Systematic Selection of Very Important Points (vip) from Digital Terrain Model for Constructing Triangular Irregular Networks

Selection of a set of significant points from a raster digital terrain model is important for constructing a triangular irregular network. The set of points should contain information of terrain surface as rich as possible. INTRODUCTION The most common form of digital terrain model is the raster data structure. Its dense grids represent terrain surface very well for some applications. However, another new data structure has obtained more and more attention recently. For representation of terrain, an efficient alternative structure to dense raster grids is the Triangular Irregular Network (TIN), which represents a surface as a set of non-overlapping contiguous triangular facets, of irregular size and shape. The TIN data structure shows a better solution to overcoming problems caused by the non-stationary property of the terrain surface. Also, for some applications, such as shading, cataloging, and visibility, TIN has a nice implementation. TIN can be directly generated from random point data. However, for constructing TIN from raster DTM, it is not so simple. First, DTM usually has too many pixels which can not all be selected for constructing TIN. Second, if one uses all pixels to construct a TIN, some advantages of TIN, such as simplification and generalization, are lost. Only a subset of pixels from the total pixels can be used for the generation of TIN. Thus, a key question is raised: 'Which pixel should be selected ? ' and 'Which pixel can be ignored?'. The principle here is that, between two pixels, the more important point should be selected. 'VIP 1 PROCEDURE Before answering the question of which are the more important points among all pixels, a significance of each pixel must be evaluated. Here the significance of a pixel means how great a contribution the pixel can make to the representation of the surface. Our goal is constructing a triangular 'irregular -network ;(TINj) -to represent the .original terrain surface by using the least number <of points. W<e ihave ,to select .some pixels, while other points 'have to be thrown away. When we say a pixel PI is more -important than .another 50 pixel P2, we mean that a more precise triangular irregular network (TIN) can be constructed if we use the pixel PI in the set instead of pixel P2. The function of the VIP procedure is to select a set of pixels. The set must have two properties: (1) For certain precision, a TIN constructed from the set has the least number of points than any other set. (2) Among all possible sets, with the same number of points selected from the DTM, the set can construct the most precise TIN than any other set. In other words, any point belonging to the selected set should be more important than any point that does not belong to the set. Evaluation of significance of a pixel We have to know how important a pixel is before selection of pixels. The VIP procedure calculates the significant degree of each pixel. An improved spatial high-pass filter is used to produce this significant degree. High-pass filtering A picture or an image can be represented in either spatial domain or frequency domain. In frequency domain, low-frequency (long wavelength) components represent major features on the original picture, such as overall skelton, major spatial distribution, etc. High-frequency (short wavelength) components represent detail features, such as edges, peaks or pits. These properties of spatial filtering have been used in digital image processing widely. For example, high-pass filters can do edge enhancement for images to find features. High-pass filters can also be used to select significant feature points from digital terrain surface models. A pixel should be selected only if we can not predict its value from its neighbor pixels. For example, if a pixel has an average value from its eight neighbors,, this pixel is not important enough to be selected. In other words, the significance of a pixel can be evaluated by measuring its changing behavior from its neighbors. This measure can be done by high-pass filters,, such as spatial differential or a Laplacian operator. For terrain surfaces, in our applications, an improved spatial differentialhigh-pass filter is used. In the one-dimension case, the second order differential of a function Y=F(X) can be noted as: d2Y/dX2 =F"(X) = 2 * [F(XO) 0.5 * (F(X1) + F(X2))] 2 * [F(XO) A] The distance AC, shown in Figure 1, can be used to measure the behavior of change.