GLOBAL REGISTRATION OF NON STATIC 3D LIDAR POINT CLOUDS: 
SVD FACTORISATION AND ROBUST GPA METHODS 
Fabio Crosilla*, Alberto Beinat 
University of Udine, Dip di Georisorse e Territorio, Via Cotonificio 114,1-33100 UDINE (Italy) 
fabio.crosilla@uniud.it, alberto.beinat@uniud.it 
KEY WORD: Registration, Non static configuration, LiDAR, SVD factorisation, Robust generalised Procrustes analysis 
ABSTRACT: 
The paper reports two analytical methods, based on correspondence points, capable to reliably perform the simultaneous global 
registration of non static 3D LiDAR point clouds, and investigates their applicability by analysing the results of some preliminary 
numerical examples. The first method, proposed by Xiao (2005), and Xiao et al. (2006), apply a direct SVD factorisation to non static 
3D fully overlapping point clouds characterised by target points. The factorisation is applied to a matrix, sequentially containing by 
rows the coordinates of the corresponding targets present in the cloud scenes. Besides the rigid transformation parameters, a number 
of shape bases is determined for each tie point dataset, whose linear combination describes the dynamic component of the scenes. A 
linear closed-form solution is finally obtained, enforcing linear constraints on orthonormality of the rigid rotations and on uniqueness 
of the linear bases. The second method analysed is the so called “Robust Generalised Procrustes Analysis”, recently proposed by the 
authors. To overcome the lack of robustness of Generalised Procrustes Analysis, a progressive sequence inspired to the “forward 
search” was developed. Starting from an initial partial tie point configuration satisfying the LMS principle, the configuration is 
updated, point by point, till a significant variation of the registration parameters occur. This reveals the presence of non stationary tie 
points among the new elements just inserted, that are therefore not included in the registration process. Both methods are capable to 
correctly determine the registration parameters, when compared to the commonly applied “two steps method”, where the registration 
of deformable shapes is biased by non - rigid deformation components. 
1. INTRODUCTION 
In some papers published a few years ago (e.g. Beinat and 
Crosilla, 2001), the authors proposed the Generalised Procrustes 
Analysis to perform a high precision simultaneous registration 
of multiple partially overlapping 3D point clouds acquired with 
terrestrial laser scanning devices. The proposed technique 
requires for each point cloud the matching of a sufficient 
number of artificial targets, eventually pre-signalised on the 
object surface to survey. Furthermore, the same authors have 
recently proposed (Beinat, Crosilla, Sepic, 2006) an automatic 
registration technique that does not require any manual 
matching of the target points, but that instead uses the 
morphological or the radiometric local variations on the 
surveyed surface. The method, by studying the differential 
properties of the sampled point surface, computes at first the 
local values of the Gaussian curvature, then applies a 
topological research to define for each pair of point clouds the 
corresponding zones characterised by the same curvature 
values. By applying an SVD algorithm, it is possible to 
automatically solve a coarse registration followed by an 
Iterative Closest Point (ICP) global refinement. 
Both registration approaches can be correctly applied if the 
object does not change its shape during the survey of the 
complete sequence of point clouds. That is, the registration 
problem consists in the definition of the correct similarity 
transformation parameters for each point cloud. On the other 
hand, registration and modelling of dynamic point cloud scenes 
is a prominent problem for robot navigation, for reconstruction 
of deformable objects, and for monitoring environmental 
phenomena. The recovery of the resulting shapes can be 
regarded as a combination of rigid similarity transformations of 
the 3D point clouds and unknown non - rigid deformations. In 
the literature (e.g. Dryden and Mardia, 1999), the problems 
solution is usually carried out in two consecutive steps. The first 
step registers the point clouds by similarity transformation, 
considering the deformable shapes as contaminated by Gaussian 
noise. The second step determines the linear deformable model 
of the registered shapes by applying Principal Component 
Analysis (PCA) to the registration residuals. Proceeding in this 
way, the registration of deformable shapes is biased by non - 
rigid deformation components. It is therefore necessary to apply 
some procedures that make possible to reliably estimate the 
roto-translation components, and the deformable shapes. 
The paper synthetically describes two methods recently 
proposed in the literature, and analyses the results obtained for 
the registration of a 3D scene characterised by static and 
dynamic elements. The first method, introduced by Xiao (2005), 
solves the combined problem of registration and dynamic shape 
modelling by a direct factorisation of the tie points coordinate 
matrix, containing by rows for each acquired scene the 3D 
sampled model tie point coordinates. The method works well 
when the dynamic object shape can be described by a linear 
combination of a small number of shape bases, that, together 
with the similarity transformation parameters for each cloud, are 
the unknown elements of the joint registration and shape 
modelling problem. The second method proposed (Crosilla, 
Beinat; 2006) represents a robust solution of the Generalised 
Procrustes problem. The described algorithm derives from the 
Robust Regression Analysis based on the Iterative Forward 
Search approach proposed by Atkinson and Riani (2000), and 
Cerioli and Riani (2003). The procedure starts from a partial tie 
point configuration only containing stationary points. At each 
iteration, the transformation parameters are determined, and the 
initial dataset is enlarged by one or more new tie points, till a 
significant variation of the transformation parameters occur. At 
this point the method allows to identify in the various 
configurations the remaining non stationary tie points that 
represent the dynamic component of the scene.