A review of recent range image registration methods with accuracy evaluation <s> Matching signed distance fields <s> We propose a method to construct a 3-D geometric shape model by registering and integrating multiple range images under a unified framework. We use 3-D points around the object surface as the correspondence key, because the closest data point from an arbitrary 3-D point should be matched if the data are registered correctly with some exceptional cases. We assume that the input shapes are roughly registered in advance, and then we solve the problem by iterative loops that consist of establishing correspondence by searching closest data points, integration of corresponded data points, and registration of each data to the integrated shape. The error function is defined by the weighted variances of the signed distance field from the surface. The weighting values are determined to trim out wrong correspondences typically caused by different sampling and measurement error. We do not need to consider the cumulative pairwise registration error because each data is registered to the integrated shape. The integrated shape information is directly used to generate a surface model. We tested the method on synthetic and real range images. <s> BIB001 </s> A review of recent range image registration methods with accuracy evaluation <s> Matching signed distance fields <s> Modelling object shapes from multiple range images requires three procedures: removal of measurement errors, registering input shapes and integrating them as a shape representation. We propose a unified framework in which these procedures can be solved simultaneously. Discrete samples of the signed distance field (SDF) from the object surface are used as the shape representation. If the data shapes are registered correctly, the SDF should match in the common coordinate system. The data shapes are first integrated by averaging the data SDF assuming that they are roughly pre-registered. The data shapes are registered to the integrated shape by matching the SDF. Integration and registration are iterated until the input shapes are registered to the integrated shape. Weighting values are controlled to reject outliers caused by measurement errors and wrong correspondences. The proposed method does not suffer from cumulative pairwise registration errors because all data shapes are registered to an integrated shape. A polygonal surface model is generated from the integrated SDF. The method was tested on synthetic and real range images, and multiresolution results are also presented. <s> BIB002
In 2001, Masuda BIB001 BIB002 presented a new registration algorithm, which was based on the matching signed distance fields. The method was a robust one so the outliers were removed, and all the views of a given object were registered at the same time, which means a multi-view registration. First, all views (a) were transformed to a reference coordinate system using the initial estimation of the motion. A set of key points was generated on a 3D grid of buckets with a fixed size d. Then, the closest point from every key point was searched for in order to establish the correspondences, limiting the distance between points to ffiffi ffi 3 p d. The process was composed by the following steps: Steps 2 and 3 are repeated until there is convergence and an integrated model of the object made by the p points is obtained. At every iteration the closest point was computed as follows: where n a p represents the normal vector of p and k a p represents the signed distance, which is computed as: where c a p is the closest point to each key point for every range image a, and d p is the average distance between the point p and each c a p . where d a p represents the distance between point p and the nearest key point and w a p is the weight of point p. Finally, once the solution has converged, it is possible to compute the points (signed distance field) and their normal vectors, obtaining the final model as follows: The advantage of this method is that it registers all the views at the same time, which implies a more robust solution and avoids the error propagation problem present in pair-wise registration methods. On the other hand, this algorithm can not be used in real time as localization and mapping because not all views are already available when the motion must be computed. Another advantage of this algorithm is that the final result is directly an integrated model, compared to pairwise registration techniques that require and off-line algorithm to eliminate the overlapping region and triangulate all the registered surfaces.