Svenja Ettl

Shape reconstruction from gradient data

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.

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 beamformers 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.

Deflectometry vs. Interferometry

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.

Limitations of Optical 3D Sensors

This chapter is about the physical limitations of optical 3D sensors. The ultimate limit of the measurement uncertainty will be discussed; in other words: “How much 3D information are we able to know?” The dominant sources of noise and how this noise affects the measurement of micro-scale topography will be discussed. Some thoughts on how to overcome these limits will be given. It appears that there are only four types of sensors to be distinguished by the dominant sources of noise and how the physical measurement uncertainty scales with the aperture or working distance. These four types are triangulation, coherence scanning interferometry at rough surfaces, classical interferometry and deflectometry. 3D sensors will be discussed as communication channels and considerations about information-efficient sensors will be addressed.

Marker-Less reconstruction of dense 4-d surface motion fields using active laser triangulation for respiratory motion management

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.

Single-shot three-dimensional sensing with improved data density

We introduce a novel concept for motion robust optical 3D sensing. The concept is based on multiline triangulation. The aim is to evaluate a large number of projected lines (high data density), in a large measurement volume, with high precision. Implementing all those attributes at the same time principally allows for the “perfect” single-shot 3D movie camera (our long-term goal). The key problem toward this goal is ambiguous line indexing: we will demonstrate that the necessary information for unique line indexing can be acquired by two synchronized cameras and a back projection scheme. The introduced concept preserves high lateral resolution, since the lines are as narrow as the sampling theorem allows. No spatial bandwidth is consumed by encoding of the lines. In principle, the distance uncertainty is only limited by shot noise and coherent noise. The concept can be also advantageously implemented as a hand-guided sensor with real-time registration, for a complete and dense 3D acquisition of complicated scenes.

Joint surface reconstruction and 4D deformation estimation from sparse data and prior knowledge for marker‐less Respiratory motion tracking

PURPOSE The intraprocedural tracking of respiratory motion has the potential to substantially improve image-guided diagnosis and interventions. The authors have developed a sparse-to-dense registration approach that is capable of recovering the patients external 3D body surface and estimating a 4D (3D + time) surface motion field from sparse sampling data and patient-specific prior shape knowledge. METHODS The system utilizes an emerging marker-less and laser-based active triangulation (AT) sensor that delivers sparse but highly accurate 3D 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 recovered, which describes the spatio-temporal 4D deformation of the complete patient body surface, depending on the type and state of respiration. It yields both a reconstruction of the instantaneous patient shape and a high-dimensional respiratory surrogate for respiratory motion tracking. The method is validated on a 4D CT respiration phantom and evaluated on both real data from an AT prototype and synthetic data sampled from dense surface scans acquired with a structured-light scanner. RESULTS In the experiments, the authors estimated surface motion fields with the proposed algorithm on 256 datasets from 16 subjects and in different respiration states, achieving a mean surface reconstruction accuracy of ± 0.23 mm with respect to ground truth data-down from a mean initial surface mismatch of 5.66 mm. The 95th percentile of the local residual mesh-to-mesh distance after registration did not exceed 1.17 mm for any subject. On average, the total runtime of our proof of concept CPU implementation is 2.3 s per frame, outperforming related work substantially. CONCLUSIONS In external beam radiation therapy, the approach holds potential for patient monitoring during treatment using the reconstructed surface, and for motion-compensated dose delivery using the estimated 4D surface motion field in combination with external-internal correlation models.

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.

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.

Flying Triangulation - Acquiring the 360 Topography of the Human Body on the Fly

We introduce a novel optical measurement principle: “Flying Triangulation”. It fills an important gap in 3D metrology because it enables an acquisition of the topography of moving objects. The immunity against relative motion between object and sensor also allows for medical applications. An easy acquisition of complex objects is possible – just by freely hand guiding the sensor around the object. No tracking is necessary. We will present a “Flying Triangulation” sensor for the intraoral measurement of teeth and a sensor realization for the full 360° 3D acquisition of a person’s head. Parts of the body can be captured with high precision by comfortably guiding the sensor, with real-time control of the result.