Inaccuracy of EEG electrode coordinates forms an error term in forward model generation and ultimate source reconstruction performance. This error arises from the combination of both intrinsic measurement noise of the digitization apparatus and manual coregistration error when selecting corresponding points on anatomical MRI volumes. A common assumption is that such an error would lead only to displacement of localized sources. Here, we measured electrode positions on a 3D-printed full-scale replica head, using three different techniques: a fringe projection 3D scanner, a novel “Flying Triangulation” 3D sensor, and a traditional electromagnetic digitizer. Using highly accurate fringe projection data as ground truth, the Flying Triangulation sensor had a mean error of 1.5 mm while the electromagnetic digitizer had a mean error of 6.8 mm. Then, again using the fringe projection as ground truth, individual EEG simulations were generated, with source locations across the brain space and a range of sensor noise levels. The simulated datasets were then processed using a beamformer in conjunction with the electrode coordinates registered with the Flying Triangulation and electromagnetic digitizer methods. The beamformer's output SNR was severely degraded with the digitizer-based positions but less severely with the Flying Triangulation coordinates. Therefore, the seemingly innocuous error in electrode registration may result in substantial degradation of beamformer performance, with output SNR penalties up to several decibels. In the case of low-SNR signals such as deeper brain structures or gamma band sources, this implies that sensor coregistration accuracy could make the difference between successful detection of such activity or complete failure to resolve the source.

We present a generalized method for reconstructing the shape of an object from measured gradient data. A certain class of optical sensors does not measure the shape of an object but rather its local slope. These sensors display several advantages, including high information efficiency, sensitivity, and robustness. For many applications, however, it is necessary to acquire the shape, which must be calculated from the slopes by numerical integration. Existing integration techniques show drawbacks that render them unusable in many cases. Our method is based on an approximation employing radial basis functions. It can be applied to irregularly sampled, noisy, and incomplete data, and it reconstructs surfaces both locally and globally with high accuracy.

Quantitative deflectometry is a new tool to measure specular surfaces. The spectrum of measurable surfaces ranges from flat to freeform surfaces with steep slopes, with a size ranging from millimeters to several meters. We illustrate this by several applications: eye glass measurements, measurements of big mirrors, and in-line measurements in ultra-precision manufacturing without unclamping of the sample. We describe important properties of deflectometry and compare its potentials and limitations with interferometry. We discuss which method is superior for which application and how the potential of deflectometry may be developing in the future.

Three-dimensional (3D) shape acquisition is difficult if an all-around measurement of an object is desired or if a relative motion between object and sensor is unavoidable. An optical sensor principle is presented-we call it "flying triangulation"-that enables a motion-robust acquisition of 3D surface topography. It combines a simple handheld sensor with sophisticated registration algorithms. An easy acquisition of complex objects is possible-just by freely hand-guiding the sensor around the object. Real-time feedback of the sequential measurement results enables a comfortable handling for the user. No tracking is necessary. In contrast to most other eligible sensors, the presented sensor generates 3D data from each single camera image.

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To manage respiratory motion in image-guided interventions a novel sparse-to-dense registration approach is presented. We apply an emerging laser-based active triangulation (AT) sensor that delivers sparse but highly accurate 3-D measurements in real-time. These sparse position measurements are registered with a dense reference surface extracted from planning data. Thereby a dense displacement field is reconstructed which describes the 4-D deformation of the complete patient body surface and recovers a multi-dimensional respiratory signal for application in respiratory motion management. The method is validated on real data from an AT prototype and synthetic data sampled from dense surface scans acquired with a structured light scanner. In a study on 16 subjects, the proposed algorithm achieved a mean reconstruction accuracy of ±0.22 mm w.r.t. ground truth data.

Multisensor systems with optical 3D sensors are frequently employed to capture complete surface information by measuring workpieces from different views. During coarse and fine registration the resulting datasets are afterward transformed into one common coordinate system. Automatic fine registration methods are well established in dimensional metrology, whereas there is a deficit in automatic coarse registration methods. The advantage of a fully automatic registration procedure is twofold: it enables a fast and contact-free alignment and further a flexible application to datasets of any kind of optical 3D sensor. In this paper, an algorithm adapted for a robust automatic coarse registration is presented. The method was originally developed for the field of object reconstruction or localization. It is based on a segmentation of planes in the datasets to calculate the transformation parameters. The rotation is defined by the normals of three corresponding segmented planes of two overlapping datasets, while the translation is calculated via the intersection point of the segmented planes. First results have shown that the translation is strongly shape dependent: 3D data of objects with non-orthogonal planar flanks cannot be registered with the current method. In the novel supplement for the algorithm, the translation is additionally calculated via the distance between centroids of corresponding segmented planes, which results in more than one option for the transformation. A newly introduced measure considering the distance between the datasets after coarse registration evaluates the best possible transformation. Results of the robust automatic registration method are presented on the example of datasets taken from a cutting tool with a fringe-projection system and a focus-variation system. The successful application in dimensional metrology is proven with evaluations of shape parameters based on the registered datasets of a calibrated workpiece.