Overlapping Range Images Research Articles

Range Image Registration Using a Photometric Metric under Unknown Lighting

Based on the spherical harmonics representation of image formation, we derive a new photometric metric for evaluating the correctness of a given rigid transformation aligning two overlapping range images captured under unknown, distant, and general illumination. We estimate the surrounding illumination and albedo values of points of the two range images from the point correspondences induced by the input transformation. We then synthesize the color of both range images using albedo values transferred using the point correspondences to compute the photometric reprojection error. This way allows us to accurately register two range images by finding the transformation that minimizes the photometric reprojection error. We also propose a practical method using the proposed photometric metric to register pairs of range images devoid of salient geometric features, captured under unknown lighting. Our method uses a hypothesize-and-test strategy to search for the transformation that minimizes our photometric metric. Transformation candidates are efficiently generated by employing the spherical representation of each range image. Experimental results using both synthetic and real data demonstrate the usefulness of the proposed metric.

Fast and effective integration of multiple overlapping range images

We present a simple and fast integration method, which can fuse registered multiple, overlapping range images effectively while preserving the detailed features. First, normal vectors of the nodes in each range image are estimated and the registered multiple overlapping range images are combined into one point set. Due to registration errors, the normal vectors of homogeneous nodes in the overlapping areas would differ from each other. Thus, the normal vectors of the nodes are corrected iteratively by weighted averaging their neighboring normal vectors. Second, the combined point set is partitioned into a number of small clusters using the k-means clustering algorithm based on user-defined space interval. The clusters subsequently are subdivided into smaller subclusters by using the standard normal vector deviation as a measure of cluster scatter. Finally, in the cluster, the local maxima model, obtained using the mean shift clustering algorithm, is employed to represent the cluster. The proposed method is fast because it does not need to detect iteratively the overlapping areas, which is usually time consuming. In addition, because of the noisy filtering property of the mean shift clustering algorithm, the novel method can produce a smooth and watertight point surface while preserving the detailed features.

Robustly registering range images using local distribution of albedo

We propose a robust method for registering overlapping range images of a Lambertian object under a rough estimate of illumination. Because reflectance properties are invariant to changes in illumination, the albedo is promising to range image registration of Lambertian objects lacking in discriminative geometric features under variable illumination. We use adaptive regions in our method to model the local distribution of albedo, which enables us to stably extract the reliable attributes of each point against illumination estimates. We use a level-set method to grow robust and adaptive regions to define these attributes. A similarity metric between two attributes is also defined to match points in the overlapping area. Moreover, remaining mismatches are efficiently removed using the rigidity constraint of surfaces. Our experiments using synthetic and real data demonstrate the robustness and effectiveness of our proposed method.

Automatic Range Image Registration in the Markov Chain

In this paper, a novel entropy that can describe both long and short-tailed probability distributions of constituents of a thermodynamic system out of its thermodynamic limit is first derived from the Lyapunov function for a Markov chain. We then maximize this entropy for the estimation of the probabilities of possible correspondences established using the traditional closest point criterion between two overlapping range images. When we change our viewpoint to look carefully at the minimum solution to the probability estimate of the correspondences, the iterative range image registration process can also be modeled as a Markov chain in which lessons from past experience in estimating those probabilities are learned. To impose the two-way constraint, outliers are explicitly modeled due to the almost ubiquitous occurrence of occlusion, appearance, and disappearance of points in either image. The estimated probabilities of the correspondences are finally embedded into the powerful mean field annealing scheme for global optimization, leading the camera motion parameters to be estimated in the weighted least-squares sense. A comparative study using real images shows that the proposed algorithm usually outperforms the state-of-the-art ICP variants and the latest genetic algorithm for automatic overlapping range image registration.

