British Journal of Radiology (2004) 77, S186-S193
© 2004 British Institute of Radiology
doi: 10.1259/bjr/80676194
Processing and visualizing three-dimensional ultrasound data
A Gee, MA, PhD
1
R Prager, PhD, CEng
1
G Treece, MA, PhD
1
C Cash, MRCP, FRCR
2 and
L Berman, MRCP, FRCR
2
1 Department of Engineering, University of Cambridge, Trumpington Street, Cambridge CB2 1PZ and 2 Department of Radiology, University of Cambridge, Addenbrooke's Hospital, Cambridge CB2 2QQ, UK
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Abstract
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This paper describes techniques for the visualization and processing of three-dimensional (3D) ultrasound data. The nature of such data demands specialized algorithms, which differ from those employed for other medical imaging modalities. In this paper, the emphasis is placed on generic processing techniques, which are relevant across a wide range of 3D ultrasound application domains.
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Introduction
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Three-dimensional (3D) ultrasound [1–3] is being applied in an ever-growing number of clinical scenarios, often replacing more costly CT and MRI studies. There are essentially two ways to acquire 3D ultrasound data: using a dedicated 3D probe, which is placed on the skin and automatically scans a small, fixed volume beneath; or using a freehand system [2], in which the position and orientation of a conventional 2D probe are recorded as the probe is swept manually over the region of interest, and a 3D volume is constructed from the resulting B-scans and their relative positions—see Figure 1
. While most commercial systems employ volume probes for good reasons of ergonomics and practicality, the freehand protocol allows the acquisition of arbitrarily sized volumes and consequently has more potential applications.
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Figure 1. 3D ultrasound acquisition protocols. Dedicated freehand probes contain motors that sweep a 2D B-scan over the area of interest: rotational and fan shaped geometries are common. Freehand systems rely on the clinician to guide a conventional 2D probe over the area of interest. The relative positions of the B-scans can be tracked using an add-on spatial locator or, alternatively and less accurately, estimated from the B-scan images themselves.
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3D ultrasound differs from other medical imaging modalities in three important ways: the often irregular sampling of space by the acquisition protocol, the way the anatomy's appearance depends on the direction of insonification, and the low signal to noise ratio of the images themselves. These differences affect the way the data is subsequently analysed. For example, visualization algorithms need to cope with the irregular spatial distribution of the B-scans; segmentation algorithms must be effective in the presence of speckle; shape fitting algorithms may need to interpolate through non-parallel contours; and registration algorithms must differentiate between real image discrepancies and those related to the direction of insonification.
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Visualization
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3D ultrasound can be visualized using techniques common to other medical imaging modalities, including any-plane reslicing, multiplanar reformatting, non-planar reslicing, volume rendering and surface rendering (following segmentation). More specific to 3D ultrasound is the way these displays are created from the raw data, which does not generally lie on a regular grid. To take advantage of the mature visualization packages already available for CT and MRI, many 3D ultrasound systems start by resampling the raw data onto a regular grid, then employ off-the-shelf techniques to visualize this grid. However, resampling inevitably involves interpolation and approximation, which can lead to artefacts in the resulting visualizations.
Consider the illustration in Figure 2, which shows two B-scans intersecting a regular voxel array. When resampling this data onto the regular grid, how do we decide on the intensity of the shaded voxel? The simplest approach is to use nearest neighbour interpolation, where we search for the nearest B-scan pixel (which in this case lies on B-scan n) and set the voxel intensity accordingly. Nearest neighbour interpolation, however, is a crude technique, often producing discontinuous voxel reconstructions with prominent artefacts. Other interpolation techniques, such as trilinear, B-spline and radial basis function interpolation, consider not just the nearest pixel but also other nearby pixels, thereby arriving at smoother reconstructions at the expense of computational speed. That said, 3D ultrasound is perhaps the only medical imaging modality for which a nearest neighbour interpolation is acceptable, since resolved structures in ultrasound images are fairly large compared with the intra-B-scan and inter-B-scan pixel spacing. Consequently, interpolation artefacts are relatively small in scale compared with the much larger structures of interest. Extensive quantitative and qualitative studies have shown that the improvement offered by radial basis function interpolation over nearest neighbour interpolation is marginal [4].
