorithm utilizes the widely used Moravec Interest Operator and two other operators: the Prewitt Operator and a new operator called Gradient Angle Variance Operator. The Interest Operator in the Moravec algorithm was used to exclude featureless areas and simple edges which are oriented in the vertical, horizontal, and two diagonals. It was incorrectly detecting points on edges which are not on the four main directions (vertical, horizontal, and two diagonals). The new algorithm uses the Prewitt operator to exclude featureless areas, so that the Interest Operator is applied only on the edges to exclude simple edges and to leave interesting points. This modification speeds-up the extraction process by approximately 5 times. The Gradient Angle Variance (GAV), an operator which calculates the variance of the gradient angle in a window around the point under concern, is then applied on the interesting points to exclude the redundant ones and leave the actual dominant ones. The matching phase is performed after the extraction of the dominant points in both stereo images. The matching starts with dominant points in the left image and does a local search, looking for corresponding dominant points in the right image. The search is geometrically constrained the epipolar line of the parallel-axes stereo geometry and the maximum disparity of the application environment. If one dominant point in the right image lies in the search areas, then it is the corresponding point of the reference dominant point in the left image. A parameter provided by the GAV is thresholded and used as a rough similarity measure to select the corresponding dominant point if there is more than one point the search area. The correlation is used as a final decision tool when there is still more than one point in the search area. If there is no dominant point in the search area of if the points in the search area are below a correlation threshold, then the dominant point in the reference image is occluded and can not be corresponded. The algorithm has been modeled, implemented and shown to be fast, robust and parallel. The parallelism is created from three main features: locality of the operators; a memory optimization scheme; and the ability to fully parallelize the extraction phase which is the most computational intensive task in the algorithm. The last feature is achieved by performing the extraction phase on the two images simultaneously.
Al-Tammami, A.↗
Conjugate point determination for multitemporal data overlay
The machine processing is discussed of spatially variant multitemporal data such as imagery obtained at different times which requires that these data be in geometrical registration so that the analysis processor may obtain the datum for a specified ground resolution element in each of the sets of imagery being utilized for analysis. Misregistration between corresponding subsets of imagery contains both a displacement and a geometrical distortion component. Search techniques utilizing the moduli of the Fourier Transforms are developed for estimating the coefficients of geometrical distortion components of this model. Following the correction of these distortion components, the displacement is located by the crosscorrelation of a template obtained from one set of data, termed the reference, with the second, or background data. This template, derived for the optimum discrimination of the reference data embedded in the background, is determined by the solution of a system of equations involving the reference data and the covariance matrix of these data.
Emmert, R. A.↗
A Search Model for Imperfectly Detected Targets
Under the assumptions that 1) the search region can be divided up into N non-overlapping sub-regions that are searched sequentially, 2) the probability of detection is unity if a sub-region is selected, and 3) no information is available to guide the search, there are two extreme case models. The search can be done perfectly, leading to a uniform distribution over the number of searches required, or the search can be done with no memory, leading to a geometric distribution for the number of searches required with a success probability of 1/N. If the probability of detection P is less than unity, but the search is done otherwise perfectly, the searcher will have to search the N regions repeatedly until detection occurs. The number of searches is thus the sum two random variables. One is N times the number of full searches (a geometric distribution with success probability P) and the other is the uniform distribution over the integers 1 to N. The first three moments of this distribution were computed, giving the mean, standard deviation, and the kurtosis of the distribution as a function of the two parameters. The model was fit to the data presented last year (Ahumada, Billington, & Kaiwi, 2 required to find a single pixel target on a simulated horizon. The model gave a good fit to the three moments for all three observers.
Ahumada, Albert↗
Optimization of contoured hypersonic scramjet inlets with a least-squares parabolized Navier-Stokes procedure
A new optimization procedure, in which a parabolized Navier-Stokes solver is coupled with a non-linear least-squares optimization algorithm, is applied to the design of a Mach 14, laminar two-dimensional hypersonic subscale flight inlet with an internal contraction ratio of 15:1 and a length-to-throat half-height ratio of 150:1. An automated numerical search of multiple geometric wall contours, which are defined by polynomical splines, results in an optimal geometry that yields the maximum total-pressure recovery for the compression process. Optimal inlet geometry is obtained for both inviscid and viscous flows, with the assumption that the gas is either calorically or thermally perfect. The analysis with a calorically perfect gas results in an optimized inviscid inlet design that is defined by two cubic splines and yields a mass-weighted total-pressure recovery of 0.787, which is a 23% improvement compared with the optimized shock-canceled two-ramp inlet design. Similarly, the design procedure obtains the optimized contour for a viscous calorically perfect gas to yield a mass-weighted total-pressure recovery value of 0.749. Additionally, an optimized contour for a viscous thermally perfect gas is obtained to yield a mass-weighted total-pressure recovery value of 0.768. The design methodology incorporates both complex fluid dynamic physics and optimal search techniques without an excessive compromise of computational speed; hence, this methodology is a practical technique that is applicable to optimal inlet design procedures.