Replicator Dynamics in the Iterative Process for Accurate Range Image Matching

Iterative algorithms are often used for range image matching. In this paper, we treat the iterative process of range image matching as a live biological system: evolving from one generation to another. Whilst different generations of the population are regarded as range images captured at different viewpoints, the iterative process is simulated using time. The well-known replicator equations in theoretical biology are then adapted to estimate the probabilities of possible correspondences established using the traditional closest point criterion. To reduce the effect of image resolutions on the final results for efficient and robust overlapping range image matching, the relative fitness difference (rather than the absolute fitness difference) is employed in the replicator equations in order to model the probability change of possible correspondences being real over successive iterations. The fitness of a possible correspondence is defined as the negative of a power of its squared Euclidean distance. While the replicator dynamics penalize those individuals with low fitness, they are further penalised with a parameter, since distant points are often unlikely to represent their real replicators. While the replicator equations assume that all individuals are equally likely to meet each other and thus treat them equally, we penalise those individuals competing for the same points as their possible replicators. The estimated probabilities of possible correspondences being real are finally embedded into the powerful deterministic annealing scheme for global optimization, resulting in the camera motion parameters being estimated in the weighted least squares sense. A comparative study based on real range images with partial overlap has shown that the proposed algorithm is promising for automatic matching of overlapping range images.

Projecting registration error for accurate registration of overlapping range images

In this paper, we propose a novel algorithm for the automatic registration of two overlapping range images. Since it is relatively difficult to compare the registration errors of different point matches, we project them onto a virtual image plane for more accurate comparison using the classical pin-hole perspective projection camera model. While the traditional ICP algorithm is more interested in the points in the second image close to the sphere centred at the transformed point, the novel algorithm is more interested in the points in the second image as collinear as possible to the transformed point. The novel algorithm then extracts useful information from both the registration error and projected error histograms for the elimination of false matches without any feature extraction, image segmentation or the requirement of motion estimation from outliers corrupted data and, thus, has an advantage of easy implementation. A comparative study based on real images captured under typical imaging conditions has shown that the novel algorithm produces good registration results.

Developing structural constraints for accurate registration of overlapping range images

Automatic image registration is an attractive and unresolved problem in the machine vision literature. This paper presents two novel structural constraints, namely proximity and closeness constraints, that improve both the accuracy and robustness of an existing motion consistency based algorithm (GICP) for automatic image registration. It also defines the conditions when such constraints are fired at specific points of the registration of two overlapping range images. The proximity constraint says that neighbouring points should be neighbouring before and after a rigid motion. The closeness constraint implements a local closest point search from the second image to the first image. While the GICP algorithm uses an exhaustive search for the closest points, in this paper, we employ the optimised k– d tree data structure to accelerate the closest point search. A large number of experiments based on real range images demonstrate that the combination of rigid motion constraints with these novel proximity and closeness constraints leads to a more accurate and robust evaluation of possible correspondences leading, in turn, to more accurate, robust and efficient automatic image registration results.

The Marching Intersections algorithm for merging range images

A new algorithm for the integration of partially overlapping range images into a triangular mesh is presented. The algorithm consists of three main steps: it locates the intersections between the range surfaces and a reference grid chosen by the user, then merges all nearly coincident and redundant intersections according to a proximity criterion, and, finally, reconstructs the merged surface(s) from the filtered intersection set. Compared with previous methods, which adopt a volumetric approach, our algorithm shows lower computational costs and improves the accuracy of the surfaces produced. It takes into account the quality of the input measurements and is able to patch small holes corresponding to the parts of the 3D scanned object that were not observed by the acquisition device. The algorithm has been tested on several datasets of range maps; graphical and numeric results are reported.

Geometrical Analysis of Two Sets of 3D Correspondence Data Patterns for the Registration of Free-Form Shapes

The iterative closest point (ICP) algorithm represents an efficient method to establish an initial set of possible correspondences between two overlapping range images. An inherent limitation of the algorithm is the introduction of false matches, a problem that has been tackled by a variety of schemes mainly based on local invariants described in a single coordinate frame. In this paper we propose using global rigid motion constraints to deal with false matches. Such constraints are derived from geometric properties of correspondence vectors bridging the points described in different coordinate frames before and after a rigid motion. In order to accurately and efficiently estimate the parameters of interest, the Monte Carlo resampling technique is used and motion parameter candidates are then synthesised by a median filter. The proposed algorithm is validated based on both synthetic data and real range images. Experimental results show that the proposed algorithm has advantages over existing registration methods concerning robustness, accuracy, and efficiency.