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Figure 2. Sampling and interpolation. The diagram shows the intersection of two B-scans and a reslice plane with a voxel array. The circles represent individual pixels on the various planes. Consider the shaded voxel. If nearest neighbour interpolation were used to construct the voxel array, the intensity of this voxel would be set according to the nearby pixel on B-scan n. Again assuming nearest neighbour interpolation, the same intensity would be attached to the reslice pixel which lies entirely inside this voxel. With direct visualization, however, the intensity of the reslice pixel would be inherited from the nearby pixel on B-scan n+1. Thus, the intermediate voxel representation causes visualization artefacts, which are avoided by direct rendering.
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If we discount the convenience of off-the-shelf voxel visualization packages, we can question the wisdom of reconstructing a regular voxel array at all. Consider again the illustration in Figure 2
. If we wish to generate a reslice of the voxel array, we would once again use some sort of interpolation to set the intensities of the pixels which constitute the reslice image. We thus have two stages of interpolation: from the B-scans to the voxel array, and then from the voxel array to the reslice. Each stage introduces errors, and it is reasonable to suppose that more faithful visualization is achievable by interpolating directly from the B-scans to the reslice. This is indeed the case, as Figure 2 shows: two stages of nearest neighbour interpolation result in some reslice pixels being assigned the wrong intensities.
Direct interpolation has other advantages: visualization can proceed immediately after (or even during) acquisition, with no delay while the voxel array is reconstructed, and there is no need for extra memory in which to store the voxel array. The one disadvantage is speed: the regularity of the voxel array makes it easy to generate reslices and volume renderings extremely quickly. In comparison, generating the same renderings directly from the B-scans is slower. While this used to be a strong argument in favour of voxel arrays, the rapid increase in processor speeds has now tipped the balance the other way: with perhaps the one exception of volume rendering, it is now possible to visualize the raw data at perfectly acceptable interactive rates, without the need for an intermediate voxel representation.
Figure 3 illustrates a nearest neighbour algorithm for generating a reslice image directly from a set of B-scans and their relative positions. Suppose we wish to interpolate up to a maximum distance d, so that if any point in the reslice plane is further than d from a B-scan pixel, we leave it blank instead of shading it with misleading data. Now consider a box of width 2d centred on B-scan n. The intersection of this box with the reslice plane is an irregular polygon, as shown in Figure 3. We calculate the B-scan coordinates (x; y; z) of every reslice pixel contained in the polygon. Note that this can be performed very quickly using incremental calculations, if we first calculate the B-scan increments (
x; y; z) corresponding to horizontal and vertical steps of one pixel in the reslice plane. Then we set the intensity of each reslice pixel according to the closest pixel on B-scan n, where the closest pixel is given by the (x; y) part of the B-scan coordinates. The magnitude of the z coordinate tells us how close this pixel is. We use it to fill a z-buffer of the same size as the reslice image, so that for each pixel shaded in the reslice image, we also write |z| to the corresponding pixel in the z-buffer. Then we repeat this process for all B-scans in the data set. Should any subsequent B-scan attempt to shade a reslice pixel which has already been set by a previous B-scan, we compare the new z value with the value already in the z-buffer, and only overwrite the reslice (and z-buffer) pixel should the new B-scan be closer (smaller |z|) than the previous one. This way, the reslice image will be influenced by B-scan pixels which lie as close to the reslice plane as possible, up to a maximum distance of d: in other words, a nearest neighbour interpolation.
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Figure 3. Direct reslice rendering. For nearest neighbour interpolation up to a maximum distance d, we consider a box of width 2d centred on each B-scan, and calculate the intersection of this box with the reslice plane. Each reslice pixel within the intersection polygon is shaded according to the intensity of the corresponding B-scan pixel. The process is repeated for all the B-scans in the data set, with a z-buffer ensuring that only those B-scans pixels closest to the reslice plane contribute to the final rendering.
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By pre-calculating the intersection polygon between each B-scan and the reslice plane, and only rasterizing the handful of pixels contained within this polygon, the reslice algorithm is optimized for speed, achieving around 20 slices per second with average size (40 MB) data sets on 2 GHz processors. Other direct algorithms have been developed for non-planar reslicing, volume rendering and a variety of segmentation and registration tasks. Some visualization examples can be found in Figure 4.
