Fully developed speckle has been used previously to estimate the out-of-plane motion of ultrasound images. However, in
real tissue the rarity of such patterns and the presence of coherency diminish both the precision and the accuracy of the
out-of-plane motion estimation. In this paper, for the first time, we propose a simple mathematical derivation for out-of-plane
motion estimation in which the coherent and non-coherent parts of the RF echo signal are separated. This method
is based on the Rician-Inverse Gaussian stochastic model of the speckle formation process, which can be considered as a
generalized form of the K-distribution with richer parameterization. The flexibility of the proposed method allows
considering any patch of the RF echo signal for the purpose of displacement estimation. The experimental results on
real tissue demonstrate the potential of the proposed method for accurate out-of-plane estimation. The underestimation
of motion in ex vivo bovine tissue at 1 mm displacement is reduced to 15.5% compared to 37% for a base-line method.
In freehand 3D ultrasound, images are acquired while the position of the transducer is recorded with a tracking device.
Calibration is essential in this technique to find the transformation from the image coordinates to the reference
coordinate system. The single wall technique is a common calibration method because a simple plane phantom is used.
Despite its advantages, such as ease of phantom construction and image analysis, this method requires large number of
images to converge to the solution. One reason is a lack of a closed-form solution. Also, the technique uses slightly illconditioned
sets of equations with a high condition number due to limited range of scanning motions that produce clear
images of the plane. Here, a novel closed-form formulation has been proposed for the single wall calibration technique.
Also, differential measurements of the plane image are used instead of absolute plane detection to improve accuracy. The
closed-form solution leads to more accurate and robust results while providing an insight into understanding error
propagation and finding the optimal set of transducer poses. Results have been compared to the conventional single wall
technique. A residual error of 0.14 mm is achieved for the proposed method compared to 0.91 mm in the conventional
approach.
In ultrasound-guided needle insertion procedures, tracking of the needle relative to the ultrasound image is beneficial for
needle trajectory planning and guidance. A single camera closed-form method is proposed for automatic real-time
trajectory tracking with a low-cost camera mounted directly on the ultrasound transducer. The camera is calibrated to the
ultrasound image coordinates. By mounting the camera on the transducer, issues of visual obstruction are reduced and
accuracy of tracking is increased compared to camera-tracking systems with a fixed case. Compared to previous work
with stereo cameras, a single camera further reduces cost, complexity and size, but requires a needle with known
markings. The proposed solution uses the depth markings etched on many common needles (e.g. epidural needle). A
fully automatic image processing method has been developed for real-time identification of the needle trajectory using a
novel closed-form solution based on three identified markings and the camera's intrinsic calibration parameters. The
trajectory of the needle relative to the ultrasound image is calculated and displayed. Validation compares the calculated
intersection of the needle trajectory to the ultrasound image with the depiction of the actual needle intersection in the
image. The overall error is 3.0 ± 2.6 mm for a low-cost 640×480 pixel USB camera.
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