Finding the relationship between two coordinate systems by using pairs of measurements of the coordinates of a number of points in both systems is a classic photogrammetric task. The solution has applications in stereo-photogrammetry and in robotics. We present here a closed-form solution to the least-squares problem for three or more points. Currently, various empirical, graphical, and numerical iterative methods are in use. Derivation of a closed form solution can be simplified by using unit quaternions to represent rotation, as was shown in an earlier paper [J.Opt. Soc. Am. A 4, 629 (1987)]. Since orthonormal matrices are used more widely to represent rotation, we now present a solution in which 3 X 3 matrices are used. Our method requires the computation of the square root of a symmetric matrix. We compare the new result with that obtained by an alternative method in which ortho-normality is not directly enforced. In this other method a best-fit linear transformation is found, and then the nearest orthonormal matrix is chosen for the rotation. We note that the best translational offset is the difference between the centroid of the coordinates in one system and the rotated and scaled centroid of the coordinates in the other system. The best scale is equal to the ratio of the root-mean-square deviations of the coordinates in the two systems from their respective centroids. These exact results are to be preferred to approximate methods based on measurements of a few selected points. NOTE: read [J.Opt. Soc. Am. A 4(4) 629--642 (1987 April)]

Introduction The ever expanding gamut of medical imaging techniques provides the clinician an increasingly multifaceted view of brain function and anatomy. The information provided by the various imaging modalities is often complementary (i.e. provides separate but useful information) and synergistic (i.e. the combination of information provides useful extra information). For example, X-ray computed tomography (CT) and magnetic resonance (MR) imaging exquisitely demonstrate brain anatomy but provide little functional information. Positron emission tomography (PET) and single photon emission computed tomography (SPECT) scans display aspects of brain function and allow metabolic measurements but poorly delineate anatomy. Furthermore, CT and MR images describe complementary morphologic features. For example, bone and calcifications are best seen on CT images, while soft-tissue structures are better differentiated by MR imaging. Clinical diagnosis and therapy planning and evaluatio

Reconstruction of 3D structures from uncalibrated image sequences has a wealthy history. Most work has been focused on rigid objects or static scenes. This paper studies the problem of perspective reconstruction of deformable structures such as dynamic scenes from an uncalibrated image sequence. The task requires decomposing the image measurements into a composition of three factors: 3D deformable structures, rigid rotations and translations, and intrinsic camera parameters. We develop a factorization algorithm that consists of two steps. In the first step we recover the projective depths iteratively using the sub-space constraints embedded in the image measurements of the deformable structures. In the second step, we scale the image measurements by the reconstructed projective depths. We then extend the linear closed-form solution for weakperspective reconstruction [23] to factorize the scaled measurements and simultaneously reconstruct the deformable shapes and underlying shape model, the rigid motions, and the varying camera parameters such as focal lengths. The accuracy and robustness of the proposed method is demonstrated quantitatively on synthetic data and qualitatively on real image sequences. 1.

A large amount of data is now available about the pattern of connections between brain regions. Computational methods are increasingly relevant for uncovering structure in such datasets. There has been recent interest in the use of Nonmetric Multidimensional Scaling (NMDS) for such analysis (Young, 1992, 1993; Scannell & Young, 1993). NMDS produces a spatial representation of the "dissimilarities" between a number of entities. Normally, it is applied to data matrices containing a large number of levels of dissimilarity, whereas for connectivity data there is a very small number. We address the suitability of NMDS for this case. Systematic numerical studies are presented to evaluate the ability of this method to reconstruct known geometrical configurations from dissimilarity data possessing few levels. In this case there is a strong bias for NMDS to produce annular configurations, whether or not such structure exists in the original data. Using a connectivity dataset derived from the pr...

Sensor location information is a prerequisite to the utility of most sensor networks. In this paper we present a robust and low-complexity algorithm to self-localize and orient sensors in a network based on angle-of-arrival (AOA) information. The proposed non-iterative subspace-based method is robust to missing and noisy measurements and works for cases when sensor orientations are either known or unknown. We show that the computational complexity of the algorithm is O(mn 2), where m is the number of measurements and n is the total number of sensors. Simulation results demonstrate that the error of the proposed subspace algorithm is only marginally greater than an iterative maximum-likelihood estimator (MLE), while the computational complexity is two orders of magnitude less. Additionally, the iterative MLE is prone to converge to local maxima in the likelihood function without accurate initialization. We illustrate that the proposed subspace method can be used to initialize the MLE and obtain near-Cramér-Rao performance for sensor localization. Finally, the scalability of the subspace algorithm is illustrated by demonstrating how clusters within a large network may be individually localized and then merged. Categories and Subject Descriptors C.2.4 [Computer-communication networks]: Distributed systems; C.3 [Special-purpose and application-based systems]: Signal processing systems