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Figure 4. Direct 3D ultrasound visualization examples. This 3D ultrasound data set comprises 652 B-scans like the one at the bottom left of the figure. The planar and non-planar reslices are interpolated directly from these B-scans, using nearest neighbour interpolation. In this example, each "reslice" is in fact a narrow volume rendering of width 3 mm: this makes the resulting image far less dependent on the precise positioning of the plane or surface, and usefully highlights bony structures in this obstetric example. The B-scan display shows the intersection with the reslice volume, while the planar reslice display shows the intersection with both the B-scan plane and the non-planar reslice volume. All three displays are shown together in the multiplanar/non-planar reformat, in their correct relative positions. This display can be rotated interactively to give a better impression of the 3D geometry.
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One point of concern when visualizing 3D ultrasound images is the long acquisition time implicit in the freehand scanning protocol. For meaningful visualization and analysis, the anatomy must remain stationary throughout the acquisition. This is clearly impractical when there is motion caused by the cardiac pulse, in which case we need to arrange instead for some form of gating, visualizing only those B-scans which belong to the same phase of the cardiac cycle. Fortunately, the pulse waveform can often be estimated using simple image analysis, without the need for an electrocardiogram signal. With Doppler ultrasound, it is often as simple as counting the number of coloured pixels in each B-scan, as illustrated in Figure 5. With grey-scale ultrasound, a crude estimate of the pulse can usually by derived by defining a region of interest (for example, around a pulsating artery) and counting the number of pixels lying in a particular grey scale range within the region of interest. This estimate can then be cleaned up by bandpass filtering [5].
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Figure 5. Cardiac gating for Doppler 3D ultrasound visualization. For this examination of the popliteal artery, the cardiac pulse was estimated by simply counting the number of coloured pixels in each B-scan. After tagging each B-scan with its cardiac phase, meaningful visualizations can be achieved, at whatever phase, by selecting only those B-scans with matching phase. Movies can be constructed from sequences of renderings, like the ones above, at progressive phases.
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Segmentation, volume measurement and shape analysis
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One of the most attractive applications of 3D ultrasound is the accurate measurement of volume and assessment of shape. However, both of these require the prior segmentation of the data, to separate the structure of interest from the background. Unfortunately, even manual segmentation of ultrasound images is difficult, given the low signal to noise ratio and the ubiquitous imaging artefacts, some of which are illustrated in Figure 6. Note that the artefacts are even harder to spot in 3D reslices, since the direction of insonification is no longer obvious as an aid to image interpretation.
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Figure 6. Artefacts in (a) 2D and (b) 3D ultrasound. The context afforded by a B-scan, in particular the known direction of insonification, allows many artefacts to be spotted by the expert eye. The disorientation of a 3D reslice makes it far harder to distinguish artefacts from true anatomical features.
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A much-cited obstacle to the automatic segmentation of ultrasound images is speckle, which is often erroneously referred to as "noise": in fact, it contains valuable information regarding the scatterer density in the imaged tissue. Admittedly, speckle could be considered "noise" by an automatic segmentation algorithm, though it is readily suppressed by median filtering [6]. A more debilitating artefact is the disappearance of tissue boundaries when they lie parallel to the direction of insonification, since it is precisely these boundaries which the segmentation algorithm is trying to detect, and no amount of filtering is going to reliably bring them back.
For these reasons, generic 3D ultrasound segmentation techniques always rely on the skill of an expert operator, who either delineates the segmentation contours entirely manually, or guides a semiautomatic algorithm (e.g. live-wire [7]) in an attempt to speed up the process. Subsequent processing of the contours, for volume measurement or shape analysis, can take the load off the operator by accepting as sparse a set of contours as possible. For example, Figure 7 shows the process of fitting a surface through a sparse contour set using a variant of shape-based interpolation [8]. In keeping with the direct approach to freehand 3D ultrasound, the contours are defined on the B-scans, not a reconstructed voxel array. This means that the operator does not have to contend with subtle 3D artefacts when deciding where to place the contours. If surface visualization is not required, then a volume estimate can be deduced directly from the contours using cubic planimetry [9]: in vivo experiments have shown these estimates to be within 5% of the true volume.
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Figure 7. Interpolating a surface through multiaxial contours. A distance field is calculated on the plane of each contour, encoding the shortest distance from each point on the plane to the contour. The shape of each contour is represented by a set of maximal disks [28]. Correspondences between these disks are used to define interpolation directions between the planes [8]. The distance field is interpolated in these directions: the zero-crossings of the resulting 3D field define the surface. The regularized marching tetrahedra algorithm [29] provides a triangulation of the surface, which can be visualized using standard surface rendering techniques. The enclosed volume is readily calculated from the triangular mesh representation [9].
