Kernel density correlation based non-rigid point set matching for statistical model-based 2D/3D reconstruction

This paper presents a kernel density correlation based nonrigid point set matching method and shows its application in statistical model based 2D/3D reconstruction of a scaled, patient-specific model from an un-calibrated x-ray radiograph. In this method, both the reference point set and the floating point set are first represented using kernel density estimates. A correlation measure between these two kernel density estimates is then optimized to find a displacement field such that the floating point set is moved to the reference point set. Regularizations based on the overall deformation energy and the motion smoothness energy are used to constraint the displacement field for a robust point set matching. Incorporating this non-rigid point set matching method into a statistical model based 2D/3D reconstruction framework, we can reconstruct a scaled, patient-specific model from noisy edge points that are extracted directly from the x-ray radiograph by an edge detector. Our experiment conducted on datasets of two patients and six cadavers demonstrates a mean reconstruction error of 1.9 mm

Synchronisation of the EDML and EDC ice cores for the last 52 kyr by volcanic signature matching

A common time scale for the EPICA ice cores from Dome C (EDC) and Dronning Maud Land (EDML) has been established. Since the EDML core was not drilled on a dome, the development of the EDML1 time scale for the EPICA ice core drilled in Dronning Maud Land was based on the creation of a detailed stratigraphic link between EDML and EDC, which was dated by a simpler 1D ice-flow model. The synchronisation between the two EPICA ice cores was done through the identification of several common volcanic signatures. This paper describes the rigorous method, using the signature of volcanic sulfate, which was employed for the last 52 kyr of the record. We estimated the discrepancies between the modelled EDC and EDML glaciological age scales during the studied period, by evaluating the ratio R of the apparent duration of temporal intervals between pairs of isochrones. On average R ranges between 0.8 and 1.2 corresponding to an uncertainty of up to 20% in the estimate of the time duration in at least one of the two ice cores. Significant deviations of R up to 1.4–1.5 are observed between 18 and 28 kyr before present (BP), where present is defined as 1950. At this stage our approach does not allow us unequivocally to find out which of the models is affected by errors, but assuming that the thinning function at both sites and accumulation history at Dome C (which was drilled on a dome) are correct, this anomaly can be ascribed to a complex spatial accumulation variability (which may be different in the past compared to the present day) upstream of the EDML core.

Accuracy of navigated surgery of the pelvis after surface matching with an a-mode ultrasound probe

Computer-aided surgery (CAS) allows for real-time intraoperative feedback resulting in increased accuracy, while reducing intraoperative radiation. CAS is especially useful for the treatment of certain pelvic ring fractures, which necessitate the precise placement of screws. Flouroscopy-based CAS modules have been developed for many orthopedic applications. The integration of the isocentric flouroscope even enables navigation using intraoperatively acquired three-dimensional (3D) data, though the scan volume and imaging quality are limited. Complicated and comprehensive pathologies in regions like the pelvis can necessitate a CT-based navigation system because of its larger field of view. To be accurate, the patient's anatomy must be registered and matched with the virtual object (CT data). The actual precision within the region of interest depends on the area of the bone where surface matching is performed. Conventional surface matching with a solid pointer requires extensive soft tissue dissection. This contradicts the primary purpose of CAS as a minimally invasive alternative to conventional surgical techniques. We therefore integrated an a-mode ultrasound pointer into the process of surface matching for pelvic surgery and compared it to the conventional method. Accuracy measurements were made in two pelvic models: a foam model submerged in water and one with attached porcine muscle tissue. Three different tissue depths were selected based on CT scans of 30 human pelves. The ultrasound pointer allowed for registration of virtually any point on the pelvis. This method of surface matching could be successfully integrated into CAS of the pelvis.

