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NASA Scientific and Technical Aerospace Reports

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produced by SRTM. In particular, we have developed a rigorous mathematical algorithm <strong>and</strong> means to fill in missing data over<br />

rough terrain from other data sets. We illustrate this method by using a higher resolution, but globally less accurate, DEM<br />

produced by the TOPSAR airborne instrument over the Galapagos Isl<strong>and</strong>s to augment the SRTM data set in this area, We<br />

combine this data set with SRTM to use each set to fill in holes left over by the other imaging system. The infilling is done<br />

by first interpolating each data set using a prediction error filter that reproduces the same statistical characterization as<br />

exhibited by the entire data set within the interpolated region. After this procedure is implemented on each data set, the two<br />

are combined on a point by point basis with weights that reflect the accuracy of each data point in its original image. In areas<br />

that are better covered by SRTM, TOPSAR data are weighted down but still retain TOPSAR statistics. The reverse is true for<br />

regions better covered by TOPSAR. The resulting DEM passes statistical tests <strong>and</strong> appears quite feasible to the eye, but as<br />

this DEM is the best available for the region we cannot fully veri@ its accuracy. Spot checks with GPS points show that locally<br />

the technique results in a more comprehensive <strong>and</strong> accurate map than either data set alone.<br />

Derived from text<br />

Algorithms; Statistical Tests; Interpolation; Digital Elevation Models<br />

20040071158 <strong>NASA</strong> Langley Research Center, Hampton, VA, USA<br />

DSP Implementation of the Retinex Image Enhancement Algorithm<br />

Hines, Glenn; Rahman, Zia-Ur; Jobson, Daniel; Woodell, Glenn; [2004]; 12 pp.; In English; SPIE Defense <strong>and</strong> Security<br />

Symposium, 12-16 Apr. 2004, Orl<strong>and</strong>o, FL, USA<br />

Contract(s)/Grant(s): NNL04AA02A; NCC1-01030; 23-728-60-30<br />

Report No.(s): SPIE-5438-37; No Copyright; Avail: CASI; A03, Hardcopy<br />

The Retinex is a general-purpose image enhancement algorithm that is used to produce good visual representations of<br />

scenes. It performs a non-linear spatial/spectral transform that synthesizes strong local contrast enhancement <strong>and</strong> color<br />

constancy. A real-time, video frame rate implementation of the Retinex is required to meet the needs of various potential users.<br />

Retinex processing contains a relatively large number of complex computations, thus to achieve real-time performance using<br />

current technologies requires specialized hardware <strong>and</strong> software. In this paper we discuss the design <strong>and</strong> development of a<br />

digital signal processor (DSP) implementation of the Retinex. The target processor is a Texas Instruments TMS320C6711<br />

floating point DSP. NTSC video is captured using a dedicated frame-grabber card, Retinex processed, <strong>and</strong> displayed on a<br />

st<strong>and</strong>ard monitor. We discuss the optimizations used to achieve real-time performance of the Retinex <strong>and</strong> also describe our<br />

future plans on using alternative architectures.<br />

Author<br />

Digital Systems; Algorithms; Signal Processing; Signal Analyzers; Image Enhancement<br />

20040073488 <strong>NASA</strong> Langley Research Center, Hampton, VA, USA<br />

A Discontinuous Galerkin Method for Parabolic Problems with Modified hp-Finite Element Approximation Technique<br />

Kaneko, Hideaki; Bey, Kim S.; Hou, Gene J. W.; [2004]; 22 pp.; In English<br />

Contract(s)/Grant(s): NAG1-01092; NAG1-2300; No Copyright; Avail: CASI; A03, Hardcopy<br />

A recent paper is generalized to a case where the spatial region is taken in R(sup 3). The region is assumed to be a thin<br />

body, such as a panel on the wing or fuselage of an aerospace vehicle. The traditional h- as well as hp-finite element methods<br />

are applied to the surface defined in the x-yvariables, while, through the thickness, the technique of the p-element is<br />

employed. Time <strong>and</strong> spatial discretization scheme based upon an assumption of certain weak singularity of double vertical line<br />

u(sub t) double vertical line 2, is used to derive an optimal a priori error estimate for the current method.<br />

Author<br />

Galerkin Method; Finite Element Method; Parabolic Differential Equations; Approximation<br />

20040073489 Old Dominion Univ., Norfolk, VA, USA<br />

Error Analysis for Discontinuous Galerkin Method for Parabolic Problems<br />

Kaneko, Hideaki; May 24, 2004; 4 pp.; In English<br />

Contract(s)/Grant(s): NAG1-01092; No Copyright; Avail: CASI; A01, Hardcopy<br />

In the proposal, the following three objectives are stated: (1) A p-version of the discontinuous Galerkin method for a one<br />

dimensional parabolic problem will be established. It should be recalled that the h-version in space was used for the<br />

discontinuous Galerkin method. An a priori error estimate as well as a posteriori estimate of this p-finite element discontinuous<br />

Galerkin method will be given. (2) The parameter alpha that describes the behavior double vertical line u(sub t)(t) double<br />

vertical line 2 was computed exactly. This was made feasible because of the explicitly specified initial condition. For practical<br />

217

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