RANSAC-based DARCES: a new approach to fast automatic registration of partially overlapping range images

In this paper, we propose a new method, the RANSAC-based DARCES method (data-aligned rigidity-constrained exhaustive search based on random sample consensus), which can solve the partially overlapping 3D registration problem without any initial estimation. For the noiseless case, the basic algorithm of our method can guarantee that the solution it finds is the true one, and its time complexity can be shown to be relatively low. An extra characteristic is that our method can be used even for the case that there are no local features in the 3D data sets.

RECONSTRUCTION OF REAL-WORLD OBJECTS VIA SIMULTANEOUS REGISTRATION AND ROBUST COMBINATION OF MULTIPLE RANGE IMAGES

Range finder devices are quite useful to measure the geometry of real-world objects. However, the reconstruction of large and complicated objects often requires the acquisition of multiple range images showing different views of the object. With our reconstruction method, the relative orientations of all range images are determined via simultaneous registration of all range images. The registration process is based on a least-squares approach where a distance metric between the overlapping range images is minimized. Registration errors are not accumulated, and it is even possible to reconstruct large objects from an arbitrary number of small range images. A resolution hierarchy accelerates the registration substantially. In order to exploit redundancies, the overlapping surfaces are optimally adapted to each other. The processed range images are converted to a signed distance function, which is based on the idea that no part of the object can lie between the scanner and the measured surface in any view. According to the signed distance function an intermediate volumetric model is sculptured out and polygonalized with isosurface techniques. The accuracy of the generated mesh is improved by moving its vertices onto the surface implicitly defined by the registered range images.

Surface Recovery from Range Images Using Curvature and Motion Consistency

A key problem in the recovery of scene descriptions from multiple views is the fusion of information from different vantage points. The contribution of this paper is a set of algorithms for reconstructing surfaces obtained from overlapping range images in a common frame of reference. Surfaces are assumed to be piecewise-smooth but not necessarily rigid. Motion parameters, rotations and translations that describe correspondence between views, are recovered locally under the assumption that the curvature structure at a point on a surface varies slowly under transformation. The recovery problem can thus be posed as finding the set of motion parameters that preserves curvature across two views. We show that an appropriate similarity functional can be devised that is convex in the vicinity of the true motion parameters. This leads to an efficient local algorithm that recovers motion parameters in gradient descent fashion. Fusion of information from different viewponts is accomplished by applying local motion estimates to map data points between frames. However, because these estimates are determined locally, they are subject to the usual effects of noise and quantization error. To increase the robustness of this reconstruction procedure the additional constraint of motion consistency is introduced, that variations in the velocities of adjacent regions are also piecewise-smooth. This is cast as a second local minimization problem which seeks to find the set of motion parameters that minimizes differences in the relative positions and orientations at adjacent points. The resulting algorithm serves to smooth out local perturbations and blend adjacent surface patches. In contrast to global rigid body motion approaches, our procedure for reconstructing surfaces from different viewpoints is tolerant of local errors in correspondence and can accommodate objects that are articulated.

Registration of multiple overlapping range images: scenes without distinctive features

A scheme is developed to register range images in an environment where distinctive features are scarce. Another issue addressed here is conflicting situations that may arise from pair-wise registration of multiple overlapping range images whether or not they contain distinctive features. There can be two causes for this: (a) error in individual registrations or (b) compression or bending in range images. The authors develop a scheme for resolving such conflicts for the case where range images share a common reference surface, i.e. when the transformation matrix between two overlapping images involves only three components: two translations and one rotation. The authors implemented this scheme to map the floor of the ocean, where the range data is obtained by a multibeam echo-sounder system installed aboard a sailing ship producing multiple overlapping range images. The system developed is the first automated system for correctly registered mapping of the ocean floor; it is efficient and robust.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>