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NASA NTRS1992

Quantitative analysis of surface characteristics and morphology in Death Valley, California using AIRSAR data

The Jet Propulsion Laboratory Airborne Synthetic Aperture Radar (JPL-AIRSAR) is used to collect full polarimetric measurements at P-, L-, and C-bands. These data are analyzed using the radar analysis and visualization environment (RAVEN). The AIRSAR data are calibrated using in-scene corner reflectors to allow for quantitative analysis of the radar backscatter. RAVEN is used to extract surface characteristics. Inversion models are used to calculate quantitative surface roughness values and fractal dimensions. These values are used to generate synthetic surface plots that represent the small-scale surface structure of areas in Death Valley. These procedures are applied to a playa, smooth salt-pan, and alluvial fan surfaces in Death Valley. Field measurements of surface roughness are used to verify the accuracy.

Kierein-Young, K. S.↗

NASA NTRS1992

Robustness of Spann-Wilson segmentation on SAR imagery

The performances of the Spann-Wilson algorithm on simulated synthetic aperture radar (SAR) images with varying degrees of speckle (one to four looks and varying amounts of white noise) is described. One hundred forty-eight test images are considered, of which the algorithm segmented most without any adjustment to the algorithm's parameters. The effect of speckle on fractal boundaries is studied. The effect of varying multiplicative and additive noise distributions for a fixed set of segmentation parameters is examined. The modified Spann-Wilson algorithm on four-look imagery is evaluated.

Daida, Jason M.↗

NASA NTRS1993

Visual information processing II; Proceedings of the Meeting, Orlando, FL, Apr. 14-16, 1993

Various papers on visual information processing are presented. Individual topics addressed include: aliasing as noise, satellite image processing using a hammering neural network, edge-detetion method using visual perception, adaptive vector median filters, design of a reading test for low-vision image warping, spatial transformation architectures, automatic image-enhancement method, redundancy reduction in image coding, lossless gray-scale image compression by predictive GDF, information efficiency in visual communication, optimizing JPEG quantization matrices for different applications, use of forward error correction to maintain image fidelity, effect of peanoscanning on image compression. Also discussed are: computer vision for autonomous robotics in space, optical processor for zero-crossing edge detection, fractal-based image edge detection, simulation of the neon spreading effect by bandpass filtering, wavelet transform (WT) on parallel SIMD architectures, nonseparable 2D wavelet image representation, adaptive image halftoning based on WT, wavelet analysis of global warming, use of the WT for signal detection, perfect reconstruction two-channel rational filter banks, N-wavelet coding for pattern classification, simulation of image of natural objects, number-theoretic coding for iconic systems.

Huck, Friedrich O.↗

NASA NTRS1990

On domains of convergence in optimization problems

Numerical optimization algorithms require the knowledge of an initial set of design variables. Starting from an initial design x(sup 0), improved solutions are obtained by updating the design iteratively in a way prescribed by the particular algorithm used. If the algorithm is successful, convergence is achieved to a local optimal solution. Let A denote the iterative procedure that characterizes a typical optimization algorithm, applied to the problem: Find x belonging to R(sup n) that maximizes f(x) subject to x belonging to Omega contained in R(sup n). We are interested in problems with several local maxima (x(sub j))(sup *), j=1, ..., m, in the feasible design space Omega. In general, convergence of the algorithm A to a specific solution (x(sub j))(sup *) is determined by the choice of initial design x(sup 0). The domain of convergence D(sub j) of A associated with a local maximum (x(sub j))(sup *) is a subset of initial designs x(sup 0) in Omega such that the sequence (x(sup k)), k=0,1,2,... defined by x(sup k+1) = A(x(sup k)), k=0,1,... converges to (x(sub j))(sup *). The set D(sub j) is also called the basin of attraction of (x(sub j))(sup *). Cayley first proposed the problem of finding the basin of attraction for Newton's method in 1897. It has been shown that the basin of attraction for Newton's method exhibits chaotic behavior in problems with polynomial objective. This implies that there may be regions in the feasible design space where arbitrarily close starting points will converge to different local optimal solutions. Furthermore, the boundaries of the domains of convergence may have a very complex, even fractal structure. In this paper we show that even simple structural optimization problems solved using standard gradient based (first order) algorithms exhibit similar features.

