Single-shot 3D motion picture camera with a dense point cloud.

We discuss physical and information theoretical limits of optical 3D metrology. Based on these principal considerations we introduce a novel single-shot 3D movie camera that almost reaches these limits. The camera is designed for the 3D acquisition of macroscopic live scenes. Like a hologram, each movie-frame encompasses the full 3D information about the object surface and the observation perspective can be varied while watching the 3D movie. The camera combines single-shot ability with a point cloud density close to the theoretical limit. No space-bandwidth is wasted by pattern codification. With 1-megapixel sensors, the 3D camera delivers nearly 300,000 independent 3D points within each frame. The 3D data display a lateral resolution and a depth precision only limited by physics. The approach is based on multi-line triangulation. The requisite low-cost technology is simple. Only two properly positioned synchronized cameras solve the profound ambiguity problem omnipresent in 3D metrology.

Better three-dimensional inspection with structured illumination: speed.

Three-dimensional (3D) inspection in the factory requires precision and speed. While customers can select from a wide spectrum of high-precision sensors, the real challenge today is "speed." We discuss the speed of 3D sensors in a general context to provide an understanding of why high-resolution 3D sensors deliver significantly fewer 3D points per second than the available camera pixel rates suggest. The major cause of low speed is the large number E of required exposures due to the unavoidable depth scanning. Through the example of structured-illumination microscopy (SIM), we demonstrate how E can be minimized without reducing precision. We further demonstrate a lateral scanning strategy that operates at a significantly higher speed for macroscopic measurements by avoiding explicit depth scanning. This paper is a follow up on an earlier paper about the precision limits of SIM and exploits the earlier results.

Better 3D inspection with structured illumination: signal formation and precision.

3D metrology faces increasing demands for higher precision and larger space-bandwidth-speed product (number of 3D points/s). In this paper we consider structured-illumination microscopy as a means for satisfying these demands, developing a theoretical model of the signal formation for both optically smooth and optically rough surfaces. The model allows us to investigate physical limits on precision and to establish rules that allow sensor parameter optimization for greatest precision or highest speed.

Improved white-light interferometry on rough surfaces by statistically independent speckle patterns.

White-light interferometry (WLI) on rough surfaces is based on interference from individual speckles. The measurement uncertainty of WLI is limited by a random shift of these individual interference patterns. The statistical error in each measurement point depends on the brightness of the corresponding speckle: a dark speckle yields a larger error than a bright speckle. In this paper, a novel method is presented to reduce the measurement uncertainty significantly: by sequentially switching the direction of the illumination, the camera sees several independent speckle patterns in sequence. From each pattern, the brightest speckles are selected to eventually calculate an accurate height map. This height map displays no outliers, and the measured surface roughness is close to the stylus measurements.

Flying triangulation--an optical 3D sensor for the motion-robust acquisition of complex objects.

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.

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.

Microdeflectometry--a novel tool to acquire three-dimensional microtopography with nanometer height resolution.

We introduce "microdeflectometry," a novel technique for measuring the microtopography of specular surfaces. The primary data are the local slope of the surface under test. Measuring the slope instead of the height implies high information efficiency and extreme sensitivity to local shape irregularities. The lateral resolution can be better than 1 microm, whereas the resulting height resolution is in the range of 1nm. Microdeflectometry can be supplemented by methods to expand the depth of field, with the potential to provide quantitative 3D imaging with scanning-electron-microscope-like features.

Reliability of a Method for Computing Facial Symmetry Plane and Degree of Asymmetry Based on 3D-data.

OBJECTIVE: The objective of this study was to analyze the reliability of a landmark-independent method for determining the facial symmetry plane and degree of asymmetry based on three-dimensional data from the facial surface from two sets of recordings, one performed consecutively and one performed on different days. MATERIALS AND METHODS: We used an optical 3D-sensor to obtain the facial data of one male subject in two sets of ten measurements: the first taken consecutively and the second on different days. The symmetry plane and degree of asymmetry were calculated for each of the resulting twenty sets of data. One set of data was analyzed ten times for control purposes. The calculation of the mean deviation angle between the symmetry planes served as a measure of the reproducibility of these results. RESULTS: Although the mean angular deviations of the computed symmetry planes, 0.134 degrees (for ten consecutively captured images) and 0.177 degrees (for the ten images captured on different days), were each significantly higher than the mean angular deviation (0.028 degrees) calculated from ten analyses of a single image, they can still be regarded as very small. There were no significant differences in the degree of asymmetry among the three measurement sets. The standard deviations revealed low values. CONCLUSIONS: This method can be used to compute with high reliability the symmetry planes and degree of asymmetry of facial 3D-data. The color-coded visualization of asymmetrical facial regions makes it possible for this analytical procedure to capture the asymmetries of facial soft tissue with substantially greater precision than 2-dimensional en face images.