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While generic ultrasound segmentation algorithms inevitably require the input of a skilled human operator, some progress towards automation has been made for specific segmentation tasks. Normally, the operator's expertise is replaced by a model of the structure to be segmented, allowing the segmentation algorithm to make informed decisions in regions of the image where the signal to noise ratio is poor. The danger of relying on anatomical models in this way is that, in describing where the segmentation boundary is most likely to be, they do not account for possible local pathology, which is often precisely what the segmentation is supposed to detect. Nevertheless, useful model-based systems have emerged for the automatic segmentation of specific structures, such as the ventricular wall in echocardiographic data sets [10, 11] and lumen and plaque in 3D intravascular data sets [12, 13].
Another case where segmentation can proceed automatically is with 3D Doppler data sets: if the aim is to segment the vessels, then automatic delineation of the high-contrast coloured regions in each B-scan is often feasible and effective. However, this relies on the quality of the Doppler signal: flash artefacts, or signal drop-out from a poorly oriented transducer, will have a detrimental effect on the resulting segmentation. High contrast boundaries are also sometimes apparent in obstetrics applications, where parts of the fetal surface may be clearly visible against the amniotic fluid. In such cases, automatic edge detection algorithms can be used to produce surface renderings of, for example, the face of the fetus in a matter of seconds. However, high contrast boundaries are the exception and not the rule in ultrasound imaging: for most applications, manual or semiautomatic segmentation is unavoidable.
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Registration
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After visualization and segmentation, registration is the final type of processing often applied to 3D ultrasound data. As with other imaging modalities, we might wish to register two 3D ultrasound volumes to highlight changes over time. Unlike other modalities, differences in the two volumes might be due to different directions of insonification, or different time-gain-compensation settings on the ultrasound machine, and not due to real anatomical changes. For this reason, it is important to use a flexible similarity criterion like the correlation ratio [14] or mutual information [15, 16], and not a simple sum of squared difference grey-level comparison.
3D ultrasound also features in multimodal registration procedures, particularly in surgical navigation applications [17–19], where relatively low quality, intraoperative 3D ultrasound scans are registered to high quality pre-operative MR or CT. The pre-operative scans are thus deformed to reflect anatomical changes induced by the intervention itself, allowing them to be used as an aid to surgical navigation throughout the entire procedure, and not just at the beginning. The registration algorithms used for these applications, though still a matter of active research, tend to reflect the mainstream in medical image registration, namely spline deformations to describe non-rigid registrations, multiresolution searches for the optimal solution, and powerful similarity criteria, such as mutual information and the correlation ratio, to compare the two volumes.
Here we will focus on different registration procedures specific to 3D ultrasound. The first is the registration of the individual B-scans which make up a freehand 3D data set. While the readings of the position sensor are sufficient to determine the location of the probe, they do not account for deformation of the anatomy caused by the contact pressure of the probe. For high resolution scans, acquired at shallow depth settings, this deformation can extend over a significant proportion of each B-scan and lead to serious artefacts in the 3D data set, as illustrated at the top of Figure 8. Nevertheless, image registration techniques can be used to correct such probe pressure artefacts. The key is to constrain the registration to allow for no more than the underlying physical process. Thus, B-scan n+1 is translated within its plane until it most closely matches B-scan n. Given that B-scans n and n+1 were acquired almost simultaneously and therefore appear very similar, a simple similarity criterion like the sum of squared grey-level differences will suffice. Following the translation, a further, non-rigid warp is applied in the axial direction to compensate for varying probe contact pressure: B-scans, which have been compressed by the probe are retrospectively expanded to match the B-scan acquired with the minimum probe pressure. The intention is to re-capture how the anatomy would have appeared if scanned with a non-contact acquisition protocol. Full details of this process can be found in [20]. The beneficial effects of the inter-B-scan registration process are illustrated at the bottom of Figure 8.
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Figure 8. Inter-B-scan registration for a high resolution scan of the forearm. Pairwise registration of neighbouring B-scans suppresses artefacts caused by varying probe contact pressure. To avoid drift in this accumulated registration process, a post-processing step warps the entire data set to ensure that the first and last B-scans are in their correct positions as indicated by the position sensor [20].
