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The question of adapting to radar images the existing hardware that form topographic maps through stereo-photogrammetric models, is examined in principle. Such hardware utilizes a human/ computer hybrid. Although the problem of brightness differentials between corresponding landmarks can be dealt with pseudo-photoclinometrically, the main problem is whether the perspective in a radar image can be conceived to mimic that of a photographic image obtained by a suitably positioned camera. This conception is found to be possible, providing the characteristic relief subtends to a very small angle at the radar and at the fictitious camera. The photogrammetric model parameters must be determined a priori. 相似文献
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Robert L. Wildey 《Earth, Moon, and Planets》1990,48(3):197-231
The project to develop a line-integral approach to 2-dimensional radarclinometry and to bring it to the status of producing topographic maps from real radar images has been concluded. The final developments of the theory itself have involved a trial-and-error resolution of the curvature decision process at each integration step over range as follows: (1) Locally Indeterminate Azimuth-Azimuth Curvature is invoked if the range-directed path of integration is within 1 in angle of the tangent to a local characteristic curve of the partial differential equation of radarclinometry (equivalent to a lapse in the necessity for an auxiliary curvature assumption); (2) Local Cylindricity is invoked if the local image isophote has a radius-of-curvature greater than 50 pixels; (3) Least-Squared Local Sphericity is invoked if the characteristic curve trends at greater than 70 to the range direction (the auxiliary curvature assumption is becoming a sufficiently strong influence as to warrant the overconstraint), and (4) the default hypothesis, which is invoked most often, is the localization through the Euler/Lagrange equation from the calculus of variations of the global principle of minimization of the surface area of the terrain. The development of the set of line integrals into a 2-dimensional topographic surface is not practically achieved by branching the line integral at the range threshold, because the radarclinometry equations are too frequently coupled but weakly to the slope component in the direction of radar-azimuth, and under circumstances for which the powerfully influential auxiliary curvature assumption is too unrealistic. In other words, a line integration in radar-azimuth is far more frequently directed orthogonally to the local characteristic curve than is one carried out over range. Such orthogonality results in stepping the strike under the exclusive control of the curvature assumption. Instead, a quasi-surface-integration step is taken by modeling the dependence on initial strike of the gravitational potential energy of the vertical slab of terrain under the range-profile. The adopted starting strike for the range integral is the one which minimizes the gravitational potential energy. This radarclinometric method, in combination with my recently published method for determining an effective radar back-scattering function from one-dimensional slope statistics and image pixel-signal statistics, was applied to three images. First, to separate theoretical difficulties from experimental impediments, an artificial radar image was generated from a topographic map of the Lake Champlain West quadrangle in the Adirondack Mountains. Except for the regional trend in elevation, to which radarclinometry is insensitive by design, the agreement between the original and derived topography appears good. The morphologies agree and the range of relief is the same to within 4%. As an example of data of the highest quality available from space-borne radar at the present time, a SIR-B image of very rugged terrain in the coastal mountains of Oregon was similarly processed. The result, after filtering to redistribute photoclinometric errors about the two-dimensional spatial spectrum, agrees with ground truth almost as well. As an example of the worst possible data, in terms of signal-to-noise ratio and radar incidence angle (no detraction from the praise due the first high resolution space-borne radar-imaging of Venus intended), a Venera-15 image segment in Sedna Planitia just north-east of Sapho was processed, using Venera altimetry and Pioneer roughness data for slope statistics, in spite of the resolution mis-match. Considerably more trial-and-error filtering was required. The result appears plausible, but an error check is, of course, impossible. 相似文献
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Robert L. Wildey 《Earth, Moon, and Planets》1988,41(2):141-153
Because radarclinometry is fundamentally describable in terms of a nonlinear, first-order, partial differential equation, one expects that it can, in principle, be carried out by direct deterministic integration beginning at a given threshold profile along the azimuthal coordinate. Such a boundary condition could be provided by the altimetry profile obtained on a preceding or succeeding orbital revolution of the radar-bearing spacecraft. Notwithstanding the mismatched resolutions of the radar altimeter and the radar imaging system as planned for the Megallan mission to Venus, there are fundamental considerations, not involving system noise, that influence the possibility of success of this approach. From the topographic map of the Lake Champlain West quadrangle in the Adirondack Mountains of the U.S., a radar image is synthesized. Radarclinometry, in surface integral form, recaptures the topographic map when the applicable radar reflectance function is weakly variable over the range of application, but it diverges beyond a certain point for nominally variable reflectance functions. The effect can be understood by using results from the shape-from-shading literature. (This literature is produced by a group within the artificial intelligence community who have been independently attacking, for all practical purposes, photoclinometry, except that they have not given primacy to images of terrain.) The ubiquity of the instability suggests that the value of the surface integral approach is much in doubt. 相似文献