Diaz, Alejandro R.↗

NASA NTRS1989

Analysis of interstellar fragmentation structure based on IRAS images

The goal of this project was to develop new tools for the analysis of the structure of densely sampled maps of interstellar star-forming regions. A particular emphasis was on the recognition and characterization of nested hierarchical structure and fractal irregularity, and their relation to the level of star formation activity. The panoramic IRAS images provided data with the required range in spatial scale, greater than a factor of 100, and in column density, greater than a factor of 50. In order to construct a densely sampled column density map of a cloud complex which is both self-gravitating and not (yet?) stirred up much by star formation, a column density image of the Taurus region has been constructed from IRAS data. The primary drawback to using the IRAS data for this purpose is that it contains no velocity information, and the possible importance of projection effects must be kept in mind.

Scalo, John M.↗

NASA NTRS1992

Analysis of interstellar cloud structure based on IRAS images

The goal of this project was to develop new tools for the analysis of the structure of densely sampled maps of interstellar star-forming regions. A particular emphasis was on the recognition and characterization of nested hierarchical structure and fractal irregularity, and their relation to the level of star formation activity. The panoramic IRAS images provided data with the required range in spatial scale, greater than a factor of 100, and in column density, greater than a factor of 50. In order to construct densely sampled column density maps of star-forming clouds, column density images of four nearby cloud complexes were constructed from IRAS data. The regions have various degrees of star formation activity, and most of them have probably not been affected much by the disruptive effects of young massive stars. The largest region, the Scorpius-Ophiuchus cloud complex, covers about 1000 square degrees (it was subdivided into a few smaller regions for analysis). Much of the work during the early part of the project focused on an 80 square degree region in the core of the Taurus complex, a well-studied region of low-mass star formation.

Scalo, John M.↗

NASA NTRS1993

Layout and cabling considerations for a large communications antenna array

Layout considerations for a large deep space communications antenna array are discussed. A fractal geometry for the antenna layout is described that provides optimal packing of antenna elements, efficient cable routing, and logical division of the array into identical sub-arrays.

Logan, R. T., Jr.↗

NASA NTRS1993

Confirmation of saturation equilibrium conditions in crater populations

We have continued work on realistic numerical models of cratered surfaces, as first reported at last year's LPSC. We confirm the saturation equilibrium level with a new, independent test. One of us has developed a realistic computer simulation of a cratered surface. The model starts with a smooth surface or fractal topography, and adds primary craters according to the cumulative power law with exponent -1.83, as observed on lunar maria and Martian plains. Each crater has an ejecta blanket with the volume of the crater, feathering out to a distance of 4 crater radii. We use the model to test the levels of saturation equilibrium reached in naturally occurring systems, by increasing crater density and observing its dependence on various parameters. In particular, we have tested to see if these artificial systems reach the level found by Hartmann on heavily cratered planetary surfaces, hypothesized to be the natural saturation equilibrium level. This year's work gives the first results of a crater population that includes secondaries. Our model 'Gaskell-4' (September, 1992) includes primaries as described above, but also includes a secondary population, defined by exponent -4. We allowed the largest secondary from each primary to be 0.10 times the size of the primary. These parameters will be changed to test their effects in future models. The model gives realistic images of a cratered surface although it appears richer in secondaries than real surfaces are. The effect of running the model toward saturation gives interesting results for the diameter distribution. Our most heavily cratered surface had the input number of primary craters reach about 0.65 times the hypothesized saturation equilibrium, but the input number rises to more than 100 times that level for secondaries below 1.4 km in size.

