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.
Another transformation found in the literature relies on finding a translation invariant Fourier transform on two Extended Gaussian Images (EGI) @cite_19 of laser scans, where the surface normals of an object are mapped onto the unit sphere. However, this approach can only be applied to smooth surfaces and fails to match surfaces with constant EGI (such as a sphere). @cite_36 proposed another approach to scan matching that projects the two scans into the Hough Radon domain @cite_36 defined on the unit sphere. Similar to the work of , a translation invariant spectrum is computed to find the rotation and cross-correlations are used to find the translation. Both EGI approaches and the ones based on transformation to Hough Radon domain are sensitive to the measurement noise and sampling density during the calculation of normals.
@cite_36 @cite_19
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We propose a new approach to appearance-based loop detection for mobile robots, using three-dimensional (3D) laser scans. Loop detection is an important problem in the simultaneous localization and mapping (SLAM) domain, and, because it can be seen as the problem of recognizing previously visited places, it is an example of the data association problem. Without a flat-floor assumption, two-dimensional laser-based approaches are bound to fail in many cases. Two of the problems with 3D approaches that we address in this paper are how to handle the greatly increased amount of data and how to efficiently obtain invariance to 3D rotations. We present a compact representation of 3D point clouds that is still discriminative enough to detect loop closures without false positives (i.e., detecting loop closure where there is none). A low false-positive rate is very important because wrong data association could have disastrous consequences in a SLAM algorithm. Our approach uses only the appearance of 3D point clouds to detect loops and requires no pose information. We exploit the normal distributions transform surface representation to create feature histograms based on surface orientation and smoothness. The surface shape histograms compress the input data by two to three orders of magnitude. Because of the high compression rate, the histograms can be matched efficiently to compare the appearance of two scans. Rotation invariance is achieved by aligning scans with respect to dominant surface orientations. We also propose to use expectation maximization to fit a gamma mixture model to the output similarity measures in order to automatically determine the threshold that separates scans at loop closures from nonoverlapping ones. We discuss the problem of determining ground truth in the context of loop detection and the difficulties in comparing the results of the few available methods based on range information. Furthermore, we present quantitative performance evaluations using three real-world data sets, one of which is highly self-similar, showing that the proposed method achieves high recall rates (percentage of correctly identified loop closures) at low false-positive rates in environments with different characteristics. © 2009 Wiley Periodicals, Inc. In this paper we propose a novel approach for detecting interest points invariant to scale and affine transformations. Our scale and affine invariant detectors are based on the following recent results: (1) Interest points extracted with the Harris detector can be adapted to affine transformations and give repeatable results (geometrically stable). (2) The characteristic scale of a local structure is indicated by a local extremum over scale of normalized derivatives (the Laplacian). (3) The affine shape of a point neighborhood is estimated based on the second moment matrix. Our scale invariant detector computes a multi-scale representation for the Harris interest point detector and then selects points at which a local measure (the Laplacian) is maximal over scales. This provides a set of distinctive points which are invariant to scale, rotation and translation as well as robust to illumination changes and limited changes of viewpoint. The characteristic scale determines a scale invariant region for each point. We extend the scale invariant detector to affine invariance by estimating the affine shape of a point neighborhood. An iterative algorithm modifies location, scale and neighborhood of each point and converges to affine invariant points. This method can deal with significant affine transformations including large scale changes. The characteristic scale and the affine shape of neighborhood determine an affine invariant region for each point. We present a comparative evaluation of different detectors and show that our approach provides better results than existing methods. The performance of our detector is also confirmed by excellent matching resultss the image is described by a set of scale affine invariant descriptors computed on the regions associated with our points. We present a technique to estimate the egomotion of an RGB-D sensor based on rotations of functions defined on the unit sphere. In contrast to traditional approaches, our technique is not based on image features and does not require correspondences to be generated between frames of data. Instead, consecutive functions are correlated using spherical harmonic analysis. An Extended Gaussian Image (EGI), created from the local normal estimates of a point cloud, defines each function. Correlations are efficiently computed using Fourier transformations, resulting in a 3 Degree of Freedom (3-DoF) rotation estimate. An Iterative Closest Point (ICP) process then refines the initial rotation estimate and adds a translational component, yielding a full 6-DoF egomotion estimate. The focus of this work is to investigate the merits of using spherical harmonic analysis for egomotion estimation by comparison with alternative 6-DoF methods. We compare the performance of the proposed technique with that of stand-alone ICP and image feature based methods. As with other egomotion techniques, estimation errors accumulate and degrade results, necessitating correction mechanisms for robust localization. For this report, however, we use the raw estimates; no filtering or smoothing processes are applied. In-house and external benchmark data sets are analyzed for both runtime and accuracy. Results show that the algorithm is competitive in terms of both accuracy and runtime, and future work will aim to combine the various techniques into a more robust egomotion estimation framework. The error sensitivity in the estimation of the 3-D motion and the normal of a planar surface from an instantaneous motion field is studied. The statistical theory or the Cramer-Rao lower bound is used for error covariance in the estimated motion and structure parameters. This enables the derivation of results valid for any unbiased estimator under the assumption of Gaussian noise in the motion field. The obtained lower-bound-matrix is studied analytically with respect to measurement noise, size of the field of view, and the motion-geometry configuration. The coupling between translation and rotation is exacerbated if the field of view and the slant of the plane become smaller, and the deviation of the translation from the viewing direction becomes larger. The relationships of the uncertainty bounds for every unknown motion parameter to the angle between translation and the plane-normal, the size of the field of view, and the distance from the perceived plane and the translation magnitude are discussed. >