A review of recent range image registration methods with accuracy evaluation <s> Method of Chen <s> The problem of creating a complete model of a physical object is studied. Although this may be possible using intensity images, the authors use range images which directly provide access to three-dimensional information. The first problem that needs to be solved is to find the transformation between the different views. Previous approaches have either assumed this transformation to be known (which is extremely difficult for a complete model) or computed it with feature matching (which is not accurate enough for integration. The authors propose an approach that works on range data directly and registers successive views with enough overlapping area to get an accurate transformation between views. This is performed by minimizing a functional that does not require point-to-point matches. Details are given of the registration method and modeling procedure, and they are illustrated on range images of complex objects. > <s> BIB001 </s> A review of recent range image registration methods with accuracy evaluation <s> Method of Chen <s> Building integrated models of existing 3-D objects is a key requirement for both reverse engineering and object recognition systems. An automatic 3-D model builder goes through three main steps: i) surface sampling from many views, ii) registration of the sampled views, and iii) integration of the registered views. The accuracy obtained depends on the acquisition and registration errors. The latter is critical since a misalignment of the range views causes their noise distributions to be centered around different means, which makes it difficult to reduce the effect of the acquisition error by simple averaging. In this paper, we propose a general algorithm that reduces significantly the level of the registration errors between all pairs in a set of range views. This algorithm refines initial estimates of the transformation matrices obtained from the calibrated acquisition setup. It considers the network of views as a whole and minimizes the registration errors of all views simultaneously. This leads to a well-balanced network of views in which the registration errors are equally distributed. Experimental results show an improvement of both the calibrated registrations and integrated models. > <s> BIB002
In 1991, Chen and Medioni BIB001 proposed an alternative to the ICP algorithm, which was based on minimizing the distance between points and planes. The minimization function was selected to be the distances between points in the first image with respect to tangent planes in the second. That is, considering a point in the first image, the intersection of the normal vector at this point with the second surface determines a second point in which the tangent plane is computed. Despite other authors that considered this algorithm just an improvement of ICP, we have considered it a new technique for several reasons. First, the paper was presented at the same time of Besl's approach. Second, the search of correspondences is an important aspect of the algorithm, consequently it should be considered a different method. A new algorithm to find these intersections between lines and range images was proposed, bearing in mind that the intersection of a given line with a cloud of points requires a high computational cost. A more accurate technique to find such a distance was proposed by Gagnon et al. BIB002 . Finally, once the distances between points and planes were obtained, the motion that minimizes these distances was estimated by least squares. The process was repeated until convergence was attained. In 2001, Rusinkiewick and Levoy  presented several variations of this algorithm to improvement the precision of the algorithm. The author proposed the Normal Space Sampling. The main idea is to select more points in the region where the normal is different from the other parts of the surface. Using this sampling technique better results are obtain in low shaped surfaces. Point-to-plane distance is normally more difficult to compute compare to point-to-point. When no normal information is given, the plane must be computed using neighborhood information, which requires a lot of time to detect this neighborhood, and not always with sufficient accuracy in the estimation of the normal vector. However, nowadays this estimation can be obtained directly from most part of range finders. This method is more robust to local minimum and, in general, results are better. Despite no robust method are applied, this method is less sensible in the presence of non-overlapping regions. The reason is that only the control points that their normal vector intersects the second view are considered in the matching. Moreover, point-to-point distance ensures a correspondence unless a distance threshold or other robust identifier is used. Chen's approach usually requires less iterations than the ICP approach.