Hartmann, William K.↗

NASA NTRS1993

On the estimation of the correlation dimension and its application to radar reflector discrimination

Recently, system theorists have recognized that low order systems of nonlinear differential equations can give rise to solutions which are neither periodic, constant, nor predictable in steady state, but which are nonetheless bounded and deterministic. This behavior, which was first described in the study of weather systems, has been termed 'chaotic.' Much study of chaotic systems has concentrated on analysis of the systems' phase space attractors. It has been recognized that invariant measures of the attractor possess inherent information about the system. One such measure is the dimension of the attractors. The dimension of a chaotic attractor has been shown to be noninteger, leading to the term 'strange attractor;' the attractor is said to have a fractal structure. The correlation dimension has become one of the most popular measures of dimension. However, many problems have been identified in correlation dimension estimation from time sequences. The most common methods for obtaining the correlation dimension have been least squares curves fitting to find the slope of the correlation integral and the Takens Estimator. However, these estimates show unacceptable sensitivity to the upper limit on the distance chosen. Here, a new method is proposed which is shown to be rather insensitive to the upper limit and to perform in a very stable manner, at least in the absence of noise. The correlation dimension is also shown to be an effective discriminant in distinguishing between radar returns resulting from weather and those from the ground. The weather returns are shown to have a correlation dimension generally between 2.0 and 3.0, while ground returns have a correlation dimension exceeding 3.0.

Barnett, Kevin D.↗

NASA NTRS1993

Dimensional analysis of acoustically propagated signals

Traditionally, long term measurements of atmospherically propagated sound signals have consisted of time series of multiminute averages. Only recently have continuous measurements with temporal resolution corresponding to turbulent time scales been available. With modern digital data acquisition systems we now have the capability to simultaneously record both acoustical and meteorological parameters with sufficient temporal resolution to allow us to examine in detail relationships between fluctuating sound and the meteorological variables, particularly wind and temperature, which locally determine the acoustic refractive index. The atmospheric acoustic propagation medium can be treated as a nonlinear dynamical system, a kind of signal processor whose innards depend on thermodynamic and turbulent processes in the atmosphere. The atmosphere is an inherently nonlinear dynamical system. In fact one simple model of atmospheric convection, the Lorenz system, may well be the most widely studied of all dynamical systems. In this paper we report some results of our having applied methods used to characterize nonlinear dynamical systems to study the characteristics of acoustical signals propagated through the atmosphere. For example, we investigate whether or not it is possible to parameterize signal fluctuations in terms of fractal dimensions. For time series one such parameter is the limit capacity dimension. Nicolis and Nicolis were among the first to use the kind of methods we have to study the properties of low dimension global attractors.

Hansen, Scott D.↗

NASA NTRS1994

An analysis of gamma ray burst time histories

Gamma ray burst time histories, ranging in durations from milliseconds to thousands of seconds, are as varied as the number of bursts. They show a wide array of structures from those that are very smooth to those that contain a seemingly uncountable number of spikes riding on top of other spikes. These profiles have tantalized researchers for years - they obviously hold important information on the nature of GRB's, but to date no one has been successful in analyzing them. For the past year the author has been working on algorithms to analyze these data. Two approaches have been followed in this investigation. The first is an attempt to quantify the amount of structure, or spikiness, in a profile. The second involves applying the latest theorems on chaos and fractals with the aim of extracting useful information from what seems to be a random collection of shot noise.

Lestrade, John Patrick↗

NASA NTRS1993

The importance of robust error control in data compression applications

Data compression has become an increasingly popular option as advances in information technology have placed further demands on data storage capabilities. With compression ratios as high as 100:1 the benefits are clear; however, the inherent intolerance of many compression formats to error events should be given careful consideration. If we consider that efficiently compressed data will ideally contain no redundancy, then the introduction of a channel error must result in a change of understanding from that of the original source. While the prefix property of codes such as Huffman enables resynchronisation, this is not sufficient to arrest propagating errors in an adaptive environment. Arithmetic, Lempel-Ziv, discrete cosine transform (DCT) and fractal methods are similarly prone to error propagating behaviors. It is, therefore, essential that compression implementations provide sufficient combatant error control in order to maintain data integrity. Ideally, this control should be derived from a full understanding of the prevailing error mechanisms and their interaction with both the system configuration and the compression schemes in use.

