3-D Ultrafast Shear Wave Absolute Vibro-Elastography Using a Matrix Array Transducer.

Real-time ultrasound imaging plays an important role in ultrasound-guided interventions. The 3-D imaging provides more spatial information compared to conventional 2-D frames by considering the volumes of data. One of the main bottlenecks of 3-D imaging is the long data acquisition time, which reduces practicality and can introduce artifacts from unwanted patient or sonographer motion. This article introduces the first shear wave absolute vibro-elastography (S-WAVE) method with real-time volumetric acquisition using a matrix array transducer. In S-WAVE, an external vibration source generates mechanical vibrations inside the tissue. The tissue motion is then estimated and used in solving a wave equation inverse problem to provide the tissue elasticity. A matrix array transducer is used with a Verasonics ultrasound machine and a frame rate of 2000 volumes/s to acquire 100 radio frequency (RF) volumes in 0.05 s. Using plane wave (PW) and compounded diverging wave (CDW) imaging methods, we estimate axial, lateral, and elevational displacements over 3-D volumes. The curl of the displacements is used with local frequency estimation to estimate elasticity in the acquired volumes. Ultrafast acquisition extends substantially the possible S-WAVE excitation frequency range, now up to 800 Hz, enabling new tissue modeling and characterization. The method was validated on three homogeneous liver fibrosis phantoms and on four different inclusions within a heterogeneous phantom. The homogeneous phantom results show less than 8% (PW) and 5% (CDW) difference between the manufacturer values and the corresponding estimated values over a frequency range of 80-800 Hz. The estimated elasticity values for the heterogeneous phantom at 400-Hz excitation frequency show the average errors of 9% (PW) and 6% (CDW) compared to the provided average values by magnetic resonance elastography (MRE). Furthermore, both imaging methods were able to detect the inclusions within the elasticity volumes. An ex vivo study on a bovine liver sample shows less than 11% (PW) and 9% (CDW) difference between the estimated elasticity ranges by the proposed method and the elasticity ranges provided by MRE and acoustic radiation force impulse (ARFI).

Hand-eye coordination-based implicit re-calibration method for gaze tracking on ultrasound machines: a statistical approach.

PURPOSE: Eye gaze tracking is proving to be beneficial in many biomedical applications. The performance of systems based on eye gaze tracking is very much dependent on how accurate their calibration is. It has been reported that the gaze tracking accuracy deteriorates cumulatively and significantly with usage time. This impedes the wide use of gaze tracking in user interfaces. METHODS: Explicit re-calibration, typically requiring the user's active attention, is time-consuming and can interfere with the user's main activity. Therefore, we propose an implicit re-calibration method, which can rectify the deterioration of the gaze tracking accuracy without bringing about the user's deliberate attention. We make use of hand-eye coordination, with the reasonable assumption that the eye gaze follows the pointer during a selection task, to acquire additional calibration points during normal usage of a gaze-contingent system. We construct a statistical model for the calibration and the hand-eye coordination and apply the Gaussian process regression framework to perform the re-calibration. RESULTS: To validate our model and method, we performed a user study on ultrasonography tasks on a gaze-contingent interface for ultrasound machines. Results suggest that our method can rectify the tracking accuracy deterioration for [Formula: see text] of all cases where deterioration occurs in our user study. With another benchmark dataset, our method can redress tracking accuracy to a level comparable to the initial calibration in more than [Formula: see text] of the cases. CONCLUSIONS: Our implicit re-calibration method is a practical and convenient fix for tracking accuracy deterioration in gaze-contingent user interfaces, and in particular for gaze-contingent ultrasound machines.

Adaptive Augmentation of Medical Data Using Independently Conditional Variational Auto-Encoders.

Current deep supervised learning methods typically require large amounts of labeled data for training. Since there is a significant cost associated with clinical data acquisition and labeling, medical datasets used for training these models are relatively small in size. In this paper, we aim to alleviate this limitation by proposing a variational generative model along with an effective data augmentation approach that utilizes the generative model to synthesize data. In our approach, the model learns the probability distribution of image data conditioned on a latent variable and the corresponding labels. The trained model can then be used to synthesize new images for data augmentation. We demonstrate the effectiveness of the approach on two independent clinical datasets consisting of ultrasound images of the spine and magnetic resonance images of the brain. For the spine dataset, a baseline and a residual model achieve an accuracy of 85% and 92%, respectively, using our method compared to 78% and 83% using a conventional training approach for image classification task. For the brain dataset, a baseline and a U-net network achieve an accuracy of 84% and 88%, respectively, in Dice coefficient in tumor segmentation compared to 80% and 83% for the convention training approach.

