Original contributionComparison of Freehand 3-D Ultrasound Calibration Techniques Using a Stylus
Introduction
Freehand 3-D ultrasound (US) (Fenster et al. 2001) is a 3-D medical imaging system with many clinical applications in anatomical visualization, volume measurements, surgery planning and radiotherapy planning (Gee et al. 2003). As a conventional 2-D US probe is swept over the anatomy of interest, the trajectory of the probe is recorded by the attached position sensor. The volume of the anatomy can be constructed by matching the US data with its corresponding position in space. However, the position sensor measures the 3-D location of the sensor, S, rather than the scan plane, P, relative to an external world coordinate system, W, as shown in Fig. 1. It is therefore necessary to find the position and orientation of the scan plane with respect to the electrical center of the position sensor. This rigid-body transformation, TS←P, is determined through a process frequently referred to as “probe calibration.” In general, a transformation involves both a rotation and a translation in 3-D space. For brevity, we will use the notation TB←A to mean a rotational transformation followed by a translation from the coordinate system A to coordinate system B.
Three-dimensional US calibration has been an active research topic for several years (Mercier et al. 2005). The usual approach is to scan an object with known dimensions (a phantom). These scans place constraints on the eight calibration parameters: 2 image scales, 3 translations in the direction of the x, y and z axes and the three rotations—azimuth, elevation and roll—about these axes.
The simplest phantom is probably a point target (Detmer et al 1994, State et al 1994, Amin et al 2001, Gooding et al 2005, Barratt et al 2006). The point is scanned from different positions and orientations and its location marked in the B-scans. The segmented points can be mapped to the sensor's coordinate system by using an assumed calibration and then to the world coordinate system from the position sensor readings. If the assumed calibration is correct, the points from the different B-scans should have the same coordinates in 3-D space. This places constraints on the calibration parameters. The calibration is solved by an iterative optimization technique.
Calibrating with the point phantom has three major disadvantages. First, it is very difficult to align the point phantom precisely with the scan plane. The finite thickness of the US beam makes the target visible in the B-scans, even if the target is not exactly at the elevational center of the scan plane. This error can be several millimeters depending on the US probe and the skill of the user. Second, automatic segmentation of isolated points in US images is seldom reliable. As a result, the point phantom is often manually or semi-automatically segmented in the US images. This makes the calibration process long and tiresome. Finally, the phantom needs to be scanned from a sufficiently diverse range of positions, so that the resulting system of constraints is not underdetermined with multiple solutions (Prager et al. 1998).
Over the last decade, much research has been undertaken to make probe calibration more reliable and, at the same time, easier and quicker to perform. These phantoms include a plane (Prager et al 1998, Rousseau et al 2005), a 2-D alignment phantom (Sato et al 1998, Gee et al 2005), Z-fiducial phantom (Comean et al 1998, Pagoulatos et al 2001, Bouchet et al 2001, Lindseth et al 2003, Chen et al 2006, Hsu et al 2008) and other wire phantoms (Boctor et al 2003, Dandekar et al 2005). As in the case with a point phantom, when these phantoms are scanned, constraints are placed on the calibration parameters, which are then solved either iteratively or algebraically depending on the phantom used. Mercier et al. (2005) and Rousseau et al. (2006) compared some of these techniques.
A 3-D localizer, often called a pointer or a stylus, can be used to aid probe calibration. It is essentially a point target connected to another position sensor at the end of the stylus, whose tip can be spherical or sharpened to a point. The rigid-body transform between the tip of the stylus and the position sensor is usually supplied by the manufacturer (Muratore and Galloway 2001). In the case where the transformation is not available, it can be determined by a simple pointer calibration (Leotta et al. 1997). During a pointer calibration, the stylus is rotated about its tip while the position sensor's readings are recorded. Because the tip of the stylus must be mapped to the same location in 3-D space, this places constraints on the possible locations of the stylus' tip, whose location can be determined by an iterative optimization algorithm. In any case, the location of the stylus' tip is known in 3-D space. The location of the point phantom can therefore be determined by pointing the stylus at the phantom. If the scales of the B-scan are known (Hsu et al. 2006), the calibration parameters can be solved in a closed-form by least-squares minimization (Arun et al. 1987).
Because a stylus can be used to locate points in 3-D space, Muratore and Galloway (2001) calibrated their probe by locating points directly in the scan plane. Assuming at least three noncollinear points have been located, calibration can be solved by least-squares optimization as described previously. This technique, nevertheless, requires two targets to be tracked simultaneously. Furthermore, it is difficult to align the tip of the stylus with the scan plane.
Khamene and Sauer (2005) improved on this technique by imaging a rod transversely. Both ends of the rod are pointer calibrated to define the location and orientation of the rod in space. Each image of the rod sets up a constraint on the calibration parameters. Probe calibration can then be found using optimization techniques.
In this paper, we study the relative merits of a particular class of calibration algorithms that locate points in the B-scan with a stylus. We begin in the next section by outlining different calibration techniques, including our novel cone phantom and cone stylus. We then performed a series of experiments to evaluate the precision and accuracy of each technique. The various calibration algorithms are compared and discussed in the final section.
Section snippets
The calibration phantoms
Figure 2 shows the four calibration styli and the cone phantom. Figure 2, a and b are standard Polaris (Northern Digital Inc., Waterloo, ON, Canada) styli with a sharp and a spherical tip. Figure 2c shows a rod stylus similar to the one used by Khamene and Sauer (2005). Figure 2, d and e show the cone phantom and the cone stylus that we have designed. The cone phantom is an improvement on one of our previous phantoms (Hsu et al. 2007). Although this phantom is not a stylus physically, it works
Results
To measure the calibration quality of the different styli and the phantom, we calibrated a Diasus (Dynamic Imaging Ltd., Birmingham, UK) 5–10 MHz linear array probe. The analog radiofrequency (RF) US data, after receive focusing and time–gain compensation, but before log compression and envelope detection, was digitized using a Gage CompuScope (GaGe Applied Technologies Inc., Lockport, IL, USA) 14200 PCI 14-bit analog to digital converter, and transferred at 25 frames per second to a Pentium® 4
Discussion
Figure 7 shows the precision of the probe calibrations with a fixed pointer calibration. These precisions can be achieved if the pointer calibration is supplied by the manufacturer of the stylus. Probe calibration precision that includes variations as a result of pointer calibration imprecision is also shown in the same figure. The slight increase in error of the sharp and cone stylus is caused by pointer calibration imprecision. The precision of the spherical stylus improved slightly. This
Conclusion
We have compared different techniques to calibrate freehand 3-D US probes using a stylus. The rod stylus is simple and quick to use, but produces poor precision and accuracy. This stylus may be useful to obtain a quick estimate of the calibration, although this may be needed in the first place for the optimization when using such a stylus. The cone stylus is clearly an improvement on both the sharp and the spherical stylus, with a small modification to the design. Better accuracies are
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