An Iterative Approach to Acquire Linear Features under the constraints of their knowledge in Object Space
Shih-Hong Chio and Shue-Chia Wang
Ph.D. Candidate and Professor
Department of Surveying Engineering, National Cheng-Kung University
No. 1, University Road, Tainan, TAIWAN
Tel:(+886)-6-2373876 ext.834; Fax:(+886)-6-2375764
E-mail: p6883102@sparc1.cc.ncku.edu.tw
Key Words
Geometric constraint, Matching, Linking, Object knowledge
Abstract
3-D linear segments are crucial primitives for reconstruction of man-made buildings. This paper presents one iterative approach to acquire more linear segments from stereo image pair with known orientations under the constraints of their knowledge in object space. The major algorithm in this iterative approach is referred as "Core Algorithm" which simultaneously match and link linear segments based on their knowledge in object space. This iterative approach consists of four processing procedures. No additional height constraint is used in the first processing procedure. The other three iterative processing procedures will employ average height from relevant 3-D linear segments as additional height constraint to acquire more 3-D linear segments by using Core Algorithm. We hope this iterative approach will increase the amount of the acquisition of 3-D linear segments.
1. Introduction
3-D linear segments are crucial primitives that constitute most of the man-made objects, especially the roof boundaries in the aerial images. Therefore, they are very important for the reconstruction of man-made object. No matter what kind of method is used to acquire those 3-D linear segments, i.e. segment stereo-matching algorithm in [1], it is impossible to obtain all the 3-D linear features. Therefore, this paper would like to presents one iterative approach to acquire more 3-D linear segments under the constraints of their knowledge in object space. The core algorithm of this iterative approach is to simultaneously match and link the linear segments based on their knowledge in object space. Firstly, Core Algorithm is used to those linear segments according to the order of their geometric structure. No additional height constraint from adjacent 3-D linear segments could be imposed in this step. During this first process, when it succeeds, the average height of this acquired 3-D linear segment will be immediately introduced as additional constraint to handle the adjacent linear segments of this successfully processed linear structure by Core Algorithm. This is the second iterative process. Subsequently the same Core Algorithm with height constraint are used in the third iterative process to handle the remaining linear segments that are the members of the successfully processed linear structure. Finally, Core Algorithm together with height constraint will be once more applied to those remaining linear segments that locate at the certain range of those already successfully processed linear segments. We will describe Core Algorithm in Section 2 and this iterative approach in Section 3. The relevant experiments will be shown in Section 4. Finally, short conclusions will be drawn in Section 5.
2. Core Algorithm for Matching and Linking in Object Space
2.1 Available Knowledge of 3-D Linear Segments in Object Space and Their Calculations
As stated before, Core Algorithm will match and link linear segments based on their object knowledge. Hence, this section will describe the relevant knowledge of 3-D linear segments and their calculations.
We assume that man-made 3-D linear segments should be either oblique or horizontal. Since they are man-made, their change rate of height in object space should be reasonable. For one horizontal 3-D linear segment, the real change rate of height should be close to zero meter per meter (short for m/m). For one oblique 3-D linear segment, the real change rate of height along this line should be constant and within a reasonable limit. These two definitions for change rate of height are the main knowledge of linear segments in object space that will be used as constraints in our method to match and link linear segments. Also, it implies that several linear segments with same change rate of height could be the same one. Of course, if this 3-D linear feature is horizontal, then the same height information will be its another knowledge. Next we will explain how to calculate the change rate of height of one 3-D line.
Fig.1: Illustration of calculation of the average change rate of height
In Fig.1, one 3-D horizontal linear segment is projected onto stereo images. One 3-D edge piece is defined as every three corresponding edge pixel in series and one 3-D linear segment could be regarded as the composition of several 3-D edge pieces. Each corresponding edge pixel will determine its 3-D coordinate in object space by the space intersection, therefore, the ground coordinates on each 3-D edge piece will be known also; then the individual information on each 3-D edge piece will be calculated accordingly (see Fig. 1). Next the object knowledge, i.e. average change rate of height, for each 3-D linear segment will be determined according to those 3-D edge pieces. Now, the details to calculate will be described below.
Firstly, the horizontal distance (dP(i)) of 3-D edge pieces i will be defined as shown in Fig.1. It should be limited in terms of pixel resolution and image scale. The limitation of dP(i) corresponds to filter the problematic and unreliable individual change rate of height dZ(i) along this 3-D linear segment. Those unreliable dZ(i) might be caused by noise or by uncertainty of edge points during the edge detection. After the unreliable edge pieces are filtered, average change rate of height dZ of this 3-D linear segment will be determined by averaging dZ(i) from all reliable 3-D edge pieces (c.f Fig.1). Fig.1 just illustrates how to get the knowledge of horizontal line segments, but it's applicable to oblique 3-D line segment.