Acoustic Shadow Detection: Study and Statistics of B-Mode and Radiofrequency Data.

An acoustic shadow is an ultrasound artifact occurring at boundaries between significantly different tissue impedances, resulting in signal loss and a dark appearance. Shadow detection is important as shadows can identify anatomical features or obscure regions of interest. A study was performed to scan human participants (N = 37) specifically to explore the statistical characteristics of various shadows from different anatomy and with different transducers. Differences in shadow statistics were observed and used for shadow detection algorithms with a fitted Nakagami distribution on radiofrequency (RF) speckle or cumulative entropy on brightness-mode (B-mode) data. The fitted Nakagami parameter and entropy values in shadows were consistent across different transducers and anatomy. Both algorithms utilized adaptive thresholding, needing only the transducer pulse length as an input parameter for easy utilization by different operators or equipment. Mean Dice coefficients (± standard deviation) of 0.90 ± 0.07 and 0.87 ± 0.08 were obtained for the RF and B-mode algorithms, which is within the range of manual annotators. The high accuracy in different imaging scenarios indicates that the shadows can be detected with high versatility and without expert configuration. The understanding of shadow statistics can be used for more specialized techniques to be developed for specific applications in the future, including pre-processing for machine learning and automatic interpretation.

A novel gaze-supported multimodal human-computer interaction for ultrasound machines.

PURPOSE: Conventional ultrasound (US) machines employ a physical control panel (PCP) as the primary user interface for machine control. This panel is adjacent to the main machine display that requires the operator's constant attention. The switch of attention to the control panel can lead to interruptions in the flow of the medical examination. Some ultraportable machines also lack many physical controls. Furthermore, the need to both control the US machine and observe the US image may lead the practitioners to adopt unergonomic postures and repetitive motions that can lead to work-related injuries. Therefore, there is a need for a more efficient human-computer interaction method on US machines. METHODS: To tackle some of the limitations with the PCP, we propose to merge the PCP into the main screen of the US machines. We propose to use gaze tracking and a handheld controller so that machine control can be achieved via a multimodal human-computer interaction (HCI) method that does not require one to touch the screen or look away from the US image. As a first step, a pop-up menu and measurement tool were designed on top of the US image based on gaze position for efficient machine control. RESULTS: A comparative study was performed on the BK Medical SonixTOUCH US machine. Participants were asked to complete the task of measuring the area of an ellipse-shaped tumor in a phantom using our gaze-supported HCI method as well as the traditional method. The user study indicates that the task completion time can be reduced by [Formula: see text] when using our gaze-supported HCI, while no extra workload is imposed on the operators. CONCLUSIONS: Our preliminary study suggests that, when combined with a simple handheld controller, eye gaze tracking can be integrated into the US machine HCI for more efficient machine control.

Automated Placenta Segmentation with a Convolutional Neural Network Weighted by Acoustic Shadow Detection.

Placental assessment through routine obstetrical ultrasound is often limited to documenting its location and ruling out placenta previa. However, many obstetrical complications originate from abnormal focal or global placental development. Technical difficulties in assessing the placenta as well as a lack of established objective criteria to classify echotexture are barriers to diagnosis of pathology by ultrasound imaging. As a first step towards the development of a computer aided placental assessment tool, we developed a fully automated method for placental segmentation using a convolutional neural network. The network contains a novel layer weighted by automated acoustic shadow detection to recognize artifacts specific to ultrasound. In order to develop a detection algorithm usable in different imaging scenarios, we acquired a dataset containing 1364 fetal ultrasound images from 247 patients acquired over 47 months was taken with different machines, operators, and at a range of gestational ages. Mean Dice coefficients for automated segmentation on the full dataset with and without the acoustic shadow detection layer were 0.92±0.04 and 0.91±0.03 when comparing to manual segmentation. Mean Dice coefficients on the subset of images containing acoustic shadows with and without acoustic shadow detection were 0.87±0.04 and 0.75±0.05. The method requires no user input to tune the detection. The automated placenta segmentation method can serve as a preprocessing step for further image analysis in artificial intelligence methods requiring large scale data processing of placental images.