Automatic coarse registration of three-dimensional surfaces by information theoretic selection of salient points.

We describe a new method to register surface data measured by optical three-dimensional (3-D) sensors from various views of an object. With our method, complete 3-D models of objects can be generated without user interaction. Circumferential acquisition of 3-D objects is done by taking several views from different directions. To generate a complete 3-D-model, the views must be aligned with each other. This process is called registration and is commonly done interactively by searching for so-called corresponding points in the different views and by use of these points to calculate the appropriate rotation and translation. Our approach is based on automatically finding points that are eye catching or salient compared with other surface points. We derive a quantitative measure of point salience and a feature definition for free-form surfaces by introducing a concept to measure pragmatic information. Experiments confirm that our salient points can be robustly located on general free-form surfaces, even if there are no corners or edges. Furthermore, the neighborhoods of the salient points are highly distinguishable from each other. This results in a large reduction of the complexity of the subsequent geometric matching. The computing time is only a few seconds. We present results from various fields of application.

Intraoperative noncontact, nonionizing, optical 3D exophthalmometry during repositioning of dislocated globes: first results.

PURPOSE: This study reports on the intraoperative use of noncontact, nonionizing, optical 3-dimensional (3D) exophthalmometry during the repositioning of dislocated globes as a result of trauma. PATIENTS AND METHODS: Ten patients (4 female, 6 male, 41.4+/-15.2 years) with a relative enophthalmos of the globe as a result of zygomatic fractures were included in the study. Preoperatively, en- and exophthalmometry data were assessed from axial CT slices and optical 3D imaging. 3D data were analyzed twice for the assessment of measurement errors. Intraoperatively, optical en- and exophthalmometry was carried out to control the globe position. Surgery was considered successful when the relative en- or exophthalmos no longer exceeded 2 mm. Optical 3D en- and exophthalmometry data were reassessed 5 days and 3 months after surgery. RESULTS: Method error was 0.184 mm for optical 3D en- and exophthalmometry. The preoperatively assessed en- and exophthalmometry data determined from axial CT scans and from optical 3D images did not differ significantly statistically (P=.538). When the preoperative en- and exophthalmometry data were compared to the values assessed at the end of surgery, a significant improvement in globe position was found (P=.005). Although a relative en- or exophthalmos of 2 mm was not exceeded in any of the patients 3 months after surgery, en- and exophthalmometry data differed significantly statistically from the data assessed at the end of the operation (P=.005). CONCLUSIONS: Intraoperative optical en- and exophthalmometry is an effective means to support the surgeon in objectively optimizing the globe position with small measurement errors.

White-light interferometer with dispersion: an accurate fiber-optic sensor for the measurement of distance.

We present a fiber-optical sensor for distance measurement of smooth and rough surfaces that is based on white-light interferometry; the sensor measures the distance from the sample surface to the sensor head. Because white light is used, the measurement is absolute. The measurement uncertainty depends not on the aperture of the optical system but only on the properties of the rough surface and is commonly approximately 1 microm. The measurement range is approximately 1 mm. The sensor includes no mechanical moving parts; mechanical movement is replaced by the spectral decomposition of light at the interferometer output. The absence of mechanical moving parts enables a high measuring rate to be reached.

Relative en- and exophthalmometry in zygomatic fractures comparing optical non-contact, non-ionizing 3D imaging to the Hertel instrument and computed tomography.

