A Robust Method for Registering Ground-based Laser Range Images of Urban Outdoor Objects

There is a potentially strong demand for detailed 3D spatial data of urban area. Ground-based laser range scanner is one of the promising devices to acquire range images of urban 3D objects. In this paper, the authors propose an automated registration method of multiple overlapping range images for the reconstruction of 3D urban objects. Registration is achieved in two steps, pair-wise registration and multiple registration assuming that one rotating axis of a laser range scanner is almost vertical. At first, pair-wise registration determines approximate values of four transformation parameters, a horizontal rotation angle and three translation parameters of a pair of neighboring range images. Then through multiple registration, the transformation parameters of all range images are adjusted using the approximate values so as to minimize the total errors. An outdoor experiment was conducted registering forty-two range images to construct a 3D model of a building in the campus of the Univ. of Tokyo. Accuracy of the model was examined using a 1:500 scale digital map and GPS measured location of viewpoints. Efficiency and Accuracy of the registration method is demonstrated in this paper. INTRODUCTION In a variety of applications ranging from visualization of urban landscape to advanced automobile/pedestrian guidance systems for ITS (intelligent transportation system), accurate and detailed 3D urban spatial databases are increasingly on demand. There are two approaches of 3D data acquisition air-based and ground-based. Air-based data acquisition techniques, typically aerial survey, can cover relatively wide area, but usually fail to capture details of urban objects such as side walls (façade) of buildings. On the other hand, ground-based methods such as using vehicle-borne CCD cameras can easily cover such details of urban objects, though the spatial coverage may be limited. Recently, the reconstruction of 3D urban objects using ground-based techniques is attracting more attention because such details of urban objects, which can be easily viewed from streets or on ground surface, are found to be of importance in guidance system, for radio disturbance analysis in telecommunication and so forth. Many applications of 3D GIS involve user viewpoints on the ground, not in the air. Several research groups in photogrammetry community invested in fusing the information from air and ground-based survey for the reconstruction of high-resolution building models within built-up area, where ground-level still images are pasted onto the building façades that are generated using air-based methods (e.g. Gruen 1998, Jaynes 1999). But an automatic calibration of ground-level view with aerial imagery is difficult to achieve, especially in highly dense urban areas. Several researches using ground-based CCD cameras have demonstrated that 3D urban objects can be extracted using motion and stereo vision techniques (e.g. Ozawa et.al.1998). However, insufficient robustness in stereo matching, distortion from limited resolution and unstable geometry of CCD cameras are major obstacles to the operational uses of these methods. Researches using range scanners are found in Thorpe et.al.1988 in a mobile navigation system; Kamgar-Parsi et.al.1991 in obtaining a map of ocean floor; Chen and Medioni 1992, Champleboux et.al.1992, Shum et.al.1994 in modeling small objects such as teeth, sculptures, mechanical parts, etc.; Ng et.al.1998 in constructing 3D models of indoor objects; Lemmens et al.1997, Haala et al.1998, Stilla and Jurkiewicz 1999 in air-borne systems. Through these research achievements, efficiency and accuracy of range scanners serving spatial data acquisition has been demonstrated. In addition, ground-based measurement using laser range scanner in urban environment has become technically feasible with the recent development of eye-safe laser range scanners. However, there is still no other researches addressing the reconstruction of 3D urban outdoor objects using ground-based laser range scanner. Since one snapshot can not cover the entire 3D PE&RS, vol.67, no.10, pp.1143-1153, 2001 2 urban object, one of the major challenges in applying ground-based laser range scanning for the reconstruction of 3D urban outdoor objects is the registration of multiple overlapping range images acquired at different locations (viewpoint) and with different viewing angles. This research is a contribution to the development of a robust method for registering a network of ground-based laser range images. Figure 1. An example of range measurement from each façade of the building. PROBLEM STATEMENT Registering multiple range images – i.e., correctly aligning range images by transforming them into a common “global” coordinate system – is typically solved as a two-step procedure, pair-wise registration and multiple registration. Figure 1 shows a motivational example of measuring a building using a network of range images } , , , { 8 2 1 V V V L . If all range images are to be aligned to the coordinate system of 1 V , while location and direction of viewpoints are unknown, the following steps are conducted. First, find the relative transformation matrixes } ) , ( | { H j i tij ∈ between the coordinate systems of neighboring range images (pair-wise registration). It is always solved as a correspondence or matching problem. Next, find the absolute transformation matrixes } 8 1 | { ≤ ≤ i Ti from each local coordinate system to the coordinate system of 1 V (multiple registration). In this step, } 8 1 | { ≤ ≤ i Ti can be obtained by sequentially aligning } ) , ( | { H j i tij ∈ , however estimation errors in pair-wise registration might get accumulated. For example, 6 V can be aligned to the coordinate system of 1 V by 76 87 18 6 t t t T = , while 5 V be aligned to the coordinate system of 1 V by 5 , 4 4 , 3 3 , 2 2 , 1 5 t t t t T = . Then relative transformation matrix from the coordinate system of 6 V to 5 V is 6 , 7 7 , 8 8 , 1 1 , 2 2 , 3 3 , 4 4 , 5 6 1 5 6 , 5 ' t t t t t t t T T t = = − . In practice, ' 6 , 5 t is not equal to 6 , 5 t due to the accumulation of estimation error in } ) , ( | { H j i tij ∈ . Thus, the key problem that has to be tackled here is to minimize the accumulation of errors in pair-wise registration. Pair-wise registration Pair-wise registration has been at the core of many previous research efforts. Kamgar-Parsi et al 1991 matched the contours that extracted from different range images. Chen and Medioni, 1992 minimized the distances from control