Automatic Localization of the Needle Target for Ultrasound-Guided Epidural Injections.

Accurate identification of the needle target is crucial for effective epidural anesthesia. Currently, epidural needle placement is administered by a manual technique, relying on the sense of feel, which has a significant failure rate. Moreover, misleading the needle may lead to inadequate anesthesia, post dural puncture headaches, and other potential complications. Ultrasound offers guidance to the physician for identification of the needle target, but accurate interpretation and localization remain challenges. A hybrid machine learning system is proposed to automatically localize the needle target for epidural needle placement in ultrasound images of the spine. In particular, a deep network architecture along with a feature augmentation technique is proposed for automatic identification of the anatomical landmarks of the epidural space in ultrasound images. Experimental results of the target localization on planes of 3-D as well as 2-D images have been compared against an expert sonographer. When compared with the expert annotations, the average lateral and vertical errors on the planes of 3-D test data were 1 and 0.4 mm, respectively. On 2-D test data set, an average lateral error of 1.7 mm and vertical error of 0.8 mm were acquired.

Ultrasound-Guided Spine Anesthesia: Feasibility Study of a Guidance System.

Spinal needle injections are guided by fluoroscopy or palpation, resulting in radiation exposure and/or multiple needle re-insertions. Consequently, guiding these procedures with live ultrasound has become more popular, but images are still challenging to interpret. We introduce a guidance system based on augmentation of ultrasound images with a patient-specific 3-D surface model of the lumbar spine. We assessed the feasibility of the system in a study on 12 patients. The system could accurately provide augmentations of the epidural space and the facet joint for all subjects. Following conventional, fluoroscopy-guided needle placement, augmentation accuracy was determined according to the electromagnetically tracked final position of the needle. In 9 of 12 cases, the accuracy was considered sufficient for successfully delivering anesthesia. The unsuccessful cases can be attributed to errors in the electromagnetic tracking reference, which can be avoided by a setup reducing the influence of the metal C-arm.

Needle detection in curvilinear ultrasound images based on the reflection pattern of circular ultrasound waves.

PURPOSE: Ultrasound imaging provides a low-cost, real-time modality to guide needle insertion procedures, but localizing the needle using conventional ultrasound images is often challenging. Estimating the needle trajectory can increase the success rate of ultrasound-guided needle interventions and improve patient comfort. In this study, a novel method is introduced to localize the needle trajectory in curvilinear ultrasound images based on the needle reflection pattern of circular ultrasound waves. METHODS: A circular ultrasound wave was synthesized by sequentially firing the elements of a curvilinear transducer and recording the radio-frequency signals received by each element. Two features, namely, the large amplitude and repetitive reflection pattern, were used to identify the needle echoes in the received signals. The trajectory of the needle was estimated by fitting the arrival times of needle echoes to an equation that describes needle reflection of circular waves. The method was employed to estimate the trajectories of needles inserted in agar phantom, beef muscle, and porcine tissue specimens. RESULTS: The maximum error rates of estimating the needle trajectories were on the order of 1 mm and 3° for the radial and azimuth coordinates, respectively. CONCLUSIONS: These results suggest that the proposed method can improve the robustness and accuracy of needle segmentation methods by adding signature-based detection of the needle trajectory in curvilinear ultrasound images. The method can be implemented on conventional ultrasound imaging systems.

A multi-vertebrae CT to US registration of the lumbar spine in clinical data.

PURPOSE: Spinal needle injections are widely applied to alleviate back pain and for anesthesia. Current treatment is performed either blindly with palpation or using fluoroscopy or computed tomography (CT). Both fluoroscopy and CT guidance expose patients to ionizing radiation. Ultrasound (US) guidance for spinal needle procedures is becoming more prevalent as an alternative. It is challenging to use US as the sole imaging modality for intraoperative guidance of spine needle injections due to the acoustic shadows created by the bony structures of the vertebra that limit visibility of the target areas for injection. We propose registration of CT and the US images to augment anatomical visualization for the clinician during spinal interventions guided by US. METHODS: The proposed method involves automatic global and multi-vertebrae registration to find the closest alignment between CT and US data. This is performed by maximizing the similarity between the two modalities using voxel intensity information as well as features extracted from the input volumes. In our method, the lumbar spine is first globally aligned between the CT and US data using intensity-based registration followed by point-based registration. To account for possible curvature change of the spine between the CT and US volumes, a multi-vertebrae registration step is also performed. Springs are used to constrain the movement of the individually transformed vertebrae to ensure the optimal alignment is a pose of the lumbar spine that is physically possible. RESULTS: Evaluation of the algorithm is performed on 10 clinical patient datasets. The registration approach was able to align CT and US datasets from initial misalignments of up to 25 mm, with a mean TRE of 1.37 mm. These results suggest that the proposed approach has the potential to offer a sufficiently accurate registration between clinical CT and US data.