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Robert L. Wildey 《Earth, Moon, and Planets》1987,38(1):59-95
Radarclinometry, the invention of which has been previously reported, is a technique for deriving a topographic map from a single radar image by using the dependence upon terrain-surface orientation of the integrated signal of an individual image pixel. The radiometric calibration required for precise operation and testing does not yet exist, but the imminence of important applications justifies parallel, rather than serial, development of radarclinometry and radiometrically calibrated radar. The present investigation reports three developmental advances: (1) The solid angle of integration of back-scattered specific intensity constituting a pixel signal is more accurately accounted for in its dependence on surface orientation than in previous work. (2) The local curvature hypothesis, which removes the requirement of a ground-truth profile as a boundary condition and enables the formulation of the theory in terms of a line integral, has been expanded to include the three possibilities of Local Cylindricity, Local Biaxial Ellipsoidal Hyperbolicity, and Least-Squares Local Sphericity. (3) The theory is integrated in the cross-ground-range direction, which is ill-conditioned compared to the ground-range direction, whereas the original formulation was based on enforced isotropy in the two-dimensional power spectrum of the topography. It was found necessary to prohibit the hypothesis of Local Biaxial Ellipsoidal Hyperbolicity in the cross-range stepping, for reasons not completely clear. Variation in the proportioning between curvature assumptions had produced topographic maps that are in good mutual agreement but not realistic in appearance. They are severely banded parallel to the ground-range direction, most especially at small radar zenith angles. Numerical experimentation with the falsification of topography through incorrect decalibration as performed on a Gaussian hill suggests that the banding and its exaggeration at high radar incidence angles could easily be due to our lack of radiometric calibration. 相似文献
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A mathematical theory and a corresponding algorithm have been developed to derive topographic maps from radar images as photometric arrays. Thus, as radargrammetry is to photogrammetry, so radarclinometry is to photoclinometry. Photoclinometry is endowed with a fundamental indeterminacy principle even for terrain homogeneous in normal albedo. This arises from the fact that the geometric locus of orientations of the local surface normal that is consistent with a given reflected specific-intensity of radiation is more complicated than a fixed line in space. For a radar image, the locus is a cone whose half-angle is the incidence angle and whose axis contains the radar. The indeterminacy is removed throughout a region if one possesses a control profile as a boundary-condition. In the absence of such ground-truth, a point-boundary-condition will suffice only in conjunction with a heuristic assumption, such as that the strike-line runs perpendicularly to the line-of-sight. In the present study I have implemented a more reasonable assumption which I call the hypothesis of local cylindricity.Firstly, a general theory is derived, based solely on the implicit mathematical determinacy. This theory would be directly indicative of procedure if images were completely devoid of systematic error and noise. The theory produces topography by an area integration of radar brightness, starting from a control profile, without need of additional idealistic assumptions. But we have also theorized separately a method of forming this control profile, which method does require an additional assumption about the terrain. That assumption is that the curvature properties of the terrain are locally those of a cylinder of inferable orientation, within a second-order mathematical neighborhood of every point of the terrain. While local strike-and-dip completely determine the radar brightness itself, the terrain curvature determines the brightness-gradient in the radar image. Therefore, the control profile is formed as a line integration of brightness and its local gradient starting from a single point of the terrain where the local orientation of the strike-line is estimated by eye.Secondly, and independently, the calibration curve for pixel brightness versus incidence-angle is produced. I assume that an applicable curve can be found from the literature or elsewhere so that our problem is condensed to that of properly scaling the brightness-axis of the calibration curve. A first estimate is found by equating the average image brightness to the point on the brightness axis corresponding to the complement of the effective radar depression-angle, an angle assumed given. A statistical analysis is then used to correct, on the one hand, for the fact that the average brightness is not the brightness that corresponds to the average incidence angle, as a result of the non-linearity of the calibration curve; and on the other hand, we correct for the fact that the average incidence angle is not the same for a rough surface as it is for a flat surface (and therefore not the complement of the depression angle).Lastly, the practical modifications that were interactively evolved to produce an operational algorithm for treating real data are developed. They are by no means considered optimized at present. Such a possibility is thus far precluded by excessive computer-time. Most noteworthy in this respect is the abandonment of area