Korte, J. J.↗
Search for Outer Satellites of Saturn to V=22.5
A wide-field, prime-focus photographic search of most of the dynamically permitted satellite space of Saturn and Uranus to limiting magnitude 22.5 revealed no new outer satellites. This search is approximately 2.5 mag deeper than previous surveys. For bodies of geometric albedo 0.04, the search would have revealed outer satellites of Saturn with diameter 20 km and greater, and outer satellites of Uranus with diameter 70 km and greater. This work was carried out with the Canada-France-Hawaii 3.6-m telescope on Mauna Kea.
Cruikshank, Dale P.↗
Use of Multi-Resolution Wavelet Feature Pyramids for Automatic Registration of Multi-Sensor Imagery
The problem of image registration, or alignment of two or more images representing the same scene or object, has to be addressed in various disciplines that employ digital imaging. In the area of remote sensing, just like in medical imaging or computer vision, it is necessary to design robust, fast and widely applicable algorithms that would allow automatic registration of images generated by various imaging platforms at the same or different times, and that would provide sub-pixel accuracy. One of the main issues that needs to be addressed when developing a registration algorithm is what type of information should be extracted from the images being registered, to be used in the search for the geometric transformation that best aligns them. The main objective of this paper is to evaluate several wavelet pyramids that may be used both for invariant feature extraction and for representing images at multiple spatial resolutions to accelerate registration. We find that the band-pass wavelets obtained from the Steerable Pyramid due to Simoncelli perform better than two types of low-pass pyramids when the images being registered have relatively small amount of nonlinear radiometric variations between them. Based on these findings, we propose a modification of a gradient-based registration algorithm that has recently been developed for medical data. We test the modified algorithm on several sets of real and synthetic satellite imagery.
Zavorin, Ilya↗
Use of multiresolution wavelet feature pyramids for automatic registration of multisensor imagery
The problem of image registration, or the alignment of two or more images representing the same scene or object, has to be addressed in various disciplines that employ digital imaging. In the area of remote sensing, just like in medical imaging or computer vision, it is necessary to design robust, fast, and widely applicable algorithms that would allow automatic registration of images generated by various imaging platforms at the same or different times and that would provide subpixel accuracy. One of the main issues that needs to be addressed when developing a registration algorithm is what type of information should be extracted from the images being registered, to be used in the search for the geometric transformation that best aligns them. The main objective of this paper is to evaluate several wavelet pyramids that may be used both for invariant feature extraction and for representing images at multiple spatial resolutions to accelerate registration. We find that the bandpass wavelets obtained from the steerable pyramid due to Simoncelli performs best in terms of accuracy and consistency, while the low-pass wavelets obtained from the same pyramid give the best results in terms of the radius of convergence. Based on these findings, we propose a modification of a gradient-based registration algorithm that has recently been developed for medical data. We test the modified algorithm on several sets of real and synthetic satellite imagery.
Evaluation Studies↗
A positional estimation technique for an autonomous land vehicle in an unstructured environment
This paper presents a solution to the positional estimation problem of an autonomous land vehicle navigating in an unstructured mountainous terrain. A Digital Elevation Map (DEM) of the area in which the robot is to navigate is assumed to be given. It is also assumed that the robot is equipped with a camera that can be panned and tilted, and a device to measure the elevation of the robot above the ground surface. No recognizable landmarks are assumed to be present in the environment in which the robot is to navigate. The solution presented makes use of the DEM information, and structures the problem as a heuristic search in the DEM for the possible robot location. The shape and position of the horizon line in the image plane and the known camera geometry of the perspective projection are used as parameters to search the DEM. Various heuristics drawn from the geometric constraints are used to prune the search space significantly. The algorithm is made robust to errors in the imaging process by accounting for the worst care errors. The approach is tested using DEM data of areas in Colorado and Texas. The method is suitable for use in outdoor mobile robots and planetary rovers.