Woolley, S. I.↗

NASA NTRS1994

System considerations for efficient communication and storage of MSTI image data

The Ballistic Missile Defense Organization has been developing the capability to evaluate one or more high-rate sensor/hardware combinations by incorporating them as payloads on a series of Miniature Seeker Technology Insertion (MSTI) flights. This publication represents the final report of a 1993 study to analyze the potential impact f data compression and of related communication system technologies on post-MSTI 3 flights. Lossless compression is considered alone and in conjunction with various spatial editing modes. Additionally, JPEG and Fractal algorithms are examined in order to bound the potential gains from the use of lossy compression. but lossless compression is clearly shown to better fit the goals of the MSTI investigations. Lossless compression factors of between 2:1 and 6:1 would provide significant benefits to both on-board mass memory and the downlink. for on-board mass memory, the savings could range from $5 million to $9 million. Such benefits should be possible by direct application of recently developed NASA VLSI microcircuits. It is shown that further downlink enhancements of 2:1 to 3:1 should be feasible thorough use of practical modifications to the existing modulation system and incorporation of Reed-Solomon channel coding. The latter enhancement could also be achieved by applying recently developed VLSI microcircuits.

Rice, Robert F.↗

NASA NTRS1994

Coagulation of grains in static and collapsing protostellar clouds

We simulate collisional evolution of grains in dense turbulent molecular cloud cores (or Bok globules) in static equilibrium and free-fall collapse, assuming spherical symmetry. Relative velocities are due to thermal motions, differential settling, and turbulence, with the latter dominant for sonic turbulence with an assumed Kolmogorov spectrum. Realistic criteria are used to determine outcomes of collisions (coagulation vs. destruction) as functions of particle size and velocity. Results are presented for a variety of cloud parameters (radial density profile, turbulent velocity) and particle properties (density, impact strength). Results are sensitive to the assumed mechanical properties (density and impact strength) of grain aggregates. Particle growth is enhanced if aggregates have low density or fractal structures. On a timescale of a few Myr, an initial population of 0.1 micrometers grains may produce dense compact particles approximately 1 micrometer in size, or fluffy aggregates approximately 100 micrometers. For impact strengths less than or equal to 10(exp 6) ergs/g, a steady state is reached between coagulation of small grains and collisional disruption of larger aggregates. Formation of macroscopic aggregates requires high mechanical strengths and low aggregate densities. We assume sonic turbulence during collapse, with varied eddy size scales determining the dissipation rate or turbulence strength. The degree of collisional evolution during collapse is sensitive to the assumed small-scale structure (inner sc ale) of the turbulence. Weak turbulence results in few collisions and preserves the precollapse particle size distribution with little change. Strong turbulence tends to produce net destruction, rather than particle growth, during infall, unless inpact strengths are greater than 10(exp 6)ergs/g.

Weidenschilling, S. J.↗

NASA NTRS1994

Multifractal characterizations of nonstationarity and intermittency in geophysical fields: Observed, retrieved, or simulated