Validation of a new method for determination of cup orientation in THA

Our goal was to validate accuracy, consistency, and reproducibility/reliability of a new method for determining cup orientation in total hip arthroplasty (THA). This method allows matching the 3D-model from CT images or slices with the projected pelvis on an anteroposterior pelvic radiograph using a fully automated registration procedure. Cup orientation (inclination and anteversion) is calculated relative to the anterior pelvic plane, corrected for individual malposition of the pelvis during radiograph acquisition. Measurements on blinded and randomized radiographs of 80 cadaver and 327 patient hips were investigated. The method showed a mean accuracy of 0.7 +/- 1.7 degrees (-3.7 degrees to 4.0 degrees) for inclination and 1.2 +/- 2.4 degrees (-5.3 degrees to 5.6 degrees) for anteversion in the cadaver trials and 1.7 +/- 1.7 degrees (-4.6 degrees to 5.5 degrees) for inclination and 0.9 +/- 2.8 degrees (-5.2 degrees to 5.7 degrees) for anteversion in the clinical data when compared to CT-based measurements. No systematic errors in accuracy were detected with the Bland-Altman analysis. The software consistency and the reproducibility/reliability were very good. This software is an accurate, consistent, reliable, and reproducible method to measure cup orientation in THA using a sophisticated 2D/3D-matching technique. Its robust and accurate matching algorithm can be expanded to statistical models.

Transconvolution and the virtual positron emission tomograph--a new method for cross calibration in quantitative PET∕CT imaging

PURPOSE Positron emission tomography (PET)∕computed tomography (CT) measurements on small lesions are impaired by the partial volume effect, which is intrinsically tied to the point spread function of the actual imaging system, including the reconstruction algorithms. The variability resulting from different point spread functions hinders the assessment of quantitative measurements in clinical routine and especially degrades comparability within multicenter trials. To improve quantitative comparability there is a need for methods to match different PET∕CT systems through elimination of this systemic variability. Consequently, a new method was developed and tested that transforms the image of an object as produced by one tomograph to another image of the same object as it would have been seen by a different tomograph. The proposed new method, termed Transconvolution, compensates for differing imaging properties of different tomographs and particularly aims at quantitative comparability of PET∕CT in the context of multicenter trials. METHODS To solve the problem of image normalization, the theory of Transconvolution was mathematically established together with new methods to handle point spread functions of different PET∕CT systems. Knowing the point spread functions of two different imaging systems allows determining a Transconvolution function to convert one image into the other. This function is calculated by convolving one point spread function with the inverse of the other point spread function which, when adhering to certain boundary conditions such as the use of linear acquisition and image reconstruction methods, is a numerically accessible operation. For reliable measurement of such point spread functions characterizing different PET∕CT systems, a dedicated solid-state phantom incorporating (68)Ge∕(68)Ga filled spheres was developed. To iteratively determine and represent such point spread functions, exponential density functions in combination with a Gaussian distribution were introduced. Furthermore, simulation of a virtual PET system provided a standard imaging system with clearly defined properties to which the real PET systems were to be matched. A Hann window served as the modulation transfer function for the virtual PET. The Hann's apodization properties suppressed high spatial frequencies above a certain critical frequency, thereby fulfilling the above-mentioned boundary conditions. The determined point spread functions were subsequently used by the novel Transconvolution algorithm to match different PET∕CT systems onto the virtual PET system. Finally, the theoretically elaborated Transconvolution method was validated transforming phantom images acquired on two different PET systems to nearly identical data sets, as they would be imaged by the virtual PET system. RESULTS The proposed Transconvolution method matched different PET∕CT-systems for an improved and reproducible determination of a normalized activity concentration. The highest difference in measured activity concentration between the two different PET systems of 18.2% was found in spheres of 2 ml volume. Transconvolution reduced this difference down to 1.6%. In addition to reestablishing comparability the new method with its parameterization of point spread functions allowed a full characterization of imaging properties of the examined tomographs. CONCLUSIONS By matching different tomographs to a virtual standardized imaging system, Transconvolution opens a new comprehensive method for cross calibration in quantitative PET imaging. The use of a virtual PET system restores comparability between data sets from different PET systems by exerting a common, reproducible, and defined partial volume effect.