170 
RANGE IMAGE REGISTRATION THROUGH 
VIEWPOINT INVARIANT COMPUTATION OF CURVATURE 
Guy Godin Pierre Boulanger 
Autonomous Systems Laboratory 
Institute for Information Technology 
National Research Council of Canada 
Ottawa, Canada K1A OR6 
tel.: (613) 991-6970 . fax: (613) 952-0215 
email: godin@iit.nrc.ca 
KEYWORDS: 3-D registration, pose estimation, curvature, range images 
ABSTRACT: 
The registration of a pair of range images is a ubiquitous problem in computer vision, for model building as well as for 
dimensional inspection. It attempts to determine, from the data, an optimal rigid transformation that minimizes the 
distance between common portions of surfaces seen in both images. The method discussed in this paper computes 
local differential invariant quantities, mean and Gaussian curvatures, to guide the matching process between images. 
In order to preserve the usefulness of these quantities, they should be computed using techniques that are themselves 
invariant to the point of view. The technique proposed here makes use of a weighting based on intrinsic distances on 
the surface in the computation of the partial derivatives. Following that step, a modified iterative closest point method 
is applied to perform the pose determination. The curvature information is used to improve the pose determination 
procedure by constraining potential matches to compatible pairs of points. 
1. INTRODUCTION 
The determination of relative pose between two or more range images, also called image registration, is a ubiquitous 
problem in 3-D computer vision, for geometric model building as well as for dimensional inspection. This process 
attempts to recover, from the measured data itself, the transformation bringing different range images together. Of 
course this can only be achieved if there is a portion of surface area which is visible in both images to be registered. 
The extent of the relative pose estimation problem and the quality of the solution that can be achieved is therefore a 
function of the object as well as viewing geometry. At the heart of this problem lies the identification of the subsets 
of the images that are common to both views. This matching can be made easier if, for each point on the surface, 
a property can be determined from the image information that is expected to be independent of the point of view. 
This information can then be used to guide the matching process towards similar areas in the two images. 
The method discussed in this paper uses a well-known class of local surface features derived from differential geometry: 
mean and Gaussian curvatures. These quantities are invariant properties of differentiable surfaces; they have been used 
in range image processing for segmentation, recognition as well as registration tasks. However, in order to preserve 
their invariance, the mean and Gaussian curvatures should be computed using techniques that are themselves invariant 
to the point of view. Such a technique based on intrinsic filtering is proposed here. It uses a weighting which is a 
function of intrinsic distances on the surface for the computation of the partial derivatives. The registration method 
first computes, for each point in the range image, the Gaussian and mean curvatures in a viewpoint-invariant manner. 
Surface points are then labelled as belonging to one of 8 categories, according to the signs of the two curvatures. 
These labels are then used to constrain the registration problem by limiting the matching of points from different 
images to those belonging to the same category. Following that step, a robust iterative closest point method is applied 
to perform the registration over the compatible pairs of points. In the worst case, when all points in the images share 
a uniform curvature label (for example polyhedra), the method degenerates into a traditional point-based registration. 
The paper will first provide an analysis of the registration problem. This will be followed with a description of the 
technique for computing viewpoint-invariant curvature properties. The proposed algorithm, called Iterative Closest 
Compatible Point, will be described. Some results will then be provided, along with a discussion on the performance 
of the algorithm. 
IAPRS, Vol. 30, Part 5W1, ISPRS Intercommission Workshop “From Pixels to Sequences”, Zurich, March 22-24 1995