integration away from a control profile. Instead, the topography is produced as a set of independent line integrations down each of the parallel range lines of the image, using the theory for control-profile formation. An adaptive technique, which now appears excessive, was also employed so that SEASAT images of sand dunes could be processed. In this, the radiometric calibration was iterated to force the endpoints of each profile to zero elevation. A secondary algorithm then employed line-averages of appropriate quantities to adjust the mean tilt and the mean height of each range profile. Following this step, a sequence of fairly ordinary filtering techniques was applied to the topography. An application is shown for a Motorola image of Crazy Jug Point in the Grand Canyon. Unfortunately, a radiometric calibration curve is unavailable. But a fictitious calibration curve has provided an encouraging qualitative test of these efforts. 相似文献
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A digital file of the lunar normal Albedo 总被引：2，自引：0，他引：2
Robert L. Wildey 《Earth, Moon, and Planets》1977,16(2):231-277
A digital file of the normal albedo of the Moon has been produced at a resolution of about 1/550 of a lunar diameter (about 6.3 km). The file was produced from five photographs taken with the 61-cm reflector of the Northern Arizona University Astrophysical Observatory. No mosaicking was necessary. Spatial control is selenodetic rather than landmark-morphologic. Photometric control is provided through a combination of electrography and regular photoelectric photometry. Pixel photometric function corrections are employed. The file was provided as data base for the Lunar Consortium. Brief discussion of the scientific implications of the frequency histogram is offered, and the negligibility of lunar limb darkening below = 77° is affirmed. It is specifically desired not to withhold these data from publication while more significant and detailed scientific interpretation is carried on. 相似文献
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Robert L. Wildey 《Earth, Moon, and Planets》1988,41(3):223-240
A method is derived for determining the dependence of radar backscatter on incidence angle that is applicable to the region corresponding to a particular radar image. The method is based on enforcing mathematical consistency between the frequency distribution of the image's pixel signals (histogram of DN values with suitable normalizations) and a one-dimensional frequency distribution of slope component, as might be obtained from a radar or laser altimetry profile in or near the area imaged. In order to achieve a unique solution, the auxiliary assumption is made that the two-dimensional frequency distribution of slope is isotropic. The backscatter is not derived in absolute units. The method is developed in such a way as to separate the reflectance function from the pixel-signal transfer characteristic. However, these two sources of variation are distinguishable only on the basis of a weak dependence on the azimuthal component of slope; therefore such an approach can be expected to be ill-conditioned unless the revision of the transfer characteristic is limited to the determination of an additive instrumental background level. The altimetry profile does not have to be registered in the image, and the statistical nature of the approach minimizes pixel noise effects and the effects of a disparity between the resolutions of the image and the altimetry profile, except in the wings of the distribution where low-number statistics preclude accuracy anyway. The problem of dealing with unknown slope components perpendicular to the profiling traverse, which besets the one-to-one comparison between individual slope components and pixel-signal values, disappears in the present approach.In order to test the resulting algorithm, an artificial radar image was generated from the digitized topographic map of the Lake Champlain West quadrangle in the Adirondack Mountains, U.S.A., using an arbitrarily selected reflectance function. From the same map, a one-dimensional frequency distribution of slope component was extracted. The algorithm recaptured the original reflectance function to the degree that, for the central 90% of the data, the discrepancy translates to a RMS slope error of 0.1 . For the central 99% of the data, the maximum error translates to 1 ; at the absolute extremes of the data the error grows to 6 . 相似文献
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Robert L. Wildey 《Icarus》1975,25(4):613-626
The present investigation develops a new theory for the photoclinometric determination of topography when the photometric function of the planetary surface (or that which corresponds to the mean optical depth of emergent scattered solar radiation from an optically thick planetary atmosphere) is not restricted beyond the expectation that it is a function of phase angle, angle of incidence, and angle of emergence. Several versions of such an operational theory, which differ according to the auxiliary conditions employed to achieve mathematical determinacy, together with several approaches to the numerical analysis, have been evolved. The differences in the numerical methods arise from a variable trade-off between computing speed and stability and computer storage requirements. Although the computer encoding process is not yet fully operational, a first result has been worked out for an early frame in the Mariner 9 mission in which the dust-laden atmosphere appears to exhibit standing-wave patterns. Provided the assumption of homologous departures from plane-parallel atmospheric configuration is valid, the photoclinometric implication is that laminar flow lines in the optically viewable dust layer undergo a near-sinusoidal rise and fall of about 40 to 50m. Regardless of assumption, the resulting surface is a rigorous mean-emission surface. 相似文献
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