Point-to-plane registration of terrestrial laser scans

Abstract

The registration of pairs of Terrestrial Laser Scanning data (TLS) is an integral precursor to 3D data analysis. Of specific interest in this research work is the class of approaches that is considered to be fine registration and which does not require any targets or tie points. This paper presents a pairwise fine registration approach called P2P that is formulated using the General Least Squares adjustment model. Given some initial registration parameters, the proposed P2P approach utilizes the scanned points and estimated planar features of both scans, along with their stochastic properties. These quantities are used to determine the optimum registration parameters in the least squares sense. The proposed P2P approach was tested on both simulated and real TLS data, and experimental results showed it to be four times more accurate than the registration approach of Chen and Medioni (1991).

Introduction

The registration of Terrestrial Laser Scanning data (TLS) is a prerequisite to the 3D modeling and/or analysis phase, whenever the data are acquired from multiple scan locations. The interest in this paper is in the so-called fine registration methods, which assume that some initial registration parameters exist. The aim is to improve these parameters. There are two main classes of such approaches: those that require targets or tie points, and those that establish correspondence features among a pair of scans. These features can involve points, lines, planes, higher order surfaces, TINs, DEMs, or geometric shapes. The scope of this paper will be limited to those methods that utilize corresponding point and planar features, as they employ minimal processing of the original data during the registration task (Habib et al., 2010). Given a pair of scans, point-to-plane registration approaches seek to obtain the optimum set of registration parameters that minimize the Euclidean distances between points on one scan and their corresponding planar features from the other scan.

Related work in this group of approaches can be found in three applications, (1) strip matching of Airborne Laser Scanning (ALS) data, (2) integration of ALS and photogrammetry, and (3) matching of 3D surface data. Early work among the first application includes Maas (2000). Here ALS data were organized into TINs, and the point-to-TIN elevation differences were used to determine registration parameters for strip matching. Schenk et al. (2000) presented a similar registration approach for ALS data. Here a study was done to compare the use of elevation differences for pseudo-observations with the use of surface normal differences. More recently Habib et al. (2010) presented an approach called ICPatch. The presented approach follows closely on the surface-normal minimization method of Schenk et al. (2000). Other point-to-plane methods exist in the literature for example, Sande et al. (2010). In this approach the planes are extracted by a segmentation process, which means that planar features involve neighborhoods of typically more than four points. We prefer to not include such methods in our study, since segmentation is itself an extensive research field.

Other researchers have used point-to-plane registration to exploit the complementary nature of photogrammetry and ALS data. For example, Jaw (1999) presented an approach for aerial triangulation with ALS data as the control surface. No TIN or DEM structure was used, but a neighborhood search was employed to obtain the nearest 3-points. The General Least Squares¹ adjustment model was used to determine the object space coordinates of photo measured points, and details were given on the stochastic model. However, a diagonal weight matrix was used in the adjustment thus sacrificing the correlation among some of the observations. Recently, Levin and Filin (2010) presented a similar approach to Jaw (1999), where close-range photogrammetric imagery were registered to ALS data. The ALS data were organized into TINs, and a similar surface-normal minimization approach to Schenk et al. (2000) was adopted. The stochastic properties of the TIN surface elements were mentioned in the mathematical explanation, but no details were provided for implementation purposes.

Among the applications of 3D surface data is the work by Habib et al. (2001). The authors here presented an approach called the Modified Iterative Hough Transform (MIHT), where the 3D similarity registration parameters were determined through a 2-step process. First there was a sequential and iterative parameter determination through the robust Hough transform to establish point-to-plane correspondences – the matching step. Second, these correspondences were used in a simultaneous least squares adjustment – the least squares solution step. Akca (2007) presented the Least Squares 3D Surface Matching (LS3D) approach. This method was designed for 3D surface data and is an extension of 2D least squares image matching. Planes were obtained from 3-point or 4-point local neighborhoods through a neighborhood search method, and the registration incorporates full 3D geometry in the estimation of the transformation parameters. However, the stochastic properties of the local surface normals were neglected in the LS3D approach. Perhaps the most popular point-to-plane approach is that of Chen and Medioni (1991). This approach involves two steps: projection of points onto the adjacent surface along their point normals (normal shooting) to obtain correspondences; and estimation of 3D coordinate transformation parameters between corresponding pairs of points.

The approach of Chen and Medioni (1991) has been used as the benchmark in many registration evaluations, and many researchers have contributed to the registration field by modifying this approach. For example, Park and Subbarao (2003) developed an approach that combined Chen and Medioni (1991) with the point-to-projection approach of Blais and Levine (1995). Blais and Levine (1995) project points along their spherical direction rather than local surface normals as in Chen and Medioni (1991). The combined approach of Park and Subbarao (2003) aimed at obtaining a fast and accurate registration. Bae (2006) proposed the use of geometric primitives (change of local curvature, the local surface normal and the error of the estimated normal) to establish correspondences. The author also employed a modified RANSAC to improve the robustness of the approach.

Many other modifications of Chen and Medioni (1991) exist. A useful review is found in Rusinkiewicz and Levoy (2001). However, the authors group the point-to-plane approach of Chen and Medioni (1991) with the point-to-point approach of Besl and McKay (1992) and refer to both as the Iterative Closest Point (ICP) approach. Other researchers distinguish these two works. Besl and McKay (1992) minimize the Euclidean distances between points on one scan with their closest point on the adjacent scan, and not the closest plane, as in Chen and Medioni (1991). Liu (2004) also provides good review and lists some improvement approaches to the collective work of Besl and McKay, 1992, Chen and Medioni, 1991 and Zhang (1994). Liu (2004) refers to this collective work as the ICP approach. Other research work focused on improving the collective ICP approach include Greenspan and Godin, 2001, Jost and Hugli, 2002, Sharp et al., 2002, Trucco et al., 1999 and Zinsser et al. (2003).

In this paper we present a new approach called the P2P approach that extends the work of Akca, 2007, Jaw, 1999 and Levin and Filin (2010). The result is expected to be better suited to the registration of TLS data, and any 3D surface data in general. We pay particular attention to the stochastic properties of the local surface normals which are neglected in the work of Akca (2007). We employ a full weight matrix instead of the diagonal version in Jaw (1999). We solve for the registration parameters, and not point coordinates thus forming a linear system of equations with fewer unknowns than in Jaw (1999). Also we do not assume any of the data to represent control surfaces, as in Jaw (1999) or Levin and Filin (2010) who used the ALS data as their control data. Instead we establish correspondences on both scans. The next section of the paper will present the mathematical formulation of both the deterministic and stochastic models of the proposed P2P registration approach. This section will also present the computational implementation of the P2P algorithm. Section 3 presents the experimental results. Tests were performed on both simulated and real TLS data to compare the registration accuracy with that of the well-established approach by Chen and Medioni (1991). The conclusions and future work are given in Section 4.