Validating the use of object-based image analysis to map commonly recognized landform features in the United States

ABSTRACT

The U.S. Geological Survey (USGS) National Geospatial Program (NGP) seeks to i) create semantically accessible terrain features from the pixel-based 3D Elevation Program (3DEP) data, and ii) enhance the usability of the USGS Geographic Names Information System (GNIS) by associating boundaries with GNIS features whose spatial representation is currently limited to 2D point locations. Geographic object-based image analysis (GEOBIA) was determined to be a promising method to approach both goals. An existing GEOBIA workflow was modified and the resulting segmented objects and terrain categories tested for a strategically chosen physiographic province in the mid-western US, the Ozark Plateaus. The chi-squared test of independence confirmed that there is significant overall spatial association between terrain categories of the GEOBIA and GNIS feature classes. Contingency table analysis also suggests strong category-specific associations between select GNIS and GEOBIA classes. However, 3D visual analysis revealed that GEOBIA objects resembled segmented regions more than they did individual landform objects, with their boundaries often failing to correspond to match what people would likely perceive as landforms. Still, objects derived through GEOBIA can provide initial baseline landscape divisions that can improve the efficiency of more specialized feature extraction methods.     

LONG LINES ON THE EARTH

Abstract

The Arc of the Geodesic.—In the first part of this paper a method was given for computing the azimuth of a geodesic. The method gives the convergence of the geodesic correctly up to the second power of e the eccentricity. The formula (9), however, also depends on the assumption that σ, the arc-length of the geodesic, can be obtained with sufficient accuracy from the Supplemental Dalby Theorem, that is to say, by a purely spherical computation. It is, therefore, needful to show that this supposition is justifiable; a means must in fact be indicated for verifying the assumption.     

EXPANSION OF PAPER AS AFFECTING AREA

Abstract

For the sake of the junior reader we may repeat an old and simple investigation. Let us suppose that the paper on which a map is printed undergoes a regular expansion p in one direction, say the X direction, and another regular expansion q in the Y direction, perpendicular to the former; it is required to know the effect of these expansions on the area of any parcel on the map. Note that, so far as the mathematics are affected, X and Y are not necessarily parallel to the margins of the sheet; we shall take them here as axes of any rectangular coordinate system. The symbols p and q are regarded as ratios, so that 100p and 100p represent the percentage expansions; if the paper contracts instead of expanding, no more is necessary than to change the sign.     

THE TRANSVERSE MERCATOR PROJECTION

Abstract

I. Introduction.—Map projection is a branch of applied mathematics which owes much to J. H. Lambert (v. this Review, i, 2, 91). In his “Beyträge zum Gebrauche der Mathematik und deren Anwendung” (Berlin, 1772) he arrived at a form of projection whereof the Transverse Mercator is a special case, and pointed out that this special case is adapted to a country of great extent in latitude but of small longitudinal width. Germain (“Traité des Projections”, Paris, 1865) described it as the Projection cylindrique orthomorphe de Lambert, but he also introduced the name Projection de Mercator transverse or renversée; he shows that Lambert's treatment of the projection was remarkably simple.     

BOWDITCH TRAVERSE ADJUSTMENT AND A MODIFICATION: NOTES

Abstract

In the second part of the paper on this subject in the last issue (30, 483) the references to the relative angular and linear closures are rather misleading. Mr Clendinning points out that the probable angular error at a station must be considered; the mean error is clearly different.     

SOME PROBLEMS OF RESECTION AND COUNTERSECTION-I

Abstract

“A Well-Defined mountain, though miles inland and never visited by the surveyors, will often prove the very keystone of a chart which cannot be regularly and theoretically triangulated” (“Hydrographic Surveying”, by Rear-Adm. Sir Wm J. L. Wharton, K.C.B., and Rear-Adm. Mostyn Field, F.R.S. 3rd Ed. 1909, p. 128). To many the reasons prohibiting the occupation of inland stations may be unknown; it may suffice to state that, in the past, British hydrographers have mapped many coastal waters where penetration of the land was at least inadvisable. Since the charts so made were in general sold to the world, seamen of all nations have benefited from the surveys.     

Using a Grid-Based Filter to Solve InSAR Phase Unwrapping

This letter presents a phase-unwrapping (PU) algorithm for synthetic aperture radar interferometry based on a grid-based filter. The proposed PU algorithm, which is based on state-space techniques, simultaneously performs noise filtering and PU. The formulation of this technique provides independence from noise statistics and is not constrained by the nonlinearity of the problem. Results obtained with synthetic data show a significant improvement with respect to other conventional PU algorithms in some situations.     

A data-driven approach to local gravity field modelling using spherical radial basis functions

We propose a methodology for local gravity field modelling from gravity data using spherical radial basis functions. The methodology comprises two steps: in step 1, gravity data (gravity anomalies and/or gravity disturbances) are used to estimate the disturbing potential using least-squares techniques. The latter is represented as a linear combination of spherical radial basis functions (SRBFs). A data-adaptive strategy is used to select the optimal number, location, and depths of the SRBFs using generalized cross validation. Variance component estimation is used to determine the optimal regularization parameter and to properly weight the different data sets. In the second step, the gravimetric height anomalies are combined with observed differences between global positioning system (GPS) ellipsoidal heights and normal heights. The data combination is written as the solution of a Cauchy boundary-value problem for the Laplace equation. This allows removal of the non-uniqueness of the problem of local gravity field modelling from terrestrial gravity data. At the same time, existing systematic distortions in the gravimetric and geometric height anomalies are also absorbed into the combination. The approach is used to compute a height reference surface for the Netherlands. The solution is compared with NLGEO2004, the official Dutch height reference surface, which has been computed using the same data but a Stokes-based approach with kernel modification and a geometric six-parameter “corrector surface” to fit the gravimetric solution to the GPS-levelling points. A direct comparison of both height reference surfaces shows an RMS difference of 0.6 cm; the maximum difference is 2.1 cm. A test at independent GPS-levelling control points, confirms that our solution is in no way inferior to NLGEO2004.     

Motion Analysis in SAR Images of Unfocused Objects Using Time–Frequency Methods

Synthetic aperture radar (SAR) image formation processing assumes that the scene is stationary, and to focus an object, one coherently sums a large number of independent returns. Any target motion introduces phases that distort and/or translate the target's image. Target motion produces a smear primarily in the azimuth direction of the SAR image. Time-frequency (TF) modeling is used to analyze and correct the residual phase distortions. An interactive focusing algorithm based on TF modeling demonstrates how to correct the phase and to rapidly focus the mover. This is demonstrated on two watercraft observed in a SAR image. Then, two time-frequency representations (TFRs) are applied to estimate the motion parameters of the movers or refocus them or both. The first is the short-time Fourier transform, from which a velocity profile is constructed based on the length of the smear. The second TFR is the time-frequency distribution series, which is a robust derivative of the Wigner-Ville distribution that works well in this SAR environment. The smear is a modulated chirp, from which a velocity profile is plotted and the phase corrections are integrated to focus the movers. The relationship between these two methods is discussed. Both methods show good agreement on the example.