Real-time ultrasound image classification for spine anesthesia using local directional Hadamard features.

PURPOSE: Injection therapy is a commonly used solution for back pain management. This procedure typically involves percutaneous insertion of a needle between or around the vertebrae, to deliver anesthetics near nerve bundles. Most frequently, spinal injections are performed either blindly using palpation or under the guidance of fluoroscopy or computed tomography. Recently, due to the drawbacks of the ionizing radiation of such imaging modalities, there has been a growing interest in using ultrasound imaging as an alternative. However, the complex spinal anatomy with different wave-like structures, affected by speckle noise, makes the accurate identification of the appropriate injection plane difficult. The aim of this study was to propose an automated system that can identify the optimal plane for epidural steroid injections and facet joint injections. METHODS: A multi-scale and multi-directional feature extraction system to provide automated identification of the appropriate plane is proposed. Local Hadamard coefficients are obtained using the sequency-ordered Hadamard transform at multiple scales. Directional features are extracted from local coefficients which correspond to different regions in the ultrasound images. An artificial neural network is trained based on the local directional Hadamard features for classification. RESULTS: The proposed method yields distinctive features for classification which successfully classified 1032 images out of 1090 for epidural steroid injection and 990 images out of 1052 for facet joint injection. In order to validate the proposed method, a leave-one-out cross-validation was performed. The average classification accuracy for leave-one-out validation was 94 % for epidural and 90 % for facet joint targets. Also, the feature extraction time for the proposed method was 20 ms for a native 2D ultrasound image. CONCLUSION: A real-time machine learning system based on the local directional Hadamard features extracted by the sequency-ordered Hadamard transform for detecting the laminae and facet joints in ultrasound images has been proposed. The system has the potential to assist the anesthesiologists in quickly finding the target plane for epidural steroid injections and facet joint injections.

Ultrasound-guided spinal injections: a feasibility study of a guidance system.

PURPOSE: Facet joint injections of analgesic agents are widely used to treat patients with lower back pain. The current standard-of-care for guiding the injection is fluoroscopy, which exposes the patient and physician to significant radiation. As an alternative, several ultrasound guidance systems have been proposed, but have not become the standard-of-care, mainly because of the difficulty in image interpretation by the anesthesiologist unfamiliar with the complex spinal sonography. METHODS: We introduce an ultrasound-based navigation system that allows for live 2D ultrasound images augmented with a patient-specific statistical model of the spine and relating this information to the position of the tracked injection needle. The model registration accuracy is assessed on ultrasound data obtained from nine subjects who had prior CT images as the gold standard for the statistical model. The clinical validity of our method is evaluated on four subjects (of an ongoing in vivo study) which underwent facet joint injections. RESULTS: The statistical model could be registered to the bone structures in the ultrasound volume with an average RMS accuracy of 2.3±0.4 mm. The shape of the individual vertebrae could be estimated from the US volume with an average RMS surface distance error of 1.5±0.4 mm. The facet joints could be identified by the statistical model with an average accuracy of 5.1 ± 1.5 mm. CONCLUSIONS: The results of this initial feasibility assessment suggest that this ultrasound-based system is capable of providing information sufficient to guide facet joint injections. Further clinical studies are warranted.

Towards real-time, tracker-less 3D ultrasound guidance for spine anaesthesia.

