Shape reconstruction from gradient data

We present a novel 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 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 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.Comment: 16 pages, 5 figures, zip-file, submitted to Applied Optic

Flying triangulation - A motion-robust optical 3D sensor for the real-time shape acquisition of complex objects

The three-dimensional shape acquisition of objects has become more and more important in the last years. Up to now, there are several well-established methods which already yield impressive results. However, even under quite common conditions like object movement or a complex shaping, most methods become unsatisfying. Thus, the 3D shape acquisition is still a difficult and non-trivial task. We present our measurement principle “Flying Triangulation” which enables a motion-robust 3D acquisition of complex-shaped object surfaces by a freely movable handheld sensor. Since “Flying Triangulation” is scalable, a whole sensor-zoo for different object sizes is presented. Concluding, an overview of current and future fields of investigation is given

Consequences of EEG electrode position error on ultimate beamformer source reconstruction performance

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

Optimized data processing for an optical 3D sensor based on flying triangulation

We present data processing methods for an optical 3D sensor based on the measurement principle “Flying Triangulation”. The principle enables a motion-robust acquisition of the 3D shape of even complex objects: A hand-held sensor is freely guided around the object while real-time feedback of the measurement progress is delivered during the captioning. Although of high precision, the resulting 3D data usually may exhibit some weaknesses: e.g. outliers might be present and the data size might be too large. We describe the measurement principle and the data processing and conclude with measurement results

Marker-less Reconstruction of Dense 4-D Surface Motion Fields using Active Laser Triangulation from Sparse Measurements for Respiratory Motion Management

Abstract. 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.

Media 1: Flying triangulation—an optical 3D sensor for the motion-robust acquisition of complex objects

Originally published in Applied Optics on 10 January 2012 (ao-51-2-281