Position determination for a mobile robot is an important part of autonomous navigation. In many cases, dead reckoning is insufficient because it leads to large inaccuracies over time. Beacon- and landmark-based estimators require the emplacement of beacons and the presence of natural or man-made structure respectively in the environment. In this paper we present a new algorithm for efficiently computing accurate position estimates based on a radially-scanning laser rangefinder that does not require structure in the environment. The algorithm employs a connected set of short line segments to approximate the shape of any environment and can easily be constructed by the rangefinder itself. We describe techniques for efficiently managing the environment map, matching the sensor data to the map, and computing the robot's position. We present accuracy and runtime results for our implementation.

The study presents a comparative analysis between first and all-author co-citation analyses, as well as comparison between two matrix generation approaches. We thus continue the latest research in author co-citation analysis (ACA), where the results of the traditional first-author analyses based on ISI citation indexes are challenged by incorporating all-authors from the cited references. Identifying all cited authors from references in source papers is an extremely cumbersome process if the Thomson ISI citation indexes are used as a basis. Due to the difficulty in obtaining all-author co-citation data few such studies exist. In order to study all-authors co-citation we use a citation index generated from documents in XML code. This allows us to carry out a comparative study between first and all-author co-citation analyses based on the hitherto largest set of references and the broadest domain of research.

Many natural objects vary the shapes as linear combinations of certain bases. The measurement of such deformable shapes is coupling of rigid similarity transformations between the objects and the measuring systems and non-rigid deformations controlled by the linear bases. Thus registration and modeling of deformable shapes are coupled problems, where registration is to compute the rigid transformations and modeling is to construct the linear bases. The previous methods [3, 2] separate the solution into two steps. The first step registers the measurements regarding the shapes as rigid and the deformations as random noise. The second step constructs the linear model using the registered shapes. Since the deformable shapes do not vary randomly but are constrained by the underlying model, such separate steps result in registration biased by nonrigid deformations and shape models involving improper rigid transformations. We for the first time present this bias problem and formulate that, the coupled registration and modeling problems are essentially a single factorization problem and thus require a simultaneous solution. We then propose the Direct Factorization method that extends a structure from motion method [16]. It yields a linear closedform solution that simultaneously registers the deformable shapes at arbitrary dimensions (2D → 2D, 3D → 3D,...) and constructs the linear bases. The accuracy and robustness of the proposed approach are demonstrated quantitatively on synthetic data and qualitatively on real shapes. 1

The point cloud alignment problem has always attracted the interest of the researchers. Two are the procedures usually applied for the close range surveys: the ICP method with all its variants, and the method based on the use of tie points identified by reflecting targets properly located on the overlapping part of two range images. The two methods are not concurrent. ICP requires an initial sufficiently accurate pre-alignment and does not work with regular surfaces; the tie points method requires the materialization and the recognition of the corresponding points, task that it is not always feasible and realizable in economical terms. This paper proposes a new hybrid technique to automatically execute the alignment of close range point clouds by evidencing the corresponding morphological singularities in the various scanning models. The point recognition is based first on the study of the local surface Gaussian curvature values, second by running a clustering procedure of laser points having extreme curvature values, and third by determining the centroids of each cluster. The computation of the local Gaussian curvature is carried out by applying to each sampled point a Taylor’s expansion local nonparametric algorithm with respect to its surrounding points. This makes it possible to locally estimate the surface function value, and its first and second order partial derivatives. The computation of the Weingarten map matrix elements, from second order Taylor’s expansion differential terms, allows to easily determine the Gaussian curvature for each point. For each point cloud, the above defined centroids, generate a vertex configuration. The punctual correspondence with the analogous vertices of an adjacent point cloud are automatically defined, according to the analysis of the respective adjacency matrices. From these sets of pairs, the pre-alignment rototranslation parameters are computed by a SVD algorithm. The final alignment is completed

Guidance systems designed for neurosurgery, hip surgery, spine surgery, and for approaches to other anatomy that is relatively rigid can use rigid-body transformations to accomplish image registration. These systems often rely on point-based registration to determine the transformation, and many such systems use attached fiducial markers to establish accurate fiducial points for the registration, the points being established by some fiducial localization process. Accuracy is important to these systems, as is knowledge of the level of that accuracy. An advantage of marker-based systems, particularly those in which the markers are bone-implanted, is that registration error depends only on the fiducial localization error (FLE) and is thus to a large extent independent of the particular object being registered. Thus, it should be possible to predict the clinical accuracy of marker-based systems on the basis of experimental measurements made with phantoms or previous patients. This paper pr...