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The inter-B-scan registration process partially estimates the relative positions of B-scans without the need for a position sensor. It can be extended to encompass the out-of-plane displacement between pairs of B-scans, by exploiting the phenomenon of speckle regression [21] or speckle de-correlation [22]. The underlying principle is that the correlation between corresponding patches of speckle diminishes the further apart the patches are. By estimating the relative displacements of several patches of speckle at different points on neighbouring B-scans, all six degrees of freedom of the B-scans' relative location can be deduced, leading ultimately to a position sensor-less freehand 3D ultrasound system.
Another form of registration peculiar to 3D ultrasound is the alignment of partially overlapping sweeps for extended field of view imaging. For the largest volumes, use of a freehand system is essential, and it might even take several sweeps of the probe to cover the entire region of interest. For instance, three sweeps might be needed for a human liver: one for the left lobe, one for the centre and another for the right lobe. But it is not only large organs, which might require multisweep acquisition: it is really an issue of organ size with respect to the B-scan resolution. The uncorrected image in Figure 9 shows a reslice through a freehand data set of the human breast, used to aid radiotherapy planning following lumpectomy. Use of a small parts probe at a 6 cm depth setting was essential to achieve the necessary axial resolution, but the small lateral footprint (3.5 cm) of the probe meant that two sweeps were required to cover the re-sectioned area. The uncorrected reslice exhibits significant probe pressure and respiration artefacts (inter-B-scan), and also a clear misregistration between the two sweeps, the latter also a consequence of anatomical deformation caused by the contact pressure of the probe. The centre image shows correction of the inter-B-scan artefacts using the registration algorithm described above. The right image shows additional correction of the intersweep misalignment using a conventional rigid registration procedure [23], which suffices since the non-rigid (B-scan compression) errors are corrected by the previous inter-B-scan stage. A multiresolution search enables the optimal intersweep alignment to be found in a couple of seconds, while the choice of similarity criterion is not critical [23].
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Figure 9. Combined inter-B-scan and intersweep registration. The figure shows reslices through a data set of the human breast, part of an experimental radiotherapy planning protocol following lumpectomy. The uncorrected reslice exhibits probe pressure and respiratory artefacts, as well as a clear misregistration between the two sweeps. Both types of artefact are effectively removed by the combined registration process.
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It is interesting to note how the combined inter-B-scan and intersweep registration protocol does appear to reveal the undeformed anatomy, as would be observed with a non-contact imaging modality. Figure 10 shows a reslice through the 3D ultrasound breast data superimposed on a corresponding reslice through a CT scan acquired at the same time. The two data sets were aligned using external fiducials, not any sort of image-based registration. The excellent alignment is testament to the careful calibration of the freehand ultrasound system [24] as well as the effectiveness of the registration algorithms.
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Figure 10. Comparison of corrected 3D ultrasound data with CT data. A reslice through the breast data is shown superimposed on a corresponding reslice through CT data of the same breast, acquired at the same time. The figure reveals excellent correspondence between the corrected ultrasound data and the non-contact CT image. The area targeted for radiotherapy is outlined in white.
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Fully overlapping sweeps can be registered for the purposes of spatial compounding [25]. The idea is to acquire the sweeps from different directions, align them [26, 27] then construct the compounded volume by averaging the individual volumes. This process can remove some of the artefacts described earlier: speckle is reduced and tissue boundaries are less susceptible to drop-out given the multiple insonification directions. However, the feasibility of this technique hinges on the availability of multiple acoustic windows, which is highly application dependent.
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Conclusions
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The visualization of 3D ultrasound data requires specialized algorithms, which allow for the irregular distribution of the B-scans in space. Opportunities for the automatic segmentation of ultrasound data are limited to specific applications where there are suitably high contrast boundaries, or where the use of a strong shape model is appropriate. Following segmentation, powerful algorithms exist to estimate a volume from, or interpolate a surface through, the resulting multiaxial contours. Finally, the quality of 3D ultrasound data can be improved by a variety of innovative registration procedures. Many of the techniques described in this paper are implemented in the Stradx freehand 3D ultrasound system, which is available for free download from http://mi.eng.cam.ac.uk/~rwp/stradx/.
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Acknowledgments
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The authors thank Charlotte Coles and Andrew Hoole for providing the CT data in Figure 10.
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Top
Abstract
Introduction