points of one view to the surfaces of another. Shum et al. 1994 exploited attribute graphs, which are generated using planar regions and their inter-relations. Krishnapuram and Casasent, 1989 determined the transformation parameters by extending the straight-line Hough Transform to three-dimensional space. Higuchi et al. 1995 converted the problem to the matching of two Spherical Attribute Images (SAI). Up to now, few works are addressed on urban outdoor area except the authors’ previous research. In Zhao and Shibasaki, 1997, the authors presented a pair-wise registration method using planar faces, however robustness of the method is still insufficient to achieve full automation in some urban outdoor environment for the following reasons. First, range data in urban area are affected by many disturbances such as trees, window glasses, passing cars, pedestrians and so forth. Secondly, planar face far from the viewpoint is difficult to extract since the spatial resolution of range points on the planar face become lower. Thirdly, there are a lot of occlusions in individual range images, which block to identify corresponding planar faces. A registration method with robustness to high range noise and large number of irregular points is required. In this research, we assume that laser range scanner is located in such a way that the horizontal rotating axis is vertical to the ground as shown in Figure 2. Based on this assumption, transformation parameters between range images are reduced from six – i.e. relative position (Δx,Δy,Δz) and three rotating angles (ω,ψ,κ) to four (Δx,Δy,Δz andκ). A “Z-image” is introduced, which is generated by projecting range points onto a horizontal (X-Y) plane. Value of each pixel in Z-image is the number of range points falling into the pixel. See next section for a definition of “Z-image”. Pair-wise registration is conducted in two steps, first matching Z-images to determine Δx,Δy andκ, then matching ground range points to estimateΔz. Multiple registration Many research efforts have focused on solving the error accumulation problem. Chen and Medioni, 1992 partially solved the problem by registering the newly added range image with the integrated range image consisting of all previously registered ones. Bergevin et al.1996 minimized the distance from a sequence of PE&RS, vol.67, no.10, pp.1143-1153, 2001 3 control points to the corresponding tangent planes in other range images as a least square problem. Shum et al. 1994 formulated the multiple registration as a problem of principal component analysis with missing data, where distance between corresponding planar faces are subject to minimization. B.Kamgar-Parsi et al. 1991 converted the problem to a resolution of conflicting situations that arise from the accumulation of pair-wise registration error. In this research, we apply a simplified approach similar to B.Kamgar-Parsi et al. 1991 by minimizing the violation of absolute transformations obtained in multiple registration to the result of pair-wise registration as a weighted least square problem. Outline of the paper In the following sections, we will discuss the issues involved in both pair-wise and multiple registration. We present two experimental results in this paper. In the first experiment, registration of two range images is analyzed in detail to examine the methodological framework for pair-wise registration. In the second experiment, 42 overlapping range images are registered. Objective of the experiment is to examine the robustness of the pair-wise registration method, and test the accuracy and efficiency of multiple registration. PAIR-WISE REGISTRATION USING Z-IMAGE Definition of Z-image A Z-image is introduced assuming that the horizontal rotating axis (Z-axis) of the laser range scanner is set vertical to the ground surface. It is generated by projecting range points onto a horizontal (X-Y) plane, where value of each pixel in Z-image is the number of range points falling into the pixel (see Figure 3). Vertical planar features like building surfaces are represented in Z-image as line segments, where a strong image feature in Z-image implies a high accumulation of range points along Z-axis. Comparing with the perspective view of range image, vertical building surfaces are emphasized in Z-image. On the other hand, trees, ground surface and other non-vertical planar features (e.g. a slope building wall) are weakened due to the low accumulation of range points along Z-axis. Strong linear features are extracted from Z-image for the purpose of pair-wise registration. Matching Z-image Matching Z-images is essentially a two-dimensional problem. Our method of matching Z-images can be generalized as follows. Figure 2. Architecture of the Laser Range Scanner. Figure 3. Generation of Z-Image from range image. PE&RS, vol.67, no.10, pp.1143-1153, 2001 4 1) Feature primitives Line segments are exploited in Z-image matching, which are extracted using CFHT (Curve Fitting Hough Transform) (P.Liang, 1991). 2) Distance measure We evaluate the similarity of the matching pairs by following the formalism defined in Boyer and Kak, 1988; Vosselman, 1992. In order to prevent mismatching of the poorly extracted features, we probabilistically evaluate the reliability of each line segment by exploiting the formalism defined in Kanatani, 1993. 3) Searching strategy Searching for the best matching consists of two steps, coarse matching and fine adjustment. Coarse matching determines approximate transformation parameters between Z-images with an exhaustive search. In fine adjustment, transformation parameters are elaborated. Speed of convergence in the fine adjustment is improved by “strength” analysis. In the following sections, we first discuss the reliability evaluation of line segments, then define the distance measure for the matching of Z-images. Searching strategy is addressed subsequently. Reliability evaluation of line segments The reliability definitions in this research follow and subsequently extend the formalism of Kanatani, 1993. Let D: } ,..., 1 | { N r = α α be a set of point measurements of line ) , ( : d n l with a standard error ε . n , m and d are line normal, directional vector and orthogonal distance respectively. Suppose α r has its truth at α r , where α α α r r r − = ∆ ) , 0 ( ~ 2 σ N . Let ) , ( : d n l be the line parameters obtained by doing linear regression on D, θ ∆ be the small angle from n to n , d d d − = ∆ . Then it has, ) ( ] [ 2 ε θ Ο = ∆ E (1) ) ( ] [ 2 ε Ο = ∆d E (2) ] [ θ ∆ V ) ( 4 2 ε σ Ο + = u N def = 2 n σ (3) ] [ d V ∆ ) ( 4 2 ε σ Ο + = Nv def = 2 d σ (4)