Registration of pre-operative CT and freehand intra-operative ultrasound of lumbar spine could aid surgeons in
the spinal needle injection which is a common procedure for pain management. Patients are always in a supine
position during the CT scan, and in the prone or sitting position during the intervention. This leads to a difference
in the spinal curvature between the two imaging modalities, which means a single rigid registration cannot be
used for all of the lumbar vertebrae. In this work, a method for group-wise registration of pre-operative CT and
intra-operative freehand 2-D ultrasound images of the lumbar spine is presented. The approach utilizes a pointbased
registration technique based on the unscented Kalman filter, taking as input segmented vertebrae surfaces
in both CT and ultrasound data. Ultrasound images are automatically segmented using a dynamic programming
approach, while the CT images are semi-automatically segmented using thresholding. Since the curvature of the
spine is different between the pre-operative and the intra-operative data, the registration approach is designed to
simultaneously align individual groups of points segmented from each vertebra in the two imaging modalities. A
biomechanical model is used to constrain the vertebrae transformation parameters during the registration and to
ensure convergence. The mean target registration error achieved for individual vertebrae on five spine phantoms
generated from CT data of patients, is 2.47 mm with standard deviation of 1.14 mm.
This paper presents a real-time, freehand ultrasound (US) calibration system, with automatic accuracy control
and incorporation of US section thickness. Intended for operating-room usage, the system featured a fully
automated calibration method that requires minimal human interaction, and an automatic accuracy control
mechanism based on a set of ground-truth data. We have also developed a technique to quantitatively evaluate
and incorporate US section thickness to improve the calibration precision. The experimental results demonstrated
that the calibration system was able to consistently and robustly achieve high calibration accuracy with real-time
performance and efficiency. Further, our preliminary results to incorporate elevation beam profile have
demonstrated a promising reduction of uncertainties to estimate elevation-related parameters.
KEYWORDS: Detection and tracking algorithms, Numerical simulations, Computer simulations, Image registration, Error analysis, Monte Carlo methods, Data modeling, Algorithm development, Matrices, Medical imaging
Estimating the alignment accuracy is an important issue in rigid-body point-based registration algorithms. The
registration accuracy depends on the level of the noise perturbing the registering data sets. The noise in the
data sets arises from the fiducial (point) localization error (FLE) that may have an identical or inhomogeneous,
isotropic or anisotropic distribution at each point in each data set. Target registration error (TRE) has been
defined in the literature, as an error measure in terms of FLE, to compute the registration accuracy at a
point (target) which is not used in the registration process. In this paper, we mathematically derive a general
solution to approximate the distribution of TRE after registration of two data sets in the presence of FLE having
any type of distribution. The Maximum Likelihood (ML) algorithm is proposed to estimate the registration
parameters and their variances between two data sets. The variances are then used in a closed-form solution,
previously presented by these authors, to derive the distribution of TRE at a target location. Based on numerical
simulations, it is demonstrated that the derived distribution of TRE, in contrast to the existing methods in the
literature, accurately follows the distribution generated by Monte Carlo simulation even when FLE has an
inhomogeneous isotropic or anisotropic distribution.
Three-dimensional, freehand ultrasound is an imaging technique
that has seen increasing applications in computer assisted
surgery. A key element of this technique is image calibration, in
order to estimate a three-dimensional homogeneous transformation
that maps the position of individual pixels from the ultrasound
image coordinate to the ultrasound probe coordinate frames. The
transformation is typically calculated through imaging a
calibration phantom of known geometry, and solving for the
transformation parameters (either in closed-form or iteratively).
The calibration error achieved through this process is usually
assumed to be constant for all the pixels in the image. In this
paper, we propose a novel method to estimate the calibration
accuracy for individual pixels within an ultrasound image by
employing the Unscented Kalman Filter (UKF). Based on the
variances of calibration parameters extracted by UKF, a mean
square residual error is estimated for each individual pixel in
the ultrasound image. We demonstrate that the calibration error
could in fact significantly vary for different pixels in the
image. This observation could potentially impact the image
registration process in computer assisted surgery applications.
The method has been validated through simulations and experiments.
Three-dimensional freehand ultrasound has found several clinical applications, such as image-guided surgery and radiotherapy, since the last decade. A key step of all the freehand ultrasound imaging systems is calibration. Calibration is the procedure to estimate a two to three-dimensional transformation matrix which precisely maps two-dimensional ultrasound images to the physical coordinate. This paper presents a novel freehand ultrasound calibration algorithm which is based on a sequential least squares method, known as the Unscented Kalman Filter (UKF) algorithm. This method has significant advantages over the prior approaches, where the block least squares techniques have been employed to perform the ultrasound probe calibration. One of the advantages is that it computes the calibration parameters as well as their variances sequentially by processing the sample points, collected from ultrasound images of a designed phantom, one by one. Variance evaluation can be used to generate a confidence measure for the estimated calibration matrix. It also enables us to stop the calibration procedure once the desired confidence measure is met or informs us to collect more sample points to improve the calibration accuracy. The proposed calibration method is evaluated by using a custom designed N-wire phantom. The simulation results confirm that the proposed calibration algorithm converges to the same solution as the block least squares algorithms, while having the above mentioned practical advantages.
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