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... one common coordinate system. Most of the techniques to perform this so-called registration task are more or less variations of the Iterative Closest Point (ICP) algorithm proposed by Besl and McKay =-=[4]-=-. The algorithm can briefly be sketched as follows. Assuming a reasonable good initial registration, the relative orientation between two datasets is iteratively refined by pairing a number of points ...

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...on the other surface and minimizing the sum of squared distances between the point sets. Closed form solutions to find the rigid body transformations between two point sets are readily available e.g. =-=[1,17,18,31]-=- and have been compared by Eggert et al [13]. Although [17] considered an isotropic noise model to reflect measurements of unequal quality, none of the methods is capable to handle anisotropic noise. ...

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...ll pairwaise registration techniques have problems to find a good solution for the case of multiple datasets, since errors in the estimated transformations accumulate if views are added consecutively =-=[9]-=-. For that reason global registration techniques are needed. The solution of Turk and Levoy [27] requires a cylindrical scan that covers a large portion of the object. Linear scans are then registered...

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...on the other surface and minimizing the sum of squared distances between the point sets. Closed form solutions to find the rigid body transformations between two point sets are readily available e.g. =-=[1,17,18,31]-=- and have been compared by Eggert et al [13]. Although [17] considered an isotropic noise model to reflect measurements of unequal quality, none of the methods is capable to handle anisotropic noise. ...

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... A number of heuristics address the problem of partially overlapping surfaces. It is very common to discard correspondences that are too far apart and correspondences that lie on the surface boundary =-=[6,27]-=-. Other authors discard point pairs that are not compatible with the neighboring pairs [11]. All pairwaise registration techniques have problems to find a good solution for the case of multiple datase...

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...t each iteration. Because of a possible accumulation of registration errors, care has to be taken that the network topology minimizes the lengths of the paths between the nodes. The solution of Pulli =-=[22]-=- enforces constraints from pairwise registration in the global registration step. The method is particularly suited to register large data sets. Since only the constraints are used in global registrat...

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...t simulated annealing, a stochastic optimization method, is used to minimize a total cost function. However, the high dimensional minimization problem requires a large processing time. Bergevin et al =-=[2]-=- build a network of transformations between different views. One view defines the reference frame. The correspondences from all possible pairings are used to simultaneously compute the transformations...

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...ed distances between the point sets. Closed form solutions to find the rigid body transformations between two point sets are readily available e.g. [1,17,18,31] and have been compared by Eggert et al =-=[13]-=-. Although [17] considered an isotropic noise model to reflect measurements of unequal quality, none of the methods is capable to handle anisotropic noise. In addition, the methods yield no informatio...

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... A number of heuristics address the problem of partially overlapping surfaces. It is very common to discard correspondences that are too far apart and correspondences that lie on the surface boundary =-=[6,27]-=-. Other authors discard point pairs that are not compatible with the neighboring pairs [11]. All pairwaise registration techniques have problems to find a good solution for the case of multiple datase...

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...Since only the constraints are used in global registration there is no need to keep the entire data set in memory, but good pairwise alignments are required. Stoddart and Hilton [24] and Eggert et als=-=[12]-=- independently followed a completely different approach. They perform a force-based optimization by simulating the interconnection of the data sets with springs between corresponding points and then s...

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...on the other surface and minimizing the sum of squared distances between the point sets. Closed form solutions to find the rigid body transformations between two point sets are readily available e.g. =-=[1,17,18,31]-=- and have been compared by Eggert et al [13]. Although [17] considered an isotropic noise model to reflect measurements of unequal quality, none of the methods is capable to handle anisotropic noise. ...

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...nd the pattern (dot, stripe, multi dot/stripe or freely programmable, e.g. LCD projector) [23,35]. More recently, authors made an effort to improve aspects like calibration, accuracy and reliability. =-=[10]-=- consider the time evolution of the reflected pattern while sweeping a laser plane over the object. Their so-called spacetime analysis considerably reduces a number of error sources in traditional met...

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...product between the local surface normal and the line of sight of the sensor. A complete framework to describe and treat uncertainty in point set registration has been developed by Pennec and Thirion =-=[20]-=-. They use extended Kalman filtering to estimate the parameters of a rigid body transformation and the parameters covariance matrix. However, the method does not solve the global registration problem....

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...nto the image plane, considering imperfect cameras and lenses. Most commonly a specially designed test object is used to effectively compute the desired quantities from a few calibration measurements =-=[8,15]-=-. Since any short-term geometrically stable object can be used for calibration, there is no need for an accurate calibration normal. Nonetheless, at least one accurate distance (e.g. from a scale bar)...

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...mon to discard correspondences that are too far apart and correspondences that lie on the surface boundary [6,27]. Other authors discard point pairs that are not compatible with the neighboring pairs =-=[11]-=-. All pairwaise registration techniques have problems to find a good solution for the case of multiple datasets, since errors in the estimated transformations accumulate if views are added consecutive...

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...s might remain uncorrected. While direct calibration techniques are very popular for light stripe range finders, projection devices that generate 2D patterns have also been modeled as inverse cameras =-=[25,28,29,34]-=-. A range finder can only acquire those parts of an object, which are visible from a given viewpoint. Hence it is necessary to transform data from different viewpoints into one common coordinate syste...