PURPOSE: Epidural needle insertions and facet joint injections play an important role in spine anaesthesia. The main challenge of safe needle insertion is the deep location of the target, resulting in a narrow and small insertion channel close to sensitive anatomy. Recent approaches utilizing ultrasound (US) as a low-cost and widely available guiding modality are promising but have yet to become routinely used in clinical practice due to the difficulty in interpreting US images, their limited view of the internal anatomy of the spine, and/or inclusion of cost-intensive tracking hardware which impacts the clinical workflow. METHODS: We propose a novel guidance system for spine anaesthesia. An efficient implementation allows us to continuously align and overlay a statistical model of the lumbar spine on the live 3D US stream without making use of additional tracking hardware. The system is evaluated in vivo on 12 volunteers. RESULTS: The in vivo study showed that the anatomical features of the epidural space and the facet joints could be continuously located, at a volume rate of 0.5 Hz, within an accuracy of 3 and 7 mm, respectively. CONCLUSIONS: A novel guidance system for spine anaesthesia has been presented which augments a live 3D US stream with detailed anatomical information of the spine. Results from an in vivo study indicate that the proposed system has potential for assisting the physician in quickly finding the target structure and planning a safe insertion trajectory in the spine.

Ultrasound RF time series for classification of breast lesions.

This work reports the use of ultrasound radio frequency (RF) time series analysis as a method for ultrasound-based classification of malignant breast lesions. The RF time series method is versatile and requires only a few seconds of raw ultrasound data with no need for additional instrumentation. Using the RF time series features, and a machine learning framework, we have generated malignancy maps, from the estimated cancer likelihood, for decision support in biopsy recommendation. These maps depict the likelihood of malignancy for regions of size 1 mm(2) within the suspicious lesions. We report an area under receiver operating characteristics curve of 0.86 (95% confidence interval [CI]: 0.84%-0.90%) using support vector machines and 0.81 (95% CI: 0.78-0.85) using Random Forests classification algorithms, on 22 subjects with leave-one-subject-out cross-validation. Changing the classification method yielded consistent results which indicates the robustness of this tissue typing method. The findings of this report suggest that ultrasound RF time series, along with the developed machine learning framework, can help in differentiating malignant from benign breast lesions, subsequently reducing the number of unnecessary biopsies after mammography screening.

Local phase tensor features for 3-D ultrasound to statistical shape+pose spine model registration.

Most conventional spine interventions are performed under X-ray fluoroscopy guidance. In recent years, there has been a growing interest to develop nonionizing imaging alternatives to guide these procedures. Ultrasound guidance has emerged as a leading alternative. However, a challenging problem is automatic identification of the spinal anatomy in ultrasound data. In this paper, we propose a local phase-based bone feature enhancement technique that can robustly identify the spine surface in ultrasound images. The local phase information is obtained using a gradient energy tensor filter. This information is used to construct local phase tensors in ultrasound images, which highlight the spine surface. We show that our proposed approach results in a more distinct enhancement of the bone surfaces compared to recently proposed techniques based on monogenic scale-space filters and logarithmic Gabor filters. We also demonstrate that registration accuracy of a statistical shape+pose model of the spine to 3-D ultrasound images can be significantly improved, using the proposed method, compared to those obtained using monogenic scale-space filters and logarithmic Gabor filters.

Statistical shape model to 3D ultrasound registration for spine interventions using enhanced local phase features.

Accurate registration of ultrasound images to statistical shape models is a challenging problem in percutaneous spine injection procedures due to the typical imaging artifacts inherent to ultrasound. In this paper we propose a robust and accurate registration method that matches local phase bone features extracted from ultrasound images to a statistical shape model. The local phase information for enhancing the bone surfaces is obtained using a gradient energy tensor filter, which combines advantages of the monogenic scale-space and Gaussian scale-space filters, resulting in an improved simultaneous estimation of phase and orientation information. A novel statistical shape model was built by separating the pose statistics from the shape statistics. This model is then registered to the local phase bone surfaces using an iterative expectation maximization registration technique. Validation on 96 in vivo clinical scans obtained from eight patients resulted in a root mean square registration error of 2 mm (SD: 0.4 mm), which is below the clinically acceptable threshold of 3.5 mm. The improvement achieved in registration accuracy using the new features was also significant (p < 0.05) compared to state of the art local phase image processing methods.

Registration of 3D ultrasound through an air-tissue boundary.

