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Title: Surface reconstruction from contour lines or LIDAR elevations by least squared-error approximation using Tensor-Product Cubic B-splines
Authors: MUKHERJI, S
Keywords: Interpolation
Issue Date: 2008
Abstract: We consider, in this paper, the problem of reconstructing the surface from contour lines of a topographic map. We reconstruct the surface by approximating the elevations, as specified by the contour lines, by tensor-product cubic B-splines using the least squared-error criterion. The resulting surface is both accurate and smooth and is free from the terracing artifacts that occur when thin-plate splines are used to reconstruct the surface. The approximating surface, S(x,y), is a linear combination of tensor-product cubic B-splines. We denote the second-order partial derivatives of S by S(xx), S(xy) and S(yy). Let h(k) be the elevations at. the points (x(k),y(k)) on the contours. S is found by minimising the sum of the squared-errors {S(x(k),y(k))-h(k)}(2) and the quantity integral integral S(xx)(2)(x, y) + 2S(xy)(2)(x, y) + S(yy)(2) (x, y) dydx, the latter weighted by a constant lambda. Thus, the coefficients of a small number of tensor-product cubic B-splines define the reconstructed surface. Also, since tensor-product cubic B-splines are non-zero only for four knot-intervals in the x-direction and y-direction, the elevation at any point can be found in constant time and a grid DEM can be generated from the coefficients of the B-splines in time linear in the size of the grid.
ISBN: 978-3-540-72134-5
ISSN: 1863-2246
Appears in Collections:Proceedings papers

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