Calibration of time-of-flight cameras for accurate intraoperative surface reconstruction.

PURPOSE: In image-guided surgery (IGS) intraoperative image acquisition of tissue shape, motion, and morphology is one of the main challenges. Recently, time-of-flight (ToF) cameras have emerged as a new means for fast range image acquisition that can be used for multimodal registration of the patient anatomy during surgery. The major drawbacks of ToF cameras are systematic errors in the image acquisition technique that compromise the quality of the measured range images. In this paper, we propose a calibration concept that, for the first time, accounts for all known systematic errors affecting the quality of ToF range images. Laboratory and in vitro experiments assess its performance in the context of IGS. METHODS: For calibration the camera-related error sources depending on the sensor, the sensor temperature and the set integration time are corrected first, followed by the scene-specific errors, which are modeled as function of the measured distance, the amplitude and the radial distance to the principal point of the camera. Accounting for the high accuracy demands in IGS, we use a custom-made calibration device to provide reference distance data, the cameras are calibrated too. To evaluate the mitigation of the error, the remaining residual error after ToF depth calibration was compared with that arising from using the manufacturer routines for several state-of-the-art ToF cameras. The accuracy of reconstructed ToF surfaces was investigated after multimodal registration with computed tomography (CT) data of liver models by assessment of the target registration error (TRE) of markers introduced in the livers. RESULTS: For the inspected distance range of up to 2 m, our calibration approach yielded a mean residual error to reference data ranging from 1.5±4.3 mm for the best camera to 7.2±11.0 mm. When compared to the data obtained from the manufacturer routines, the residual error was reduced by at least 78% from worst calibration result to most accurate manufacturer data. After registration of the CT data with the ToF data, the mean TRE ranged from 3.7±2.1 mm for point-based and 5.7±1.9 mm for surface-based registration for the best camera to 6.2±3.4 and 11.1±2.8 mm, respectively. Compared to data provided by the manufacturer, the mean TRE decreased by 8%-60% for point-based and by 18%-74% for surface-based registration. CONCLUSIONS: Using the proposed calibration approach improved the measurement accuracy of all investigated ToF cameras. Although evaluated in the context of intraoperative image acquisition, the proposed calibration procedure can easily be applied to other medical applications using ToF cameras, such as patient positioning or respiratory motion tracking in radiotherapy.

Correlated speckle noise in white-light interferometry: theoretical analysis of measurement uncertainty.

The partial coherent illumination of the specimen, which is required for white-light interferometric measurements of optically rough surfaces, directly leads to speckle. The electric field of such speckle patterns strongly fluctuates in amplitude and phase. This spatially correlated noise influences the accuracy of the measuring device. Although a variety of noise sources in white-light interferometry has been studied in recent years, they do not account for spatial correlation and, hence, they cannot be applied to speckle noise. Thus, we derive a new model enabling quantitative predictions for measurement uncertainty caused by speckle. The model reveals that the accuracy can be attributed mainly to the degree of spatial correlation, i.e., the average size of a speckle, and to the coherence length of the light source. The same parameters define the signal-to-noise ratio in the spectral domain. The model helps to design filter functions that are perfectly adapted to the noise characteristics of the respective device, thus improving the accuracy of postprocessing algorithms for envelope detection. The derived expressions are also compared to numerical simulations and experimental data of two different types of interferometers. These results are a first validation of the theoretical considerations of this article.

Operator representation as a new differential optical absorption spectroscopy formalism.

UV-visible absorption spectroscopy with extraterrestrial light sources is a widely used technique for the measurement of stratospheric and tropospheric trace gases. We focus on differential optical absorption spectroscopy (DOAS) and present an operator notation as a new formalism to describe the different processes in the atmosphere and the simplifying assumptions that compose the advantage of DOAS. This formalism provides tools to classify and reduce possible error sources of DOAS applications.

Spatiotemporal anisotropic diffusion filtering to improve signal-to-noise ratios and object restoration in fluorescence microscopic image sequences.

We present an approach for significantly improving the quantitative analysis of motion in noisy fluorescence microscopic image sequences. The new partial differential equation based method is a general extension of a 2-D nonlinear anisotropic diffusion filtering scheme to a specially adapted 3-D nonlinear anisotropic diffusion filtering scheme, with two spatial image dimensions and the time t in the image sequence as the third dimension. Motion in image sequences is considered as oriented, line-like structures in the spatiotemporal x,y,t domain, which are determined by the structure tensor method. Image enhancement is achieved by a structure adopted smoothing kernel in three dimensions, thereby using the full 3-D information inherent in spatiotemporal image sequences. As an example for low signal-to-noise ratio (SNR) microscopic image sequences we have applied this method to noisy in vitro motility assay data, where fluorescently labeled actin filaments move over a surface of immobilized myosin. With the 3-D anisotropic diffusion filtering the SNR is significantly improved (by a factor of 3.8) and closed object structures are reliably restored, which were originally degraded by noise. Generally, this approach is very valuable for all applications where motion has to be measured quantitatively in low light level fluorescence microscopic image sequences of cellular, subcellular, and molecular processes.