In this study we evaluated a new method for registering three-dimensional ultrasound (3DUS) data to external coordinate systems. First, 3DUS was registered to the stereo endoscope of a da Vinci Surgical System by placing a registration tool against an air-tissue boundary so that the 3DUS could image ultrasound fiducials while the stereo endoscope could image camera markers on the same tool. The common points were used to solve the registration between the 3DUS and camera coordinate systems. The target registration error (TRE) when imaging through a PVC tissue phantom ranged from 3.85 1.76 mm to 1.82 1.03 mm using one to four registration tool positions. TRE when imaging through an ex-vivo liver tissue sample ranged from 2.36 1.01 mm to 1.51 0.70 mm using one to four registration tool positions. Second, using a similar method, 3DUS was registered to the kinematic coordinate system of a da Vinci Surgical System by using the da Vinci surgical manipulators to identify common points on an air-tissue boundary. TRE when imaging through a PVC tissue phantom was 0.95 0.38 mm. This registration method is simpler and potentially more accurate than methods using commercial motion tracking systems. This method may be useful in the future in augmented reality systems for laparoscopic and robotic-assisted surgery.

Tissue tracking and registration for image-guided surgery.

Vision-based tracking of tissue is a key component to enable augmented reality during a surgical operation. Conven- tional tracking techniques in computer vision rely on identifying strong edge features or distinctive textures in a well-lit environ- ment; however endoscopic tissue images do not have strong edge features, are poorly lit and exhibit a high degree of specular reflection. Therefore, prior work in achieving densely populated 3D features for describing tissue surface profiles require complex image processing techniques and have been limited in providing stable, long-term tracking or real-time processing. In this paper, we present an integrated framework for ac- curately tracking tissue in surgical stereo-cameras at real-time speeds. We use a combination of the STAR feature detector and Binary Robust Independent Elementary Features to acquire salient features that can be persistently tracked at high frame rates. The features are then used to acquire a densely-populated map of the deformations of tissue surface in 3D. We evaluate the method against popular feature algorithms in in-vivo animal study video sequences, and we also apply the proposed method to human partial nephrectomy video sequences. We extend the salient feature framework to support region tracking in order to maintain the spatial correspondence of a tracked region of tissue or a medical image registration to the surrounding tissue. In-vitro tissue studies show registration accuracies of 1.3-3.3 mm using a rigid-body transformation method.

Automatic bone localization and fracture detection from volumetric ultrasound images using 3-D local phase features.

This article presents a novel method for bone segmentation from three-dimensional (3-D) ultrasound images that derives intensity-invariant 3-D local image phase measures that are then employed for extracting ridge-like features similar to those that occur at soft tissue/bone interfaces. The main contributions in this article include: (1) the extension of our previously proposed phase-symmetry-based bone surface extraction from two-dimensional (2-D) to 3-D images using 3-D Log-Gabor filters; (2) the design of a new framework for accuracy evaluation based on using computed tomography as a gold standard that allows the assessment of surface localization accuracy across the entire 3-D surface; (3) the quantitative validation of accuracy of our 3-D phase-processing approach on both intact and fractured bone surfaces using phantoms and ex vivo 3-D ultrasound scans; and (4) the qualitative validation obtained by scanning emergency room patients with distal radius and pelvis fractures. We show a 41% improvement in surface localization error over the previous 2-D phase symmetry method. The results demonstrate clearly visible segmentations of bone surfaces with a localization accuracy of <0.6 mm and mean errors in estimating fracture displacements below 0.6 mm. The results show that the proposed method is successful even for situations when the bone surface response is weak due to shadowing from muscle and fascia interfaces above the bone, which is a situation where the 2-D method fails.

Automatic adaptive parameterization in local phase feature-based bone segmentation in ultrasound.

Intensity-invariant local phase features based on Log-Gabor filters have been recently shown to produce highly accurate localizations of bone surfaces from three-dimensional (3-D) ultrasound. A key challenge, however, remains in the proper selection of filter parameters, whose values have so far been chosen empirically and kept fixed for a given image. Since Log-Gabor filter responses widely change when varying the filter parameters, actual parameter selection can significantly affect the quality of extracted features. This article presents a novel method for contextual parameter selection that autonomously adapts to image content. Our technique automatically selects the scale, bandwidth and orientation parameters of Log-Gabor filters for optimizing local phase symmetry. The proposed approach incorporates principle curvature computed from the Hessian matrix and directional filter banks in a phase scale-space framework. Evaluations performed on carefully designed in vitro experiments demonstrate 35% improvement in accuracy of bone surface localization compared with empirically-set parameterization results. Results from a pilot in vivo study on human subjects, scanned in the operating room, show similar improvements.