Reconstructing Architectural Environment from the Perspective Image

Abstract

The perspective representation of architectural objects can be used for illustrative purposes, technical documentation and research. An inverse process, namely reconstruction of such objects on the basis of their single perspective image may prove difficult. The aim of the hereby study is to determine the requirements which the perspective image should meet for restitution purposes, as well as developing an effective method of the reconstruction of architectural objects on the basis of their perspective mapping. Our considerations were constrained to linear perspective as it is the most popular form of perspective presentation. It was stressed that the crucial point of linear perspective restitution is the determination of its base elements; a main point, a horizon line, a ground line and the distance of the station point from the picture plane, which define the method of the perspective representation. The reconstruction attempt was based on geometrical rules and relations occurring between the points of the given 3D object and their perspective 2D mappings. Due to the fact that straight lines are very common in every urban environment, algorithms were developed, with changeable base elements of perspective to draw linear perspective image of any straight line passing through two points of the given object. On the basis of these algorithms the equations were formulated for calculation of the 3D location of the object characteristic points presented in the perspective 2D image, which determined the edge 3D model. Our method of restitution can be useful for reconstruction of different forms of perspective presentation; technical drawings, paintings, photographs and sketches, as well as it can be applied for improving or finding missing building contour in the perspective image. The study shows that retrieving some information about a spatial structure of the architectural object from the single perspective image is not always easy, although it is possible in some cases.

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