Keywords: Semi-Automatic, Roof Reconstruction, Object Knowledge, 3-D Line

Abstract
Up to now, the automatic reconstruction for buildings can’t satisfy all the current requirements. Hence, the problem of roof reconstruction becomes to how to effectively integrate the interpretation ability of the operator into the reconstruction system and help this system to accomplish the task. This paper presents a semi-automatic system for roof reconstruction based on 3-D linear segments by the effective integration of the interpretation ability of the operator. After verifying of the shown 3-D linear segment, the operator selects other 2-D or 3-D lines of roof patch in any image with the mouse device and then decides the reconstruction model to automatically find the equivalent in the other image. We will present three models for roof reconstruction and compare these results. Preliminary experiments prove this framework of this system is feasible and the interface model by the operator is also effective.

Introduction
The general procedure for roof reconstruction could be simply divided into the three subtasks: geometrical feature extraction, the detection of possible locations of roofs or roof boundaries and the final roof reconstruction. Even though the rapid development of the computer technology, it is still a great problem to make the computer deal with the interpretation task correctly. The central point lies on the lack of complete theory to handle this problem as far so that the automatic reconstruction for building[ Collgins et al., 1995;Fischer et al., 1997; Henriccson and Baltsavias, 1997; Lin et al., 1995; McGlone and Shuffel, 1994; Nevatia et al, 1997; Shuffelt 1996] can’t satisfy all the current requirements. Hence, the reconstruction problem becomes to another issue that is how to effectively integrate the interpretation ability of operator into the system and help this system to accomplish the reconstruction correctly, i.e. semi-automatic system for roof reconstruction[ Gruen,1998; Gülch, 1997; Heuel and Nevatia,1995; Hsieh, 1995; Lang and Förstner,1996]. Therefore, this paper would like to present a semi-automatic system for roof reconstruction based on 3-D linear segments by the effective integration of the interpretation ability of the operator. First of all, one 3-D linear segment is verified whether it belongs to the boundaries of roofs or not. Then, the operator selects other 2-D or 3-D lines of this roof patch in one single image with the mouse device. Finally, the system automatically finds the equivalent of this roof patch in the other image after the operator decides the reconstruction model. Of course, the result would be verified by the operator again. The 3-D linear segments verified by the operator play an important role, i.e. to give a constraint information, when conducting the reconstruction. We will present three models for reconstruction and compare these results. Another issue in our paper is to investigate the feasibility of our system in the urban areas and analyze the possible questions. Meanwhile, we also express our opinion about the effective interface model by the operator.

System Design and Illustration
Fig. 1 illustrates the whole diagram of this semi-automatic system. The 3-D linear segments are obtained by considering the object knowledge of 3-D lines in object space when simultaneously linking and matching the 2-D lines from the stereo images with known orientation [Chio et al., 1999]. This algorithm exploits the change rate of height and plane distance to improve the linking of linear feature in the images of urban areas, where might capture the "false" collinear features in image space because of the affection of projection position or occlusion.


Fig.1: Diagram for roof reconstruction
At the beginning of roof reconstruction, the system will display one 3-D linear segment. Then, the operator verifies if the linking result is correct and if this one represents the border of the roof patch or not. If the answer is no, the system will ignore this 3-D linear segment and shows the next one; otherwise, the operator can select other 2-D or 3-D lines, which could consist of the complete roof patch, with the mouse device in any single image. What we need are the intersection points of linear segments to decide the roof corners, therefore, the selected 2-D or 3-D lines could be only a part of one complete roof boundary. Our system now could deal with the quadrangular roof, which is not only limited to parallelism or rectangle, and the selected order should be clockwise or counterclockwise. Moreover, one feature for our system is that the way of line-selection could not be as accurate as the way of point-selection. In this procedure, the recognition ability of the operator is fused into system to correctly choose the borders of roof patch. The selection of lines for roof patch is corresponding to the detection of roof. The advantage of such a handling is to reduce the judgement of computer and compensate for the ability of the computer to identity those roof boundaries from the numerous linear segments.