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...ster large data sets. Since only the constraints are used in global registration there is no need to keep the entire data set in memory, but good pairwise alignments are required. Stoddart and Hilton =-=[24]-=- and Eggert et als[12] independently followed a completely different approach. They perform a force-based optimization by simulating the interconnection of the data sets with springs between correspon...

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...nd discusses the obtained results. 1.1 Previous Work A number of different sensor architectures have been proposed for the construction of range sensors. Comprehensive reviews can be found in [3] and =-=[14]-=-. Active triangulation is one of the most common methods for 3D surface acquisition. Such systems project specific light patterns onto the object. The light patterns are distorted by the object surfac...

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...loit the whole resolution of the projector (plus 20 Gray code images for ambiguity resolution). The line centers are detected with sub-pixel accuracy using a peak detector proposed by Blais and Rioux =-=[5]-=-. The detector performs a convolution of the greyvalue image with a fourth or eighth order linear filter (derivative operator). It then determines the sub-pixel position of the zero crossing in the co...

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...bject. Their so-called spacetime analysis considerably reduces a number of error sources in traditional methods if surface discontinuities and changes in surface reflectance are present. Trucco et al =-=[26]-=- addressed the issues of calibration, stripe location and measurement consistency. They proposed several explicit consistency tests based on two-camera geometry. Calibration is usually performed using...

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...llumination (laser or incoherent light source) and the dimensionality of the camera (matrix or linear array) and the pattern (dot, stripe, multi dot/stripe or freely programmable, e.g. LCD projector) =-=[23,35]-=-. More recently, authors made an effort to improve aspects like calibration, accuracy and reliability. [10] consider the time evolution of the reflected pattern while sweeping a laser plane over the o...

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...nto the image plane, considering imperfect cameras and lenses. Most commonly a specially designed test object is used to effectively compute the desired quantities from a few calibration measurements =-=[8,15]-=-. Since any short-term geometrically stable object can be used for calibration, there is no need for an accurate calibration normal. Nonetheless, at least one accurate distance (e.g. from a scale bar)...

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...tion and the parameters covariance matrix. However, the method does not solve the global registration problem. Stoddart et al [24] extended this framework to the problem of surface registration. Pito =-=[21]-=- addressed the problem of insufficient shape information. He performed a qualitative analysis of geometric constraints with respect to rotation and translation and introduced a mechanical registration...

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...s might remain uncorrected. While direct calibration techniques are very popular for light stripe range finders, projection devices that generate 2D patterns have also been modeled as inverse cameras =-=[25,28,29,34]-=-. A range finder can only acquire those parts of an object, which are visible from a given viewpoint. Hence it is necessary to transform data from different viewpoints into one common coordinate syste...

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... performed a qualitative analysis of geometric constraints with respect to rotation and translation and introduced a mechanical registration aid, on which he places the object. Williams and Bennamoun =-=[33]-=- recently described a global method for point set registration considering a three dimensional Gaussian error model. They also applied a robust (least median of squares) estimation technique but did n...

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...a token in one image, find the corresponding tokens in all other images. Once the correspondence problem is solved, the computation of object coordinates is straightforward. In a previous publication =-=[16]-=- we have proposed a new pattern design, together with a new evaluation method. The so-called line shift pattern consists of a Gray code sequence, followed by a sequence of parallel lines, achieved by ...

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...s might remain uncorrected. While direct calibration techniques are very popular for light stripe range finders, projection devices that generate 2D patterns have also been modeled as inverse cameras =-=[25,28,29,34]-=-. A range finder can only acquire those parts of an object, which are visible from a given viewpoint. Hence it is necessary to transform data from different viewpoints into one common coordinate syste...

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...alidation using Statistical Error Models Coordinate measuring machines are the defacto standard for industrial part inspection, but suffer from limitations such as high cost and low measurement speed =-=[7]-=-. On the other hand, optical 3D shape acquisition systems provide fast and dense surface measurements without the need for physically probing surfaces, thus making them ideally suited for various appl...

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...llumination (laser or incoherent light source) and the dimensionality of the camera (matrix or linear array) and the pattern (dot, stripe, multi dot/stripe or freely programmable, e.g. LCD projector) =-=[23,35]-=-. More recently, authors made an effort to improve aspects like calibration, accuracy and reliability. [10] consider the time evolution of the reflected pattern while sweeping a laser plane over the o...

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... paper and discusses the obtained results. 1.1 Previous Work A number of different sensor architectures have been proposed for the construction of range sensors. Comprehensive reviews can be found in =-=[3]-=- and [14]. Active triangulation is one of the most common methods for 3D surface acquisition. Such systems project specific light patterns onto the object. The light patterns are distorted by the obje...

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...coordinate measurement machines on a national and international level [19]. To fill this gap, some national standard organizations are now working on similar standards for optical measurement systems =-=[30]-=-. Another reason is measurement uncertainty, which is not constant over the measurement volume. It rather depends on a number of factors like sensor hardware, sensing geometry and the shape and reflec...

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...he points s i and d i to be independent, the covariance Matrix Σ i is computed as T Σ i =Σ d + RΣ i s R (5) i We use a modified version of the iterative non-linear least squares solution described in =-=[32]-=-. They derive a simple form for the Jacobian of rotation with respect to quaternions when evaluated at the identity quaternion q I . In fact, only three rotation parameters (the vector part T [ q1 q2 ...