Talluri, Raj↗
Fast Integer Ambiguity Resolution for GPS Attitude Determination
In this paper, a new algorithm for GPS (Global Positioning System) integer ambiguity resolution is shown. The algorithm first incorporates an instantaneous (static) integer search to significantly reduce the search space using a geometric inequality. Then a batch-type loss function is used to check the remaining integers in order to determine the optimal integer. This batch function represents the GPS sightline vectors in the body frame as the sum of two vectors, one depending on the phase measurements and the other on the unknown integers. The new algorithm has several advantages: it does not require an a-priori estimate of the vehicle's attitude; it provides an inherent integrity check using a covariance-type expression; and it can resolve the integers even when coplanar baselines exist. The performance of the new algorithm is tested on a dynamic hardware simulator.
Lightsey, E. Glenn↗
Navigation path planning for autonomous aircraft - Voronoi diagram approach
The present technique for generating a search graph depicting topologically unique paths around mountain boundaries at constant altitudes involves a description of mountain boundaries as polygons; the search graph is then generated on the basis of a geometric construct. All nodes and arcs of the search graph are guaranteed to lie in free space, thereby ensuring an autonomous aircraft's avoidance of mountain obstacles. The solution path is generated by searching the graph for the optimal path from a start location to a finish location.
Krozel, Jimmy↗
Identification and verification of termination conditions in fine motion in presence of sensor errors and geometric uncertainties
Results are reported from a search for reasonable constraints under which an automatic uncertainty-handling strategy (for robot part-mating tasks) is guaranteed to succeed. The concept of contact formations is introduced to describe contacts among parts in a system, aiming at reducing the dimensionality of assembly verification. Also described is a technique for identifying contact formations in spite of errors in sensing and geometric uncertainties. It is impossible to verify termination conditions in general. Design constraints for which verification can be guaranteed are formulated and shown to be reasonable in the sense that they do not impose unrealistic conditions on typical designs. Results of implementation on a robot system consisting of a PUMA robot with RTI force/torque sensors support the theoretical derivations and show empirically that good results can still be obtained when the theoretical constraints are relaxed somewhat.
Desai, Rajiv S.↗
Short- and Long-Term Propagation of Spacecraft Orbits
The Planetary Observer Planning Software (POPS) comprises four computer programs for use in designing orbits of spacecraft about planets. These programs are the Planetary Observer High Precision Orbit Propagator (POHOP), the Planetary Observer Long-Term Orbit Predictor (POLOP), the Planetary Observer Post Processor (POPP), and the Planetary Observer Plotting (POPLOT) program. POHOP and POLOP integrate the equations of motion to propagate an initial set of classical orbit elements to a future epoch. POHOP models shortterm (one revolution) orbital motion; POLOP averages out the short-term behavior but requires far less processing time than do older programs that perform long-term orbit propagations. POPP postprocesses the spacecraft ephemeris created by POHOP or POLOP (or optionally can use a less accurate internal ephemeris) to search for trajectory-related geometric events including, for example, rising or setting of a spacecraft as observed from a ground site. For each such event, POPP puts out such user-specified data as the time, elevation, and azimuth. POPLOT is a graphics program that plots data generated by POPP. POPLOT can plot orbit ground tracks on a world map and can produce a variety of summaries and generic ordinate-vs.-abscissa plots of any POPP data.
Smith, John C., Jr.↗
Planetary optical and infrared imaging
Images were acquired of a circumstellar disk of orbiting material around the nearby star beta Pictoris. This material is believed to be associated with the formation of planets and provides a first look at a planetary system much younger than our own. Preliminary work was also done to acquire multicolor photometric data and polarimetry on the beta Pictoris disk as well. A coronagraphic search for other proto-planetary systems is also underway. Coronagraphic imaging provided the first clear images and a determination of the geometric albedo of the rings of Uranus. A search for material around the asteroid Amphitrite showed that the region around the asteroid was free of particles larger than 500 meters in radius or diffuse material with an optical depth larger than .000001. NASA IRTF infrared images of Jupiter and Saturn are providing information on the relative heights and cloud top temperatures of atmospheric features.
Terrile, R. J.↗