Image registration plays a crucial role for the accurate reconstruction of an organ from partial ultrasound volumes and the subsequent accurate resection of a lesion/tumor with an optimally minimal damage of the healthy tissue. With the help of the Insight Toolkit (ITK), various state-of-the-art voxel-based 3D image registration algorithms were investigated, implemented and evaluated, allowing for the assessment of an accurate ultrasound image registration scheme. The investigation of the 3D space was based on an investigation of the 2D space, where the image registration components showing low performance were sorted out. The performance was assessed by calculating the standard deviation (SD) of the resulting difference images. Overall the mutual information and joint histogram based metrics showed low performance (2D - SD up to 25,9), whereas the Powell direction set algorithm in combination with the mean squares metric showed a better performance (3D - SD: 22,4).
In order to assess for an optimal image registration method for accurate ultrasound image registration, several initial experiments were conducted in the 2D space, investigating various combinations of metrics and optimizers. Based on these initial experiments, optimizer-metric combinations with low performance were excluded from the experiments in the 3D space. Due to the common characteristics of the 2D and 3D ultrasound images, we assume that this convention is valid. The investigation of various metrics allows the assessment of the quality of the representation of the similarity of two images. Additionally, the investigation of various optimizers allows the assessment of the quality of the optimization succeeded, i.e. how good the optimizer suits to the metric and guides itself to the extremum of the metric. The experiments were succeeded through the development of an image registration framework, which utilizes already implemented image registration components by the Insight Toolkit (ITK). This accounts for robustness of the algorithms used and minimization of the researcher bias and promotes the reproducibility of the results. The experiments investigated the performance of a registration with respect to both the choice of a metric and an optimizer (Figure 1). Their influence on the registration result is considered much more significant than the influence of the interpolator. For this reason, a linear interpolator was utilized, because of its very good quality to computational load ratio. In addition, the transformation between successive acquisitions can be theoretically given by a translation or rigid transformation, but due to ultrasound imaging inaccuracies and taking into account that the non-deformable-body constraint is well fulfilled for the utilized liver phantom, affine transformations were applied. Although the results of the current study cannot be directly applied to clinical cases, where deformable transformations have to be considered, they provide important information for applications, where complex multiple level image registration schemes are used. Binary masking was also used in order to determine the regions of interest within the images under registration.
Fixed Image
Metric
Optimizer Interpolator Moving Image
Transformation
Fig. 1: Image registration algorithm: a) transformation: maps the moving on the fixed image, b) interpolator: maps the
non-grid positions of the transformed moving image on the grid positions of the fixed image, c) metric: evaluates the
quality of the registration, d) optimizer: minimizes/maximizes the metric in the transformation parameter space
In particular, the selection of optimizers and metrics was based on the state-of-the-art ultrasound image registration
algorithms [
Powell direction set LBFGS (quasi-Newton) Polak-Ribiere (conjugate gradient) Regular Step Gradient Descent (RSGD)
Normalized Cross Correlation (NCC) Correlation Coefficient (CC) Histogram-based Mutual Information (HMI) Histogram-based Normalized Mutual Information (HNMI)
Mattes Mutual Information (MMI)
Fig. 2: Examples of 2D and 3D ultrasound images and the respective difference images
Due to its high computation times and high susceptibility to noise the Viola-Wells mutual information was excluded
from the research. Histogram binning with 64 bins was used in the case of the joint histogram-based metrics. Based on
an evaluation of similarity measures for subtraction radiology [
The 2D and 3D ultrasound images used referred to respective freehand ultrasound acquisitions of a liver phantom (Kyoto Kagaku IOUSFAN) acquired with identical settings with an ALOKA ProSound α7 ultrasound system. In 2D, the ultrasound images were pre-processed with a Gaussian filter with variance 2,0 . Since the Gaussian filter is a typical low-pass filter, it suppresses the speckle only partially, in comparison to filters specially developed for speckle suppression. For two manually chosen pairs of ultrasound images (with small and large displacements respectively), the experiments in 2D concerned the convergence of an optimizer to a metric from a 7 7 grid of different start points centered on the extremum of the metric lying on intervals of 10 pixels. This results in 2940 ultrasound image registration experiments (2 image pairs 49 starting points 5 optimizers 6 metrics).
In 3D, a homogeneous three-level image resolution pyramid with downsampling factors of 8, 4 and 2 per level with prior variable Gaussian filtering was utilized. Here, the experiments concerned the registration of a pool of eleven ultrasound images with each other initially aligned on their centers of mass. 3
As an image registration quality measure, the standard deviation of the difference image computed over the overlapping region of the moving and fixed images was calculated for all the resulting difference images. The diagram given in Figure 3 displays the mean standard deviations of the resulting difference images of the 2D registration experiments for every combination of optimizers and metrics. Best results were obtained with the LBFGS optimizer and the MS metric (SD: 19,9), while the same optimizer and the HNMI metric performed worst (SD: 25,9). With regard to the 2D registration experiments, the most robust optimizer-metric combinations of the 2D experiments, namely the mean squares and normalized cross correlation metrics and all the optimizers (apart from the Nelder-Mead downhill simplex) yielded good results and were further investigated in the 3D registration experiments. The diagram given in Figure 4 displays the mean standard deviations of the resulting difference images of the 3D registration experiments for every combination of the optimizers, except for Amoeba, and the MS and NCC metrics. Best results were obtained with the Powell optimizer and the MS metric (SD: 22,4), while the LBFGS optimizer and the NCC metric perform worst (SD: 26,6).
With respect to the computation times, a 2D image registration experiment has an approximate duration of less than 5min (image size 800 600 ), whereas a 3D image registration experiment has an approximate duration of 7 to 12min (image size 281 211 254 ). In both cases the full image content was used after applying binary masking. 4