DETECTION OF BUILDING ALIGNMENTS BY USING PARABOLIC AND CIRCLE REGRESSION
ISBN 978-85-88783-11-9
Authors
1Cetinkaya, S.
1YILDIZ TECHICAL UNIVERSITY Email: sicetin@yildiz.edu.tr
Abstract
Spatial patterns have crucial important during cartographic generalisation since they contains several characteristics that are so vital in order to communicate the right information. Building alignments as a kind of spatial pattern are too vulnerable to the generalisation operators. In other words, they can easily be affected negatively if they had not been extracted and carefully handled. The building generalisation can be performed in two different ways 1) the generalisation of each individual building and 2) contextual generalisation of a set of buildings. While former approach comprises simplification, enlargement, squaring operators, latter one that should be handled with the spatial patterns issues involves selection, typification aggregation and displacement. Contextual generalisation is usually required at medium scale in which it is impossible to represent all buildings without spoiling the geometric accuracy. Therefore, appropriate building alignment characteristics should be preserved while the quantity is reduced at the same time. Building alignments should be detected to be avoided from the side effects of the generalisation operators and emphasize their characteristics as well. Although there are several approaches available for extraction of the alignments, they are designed for either only linear or only curvilinear alignments. In this study, parabolic and circle regression have been proposed for the detection of the building alignments. Algorithms developed in this study use the previously determined building groups in urban blocks as input data. Due to both requirements of the regression equations and perceptual reasons, building alignments have to consist at least three individual buildings. For parabolic regression, vertices of buildings are rotated with a three degree step by Helmert transformation, as the shape of parabola depends on the coordinate axes. Both building centroids and building vertices have been used to determine the parameters of the regression equations. One quality measure of the alignments has been calculated by the amount of the total deviation from the regression curve (circle or parabola). Because a detailed quality assessment is required, successive buildings have been determined by using minimum spanning tree (MST) after the regression processes. Then, the quality assessment has been carried out by using the homogeneity of the inter distances between the successive buildings in a candidate alignment. According to the quality measures, all alignment candidates have been ordered by descending. Therefore, all possible building alignments have been obtained by their quality grades. Finally, a comparison has been made between the results of parabolic and circle regression. Besides, the results obtained by using only centroids, only vertices and combination of centroids and vertices have been examined. Main advantage of the using parabolic and circle regression is the ability of finding both linear and curvilinear alignments simultaneously. Furthermore, changings of a building alignment characteristic can be observed during the scale transitions by using the parameters of the regression equations in evaluation and comparison of the generalisation processes.
Keywords
building alignments; regression; generalisation