DSpace at IIT Bombay >
IITB Publications >
Proceedings papers >
Please use this identifier to cite or link to this item:
http://dspace.library.iitb.ac.in/jspui/handle/100/2137

Title:  Surface reconstruction from contour lines or LIDAR elevations by least squarederror approximation using TensorProduct Cubic Bsplines 
Authors:  MUKHERJI, S 
Keywords:  interpolation 
Issue Date:  2008 
Publisher:  SPRINGERVERLAG BERLIN 
Citation:  ADVANCES IN 3D GEOINFORMATION SYSTEMS,213227 
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 tensorproduct cubic Bsplines using the least squarederror criterion. The resulting surface is both accurate and smooth and is free from the terracing artifacts that occur when thinplate splines are used to reconstruct the surface. The approximating surface, S(x,y), is a linear combination of tensorproduct cubic Bsplines. We denote the secondorder 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 squarederrors {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 tensorproduct cubic Bsplines define the reconstructed surface. Also, since tensorproduct cubic Bsplines are nonzero only for four knotintervals in the xdirection and ydirection, the elevation at any point can be found in constant time and a grid DEM can be generated from the coefficients of the Bsplines in time linear in the size of the grid. 
URI:  http://dx.doi.org/10.1007/9783540721352_13 http://dspace.library.iitb.ac.in/xmlui/handle/10054/15370 http://hdl.handle.net/100/2137 
ISBN:  9783540721345 
ISSN:  18632246 
Appears in Collections:  Proceedings papers

Files in This Item:
There are no files associated with this item.

Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.