Geophysical data rarely show any smoothness at any scale, and this often makes comparison with theoretical model output difficult. However, highly fluctuating signals and fractal structures are typical of open dissipative systems with nonlinear dynamics, the focus of most geophysical research. High levels of variability are excited over a large range of scales by the combined actions of external forcing and internal instability. At very small scales we expect geophysical fields to be smooth, but these are rarely resolved with available instrumentation or simulation tools; nondifferentiable and even discontinuous models are therefore in order. We need methods of statistically analyzing geophysical data, whether measured in situ, remotely sensed or even generated by a computer model, that are adapted to these characteristics. An important preliminary task is to define statistically stationary features in generally nonstationary signals. We first discuss a simple criterion for stationarity in finite data streams that exhibit power law energy spectra and then, guided by developments in turbulence studies, we advocate the use of two ways of analyzing the scale dependence of statistical information: singular measures and qth order structure functions. In nonstationary situations, the approach based on singular measures seeks power law behavior in integrals over all possible scales of a nonnegative stationary field derived from the data, leading to a characterization of the intermittency in this (gradient-related) field. In contrast, the approach based on structure functions uses the signal itself, seeking power laws for the statistical moments of absolute increments over arbitrarily large scales, leading to a characterization of the prevailing nonstationarity in both quantitative and qualitative terms. We explain graphically, step by step, both multifractal statistics which are largely complementary to each other. The geometrical manifestations of nonstationarity and intermittency, 'roughness' and 'sparseness', respectively, are illustrated and the associated analytical (differentiability and continuity) properties are discussed. As an example, the two techniques are applied to a series of recent measurements of liquid water distributions inside marine stratocumulus decks; these are found to be multifractal over scales ranging from approximately 60 m to approximately 60 km. Finally, we define the 'mean multifractal plane' and show it to be a simple yet comprehensive tool with many applications including data intercomparison, (dynamical or stochastic) model and retrieval validations.

Davis, Anthony↗

NASA NTRS1995

Exobiology research on Space Station Freedom

The Gas-Grain Simulation Facility (GGSF) is a multidisciplinary experiment laboratory being developed by NASA at Ames Research Center for delivery to Space Station Freedom in 1998. This facility will employ the low-gravity environment of the Space Station to enable aerosol experiments of much longer duration than is possible in any ground-based laboratory. Studies of fractal aggregates that are impossible to sustain on Earth will also be enabled. Three research areas within exobiology that will benefit from the GGSF are described here. An analysis of the needs of this research and of other suggested experiments has produced a list of science requirements which the facility design must accommodate. A GGSF design concept developed in the first stage of flight hardware development to meet these requirements is also described.

Huntington, J. L.↗

NASA NTRS1993

A diffusion-limited aggregation model for the evolution of drainage networks

We propose a modified diffusion-limited aggregation (DLA) model for the evolution of fluvial drainage networks. Random walkers are introduced randomly on a grid, and each two-dimensional random walk proceeds until the walker finds a drainage network on which to accrete. This model for headward growth of drainage networks generates drainage patterns remarkably similar to actual drainages. The model also predicts statistical features which agree with actual networks, including the frequency-order (bifurcation) ratio (R(sub b) = 3.98) and the stream length-order (R(sub r) = 2.09). Using the definition of network fractal dimension D = log R(sub b)/log R(sub r), we find that our DLA model gives D = 1.87, near the observed range of D approximately equal to 1.80 - 1.85.

Masek, Jeffrey G.↗

NASA NTRS1995

A count probability cookbok: Spurious effects and the scaling model

We study the errors brought by finite volume effects and dilution effects on the practical determination of the count probability distribution function P(sub N)(n,l), which is the probability of having N objects in a cell of volume l cubed for a set of average number density n. Dilution effects are particularly revelant to the so-called sparse sampling strategy. This work is mainly done in the framework of the Bailan & Schaeffer scaling model, which assumes that the Q-body correlation functions obey the scaling relation Xi(sub Q)(lambda r(sub l),....lambda r(sub Q) = lambda(exp -(Q-1)gamma) Xi(sub Q)(r(sub 1),....r(sub Q)). We use three synthetic samples as references to perform our analysis: a fractal generated by a Rayleigh-Levy random walk with approximately 3 x 10(exp 4) objects, a sample dominated by a spherical power-law cluster with approximately 3 x 10(exp 4) objects and a cold dark matter (CDM) universe involving approximately 3 x 10(exp 5) matter particles.

Colombi, S.↗