AIM: It is the aim of the present study to introduce non-contact, non-invasive optical 3D imaging to relative exophthalmometry and to compare the resulting data to exophthalmometry values assessed by the Hertel instrument and computed tomography. PATIENTS AND METHODS: 20 patients (3 female, 17 male, 44.4+/-16.6 years) without orbital pathology, who were examined by computed tomography of head and neck for the exclusion of different diseases, and seven patients (1 female, 6 male, 40.1+/-14.4 years), who received routine orbital computed tomography because of zygomatic fractures, were included in the study. Optical 3D images of the facial surface were assessed and Hertel exophthalmometry was carried out to determine the relative globe position. In patients with zygomatic fractures the assessment of optical 3D images and Hertel values was repeated 5 days after surgery. RESULTS: For patients without orbital pathology relative exophthalmometry data were 1.4+/-1.1 mm for the Hertel instrument, 0.9+/-1.0 mm for computed tomography and 0.5+/-0.5 mm for optical 3D imaging. The values for Hertel exophthalmometry and computed tomography did not differ statistically significantly (p(Herteldifferencepreop/CTdifferencepreop)=0.284), while there was a significant difference between Hertel exophthalmometry and optical 3D imaging (p(Herteldifferencepreop/opticaldifferencepreop)=0.008). In the cases of zygomatic fractures, Hertel exophthalmometry revealed less pronounced relative differences in globe position than CT and optical 3D imaging data (Hertel 0.7+/-1.1 mm, CT 1.9+/-1.0 mm, optical 3D imaging 1.9+/-1.0 mm). Postoperatively, relative Hertel exophthalmometry showed an increased value revealing a more pronounced enophthalmos (1.7+/-1.0 mm), while the corresponding value of the optical 3D images decreased as a sign for normalization of the globe position (1.1+/-0.7 mm). CONCLUSION: Because of its reliance on the lateral orbital rims Hertel exophthalmometry can lead to an under- or overestimation of enophthalmos, when soft tissue oedema or a dislocation of the orbital rim are present. The combination of computed tomography as baseline measurement and optical 3D imaging for the follow-up examinations reveal more realistic data in cases of zygomatic fractures. Therefore, they should be preferred to the determination of Hertel values especially in more complex cases.

Information theoretical optimization for optical range sensors.

Most of the known optical range sensors require a large amount of two-dimensional raw data from which the three-dimensional (3D) data are decoded and so are associated with considerable cost. The cost arises from expensive hardware as well as from the time necessary to acquire the images. We will address the question of how one can acquire maximum shape information with a minimum amount of image raw data, in terms of information theory. It is shown that one can greatly reduce the amount of raw data needed by proper optical redundancy reduction. Through these considerations, a 3D sensor is introduced, which needs only a single color (red-green-blue) raw image and still delivers data with only approximately 2-microm longitudinal measurement uncertainty.

Validation of in vivo assessment of facial soft-tissue volume changes and clinical application in midfacial distraction: a technical report.

The purpose of this study was to validate the assessment of visible volume changes of the facial soft tissue with an optical three-dimensional sensor and to introduce new parameters for the evaluation of the soft-tissue shape achieved from three-dimensional data of selected cases of midfacial distraction. Images of a truncated cone of known volume were assessed repeatedly with an optical three-dimensional sensor based on phase-measuring triangulation to calculate the volume. Two cubic centimeters of anesthetic solution was injected into the right malar region of 10 volunteers who gave their informed consent. Three-dimensional images were assessed before and immediately after the injections for the assessment of the visible volume change. In five patients who underwent midfacial distraction after a high quadrangular Le Fort I osteotomy, three-dimensional scans were acquired before and 6 and 24 months after the operation. The visible soft-tissue volume change in the malar-midfacial area and the mean distance of the accommodation vector that transformed the preoperative into the postoperative surface were calculated. The volume of the truncated cone was 235.26 +/- 1.01 cc, revealing a measurement uncertainty of 0.4 percent. The injections of anesthetic solution into the malar area resulted in an average visible volume change of 2.06 +/- 0.06 cc. The measurement uncertainty was 3 percent. In the five patients, the average distance of maxillary advancement was 6.7 +/- 2.3 mm after 6 months and 5.4 +/- 3.0 mm after 2 years. It was accompanied by a mean visible volume increase of 8.92 +/- 5.95 cc on the right side and 9.54 +/- 4.39 cc on the left side after 6 months and 3.54 +/- 3.70 cc and 4.80 +/- 3.47 cc, respectively, after 2 years. The mean distance of the accommodation vector was 4.41 +/- 1.94 mm on the right side and 4.74 +/- 1.32 mm on the left side after 6 months and 1.62 +/- 1.96 mm and 2.16 +/- 1.52 mm, respectively, after 2 years. The assessment of visible volume changes by optical three-dimensional images can be carried out with considerable accuracy. The determination of volume changes and accompanying accommodation vectors completes the cephalometric analysis during the follow-up of patients undergoing midfacial distraction. The new parameters will help to assess normative soft-tissue data on the basis of three-dimensional imaging with a view to an improved three-dimensional prediction of the operative outcome of orthognathic surgery.