Topological spatial relation between spatial objects is a very important topic for spatial analysis, query and reasoning in
Geographic Information Science (GIS). In this paper, an algebraic method using constrained Delaunay triangulation (CDT) for topological spatial relation is presented. In the part of foundational theory, (i) prove CDT is simplicial complex in R<sup>2</sup>. (ii) import chain structure in CDT and prove including & approximating theorem and reduced including & approximating theorem, and are used for estimating left, middle and right side properties of triangle. (iii) define the region in CDT and establish region algebra (RA), which use the set of region as computational space and use the intersection operator as a binary operation. (iv) describe basic forms of node and chain which are contained in a set of triangles. In the part of spatial relation calculation, (i) describe spatial object as three entries, i.e. exterior, boundary and interior, with left, middle and right of triangle and their combination. (ii) establish the topological spatial relation calculation model-region nine intersection model (R9IM), which is used the intersection operation and the form operation as basic operations. (iii) calculate thirty-three spatial relations of simple objects with R9IM in the practice application of topological examination.
Targets based on linear feature often need to be extracted and identified with high precision in the application of
photogrammetry. Linear features such as hydrological object boundaries, roads and the boundary of other man made
objects are very important for geospatial information extraction and analysis from remotely sensed imagery. This paper
deals with subpixel accuracy extraction of linear features, especially specific parallel straight lines. There are many
algorithms for localization, such as Gray moment operator, Hough transformation algorithm Forstner operator and so on,
just only adopting a single algorithm, the precision of localization is low, and the calculation is complicated. So a new
mixed method is proposed in the paper and the procedure can be divided into two steps. Firstly, the rough location of the
parallel straight lines was extracted with Hough transformation algorithm. We could get the initial value of parallel
straight line in this step. Secondly, straight linear fitting based on Gray moment operator for edge location was adopted
to extract the straight lines with high precision. The experimental results indicate that the mixed method for subpixel
localization locates the target very validly, and some practicable conclusions are received.