By Zhilin Li
With the common use of GIS, multi-scale illustration has develop into a tremendous factor within the realm of spatial information dealing with. concentrating on geometric changes, this source offers finished assurance of the low-level algorithms to be had for the multi-scale representations of other forms of spatial positive aspects, together with aspect clusters, person strains, a category of traces, person components, and a category of components. It additionally discusses algorithms for multi-scale illustration of three-D surfaces and 3-D good points. Containing over 250 illustrations to complement the dialogue, the publication offers the latest examine effects, similar to raster-based paintings, set of rules advancements, snakes, wavelets, and empirical mode decomposition.
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Extra info for Algorithmic Foundation of Multi-Scale Spatial Representation (2006)(en)(280s)
It was developed by French geostatistical scientists G. Matheron and J. Serra in the 1960s (Matheron, 1975; Serra, 1982). Since then it has found increasing applications in digital image processing. , 1996, 1997a, 1997b, 1998). 1 BASIC MORPHOLOGICAL OPERATORS Because morphological operators are based on set operators, it is necessary to have a brief outline of set operators in this subsection. A spatial feature can be considered as a set. Then set operators can be employed to manipulate spatial features.
1 Mathematical Functions for Geometric Elements Geometric elements Mathematical function 1 Straight line (Ln) ax + by + c = 0 2 Plane (Pl) ax + by + cz + d = 0 3 Curved line (Cl) y = a + bx + cx 2 + .... 4 Circle (Cr) ( x − x 0 )2 + ( y − y0 )2 = r 2 5 Curved surface (Cs) z = a0 + a1 x + b1 y + a2 x 2 + b2 y 2 + ... 1) where L is the length along the curved line, sometimes called the arc length. In this equation each of the X and Y coordinates has become a monotonic function of L. 5 shows the parametric representation of a curved line.
13, where the features are represented by gray pixels marked with 1. 13a is the original feature (image) A. 13b is the structuring element B. The origin of a structuring element is considered to be its geometric center if there is no other specific indication. 13c is the result of feature A dilated by B. The symbol + indicates pixels that are a result of this dilation process. In ordinary terms, this dilation is achieved by moving the structuring element (as a template) along row and column. If a black (or 1) pixel is encountered, the template center is placed on the pixel position and the template is stamped onto this position to produce a set of output pixels.
Algorithmic Foundation of Multi-Scale Spatial Representation (2006)(en)(280s) by Zhilin Li