text: Topographic mapping in planetary environments relies on accurate 3D scan registration methods. However, most global registration algorithms relying on features such as FPFH and Harris-3D show poor alignment accuracy in these settings due to the poor structure of the Mars-like terrain and variable resolution, occluded, sparse range data that is hard to register without some a-priori knowledge of the environment. In this paper, we propose an alternative approach to 3D scan registration using the curvelet transform that performs multi-resolution geometric analysis to obtain a set of coefficients indexed by scale (coarsest to finest), angle and spatial position. Features are detected in the curvelet domain to take advantage of the directional selectivity of the transform. A descriptor is computed for each feature by calculating the 3D spatial histogram of the image gradients, and nearest neighbor based matching is used to calculate the feature correspondences. Correspondence rejection using Random Sample Consensus identifies inliers, and a locally optimal Singular Value Decomposition-based estimation of the rigid-body transformation aligns the laser scans given the re-projected correspondences in the metric space. Experimental results on a publicly available data-set of planetary analogue indoor facility, as well as simulated and real-world scans from Neptec Design Group's IVIGMS 3D laser rangefinder at the outdoor CSA Mars yard demonstrates improved performance over existing methods in the challenging sparse Mars-like terrain.
  @cite_28: The authors describe a general-purpose, representation-independent method for the accurate and computationally efficient registration of 3-D shapes including free-form curves and surfaces. The method handles the full six degrees of freedom and is based on the iterative closest point (ICP) algorithm, which requires only a procedure to find the closest point on a geometric entity to a given point. The ICP algorithm always converges monotonically to the nearest local minimum of a mean-square distance metric, and the rate of convergence is rapid during the first few iterations. Therefore, given an adequate set of initial rotations and translations for a particular class of objects with a certain level of 'shape complexity', one can globally minimize the mean-square distance metric over all six degrees of freedom by testing each initial registration. One important application of this method is to register sensed data from unfixtured rigid objects with an ideal geometric model, prior to shape inspection. Experimental results show the capabilities of the registration algorithm on point sets, curves, and surfaces. >
  @cite_9: 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. >
  @cite_42: A heuristic method has been developed for registering two sets of 3-D curves obtained by using an edge-based stereo system, or two dense 3-D maps obtained by using a correlation-based stereo system. Geometric matching in general is a difficult unsolved problem in computer vision. Fortunately, in many practical applications, some a priori knowledge exists which considerably simplifies the problem. In visual navigation, for example, the motion between successive positions is usually approximately known. From this initial estimate, our algorithm computes observer motion with very good precision, which is required for environment modeling (e.g., building a Digital Elevation Map). Objects are represented by a set of 3-D points, which are considered as the samples of a surface. No constraint is imposed on the form of the objects. The proposed algorithm is based on iteratively matching points in one set to the closest points in the other. A statistical method based on the distance distribution is used to deal with outliers, occlusion, appearance and disappearance, which allows us to do subset-subset matching. A least-squares technique is used to estimate 3-D motion from the point correspondences, which reduces the average distance between points in the two sets. Both synthetic and real data have been used to test the algorithm, and the results show that it is efficient and robust, and yields an accurate motion estimate.
  @cite_25: Registration and integration of measured data of real objects are becoming important in 3D modeling for computer graphics and computer-aided design. We propose a new algorithm of registration and integration of multiple range images for producing a geometric object surface model. The registration algorithm determines a set of rigid motion parameters that register a range image to a given mesh-based geometric model. The algorithm is an integration of the iterative closest point algorithm with the least median of squares estimator. After registration, points in the input range are classified into inliers and outliers according to registration errors between each data point and the model. The outliers are appended to the surface model to be used by registration with the following range images. The parts classified as inlier by at least one registration result is segmented out to be integrated. This process consisting of registration and integration is iterated until all views are integrated. We successfully experimented with the proposed method on real range image sequences taken by a rangefinder. The method does not need any preliminary processes.
summary: One of the most popular scan registration methods, the iterative closest point (ICP) @cite_28 @cite_9 @cite_42 , relies on point-to-point correspondences to estimate the relative transformation of scans by minimizing the Euclidean distance error metric. The original ICP algorithm assumes that there exists a correspondence between each point of the source and model data-sets. This assumption is often violated with partially overlapping scans. Some modifications to the ICP algorithm have included the maximum error cutoff metric @cite_25 to account for false correspondences, and did not require every point to be matched. One of the key problems with scan registration is that the sparsely sampled corresponding points in two different scans often do not correspond to the same point in the 3D environment, but ICP assumes that they do. In addition, the quality of the ICP solution depends heavily on the availability of good initial estimates of the transformation @cite_28 .