3.2. Workflow implementation
3.2.2. Second Approach – Based on Image Registration
The knowledge acquired from the pre-processing study, concerning the best methods to provide an accurate segmentation, led to the registration test, where several registration techniques were approached. To determine the most appropriate, two criteria were taken into account: the DICE score (Sørensen 1948, Cheung 2012) and the computational cost.
Four registration algorithms were tested in two different registration models, pairwise and reference slice (more details in section 2.3.).
The first algorithm implemented is a feature-based registration method and the second an intensity-based algorithm. The feature registration method only enables rotation and translation to the moving images, since the only type of transformation implemented is similarity. On the other hand, the intensity–based model allows other two types of transformation, the rigid and the affine (section 2.3.). The other two algorithms tested, the Demon algorithm and the B-spline algorithm, which are both capable of performing non-rigid registration. All these methods are explained further in this section.
The automatic feature-based registration starts by detecting image features in both images, moving and fixed, mainly through the implementation of the Speed-Up Robust Features (SURF) algorithm (Bay, Ess et al. 2008), an algorithm that searches blob features, regions of the image where several properties (for example, brightness and intensity) remain constant. The detected features are then extracted including their location in the image, through the pixels surrounding the interest point or feature blob (Bay, Ess et al. 2008). The detected and extracted feature regions in the moving and fixed images are matched using parallel hierarchical clustering trees (Muja and Lowe 2012), resulting in a pair of indexes from the matched features. The locations of those matching points are also retrieved and the transformation is performed based on the matched points of both fixed and moving image, resorting to M-estimator Sample Consensus (MSAC) algorithm (Torr and Zisserman 2000) to exclude outliers. The inliers of both sets of matching points are mapped and originate a 2D geometric transform object (Hartley and Zisserman 2003). In the last step, the geometric transformation object generated is applied to the moving image, creating this way the registered image. The scale and angle applied (considering that it is a similarity transform) with the transform object to create the final image are recovered to serve as quality control of the whole procedure, allowing this way the removal of completely distorted images, possible outcomes of the registration process. The stated framework was performed based on (MathWorks).
Concerning the intensity-based registration three key components have to be previously defined in order to configure the whole registration process, the optimizer, the metric and the
transformation type (section 2.3.). The metric is, in fact, the image similarity metric responsible for evaluating the registration’s accuracy and the optimizer (Regular Step Gradient Optimizer, whose algorithm is described in (Pennec, Cachier et al. 1999)) defines the procedure for minimization or maximization of this similarity metric (Mean Squares metric implementation in (MathWorks)). This registration method is an iterative process that can be performed in three different transformation types (rigid, similarity and affine) and always requires two images, a fixed and a moving image. The whole registration process starts with an internally determined transformation matrix combined with the transformation type specified, determining the image transformation that is going to be applied to the moving image with bilinear interpolation (MathWorks). After the interpolation the metric compares both transformed moving image and fixed image, computing the metric value and then the optimizer checks for ending conditions to stop the registration process. These conditions can be the maximum number of iterations (defined by the optimizer) or a certain metric value threshold. If the stop condition does not verify the optimizer adjusts the transformation matrix to initiate a new registration cycle. The maximum number of iterations and the optimizer step size the registration can be altered to improve the registration, but always with a greater computational cost (MathWorks). The explained workflow is presented in Figure 23Figure 23.
Figure 23. Representation of the intensity-based registration framework implemented.
Adapted from (MathWorks).
The first non-rigid registration methodology tested was the B-Spline Grid, Image and Point
Registration developed by (Kroon 2008), based on the algorithm developed in (Rueckert,
Sonoda et al. 1999). This is an intensity based registration technique whose algorithm implements a grid of B-spline control points (section 2.3.) that control the transformation of
the moving image over the fixed one. It measures the registration error, through squared pixel distance (Vercauteren, Pennec et al. 2009), a similarity criterion based on the information theory and calculates the amount of information existent in the registered moving image about the fixed one (considering a registration procedure). The B-Spline method applies the Fast Limited Memory Optimizer (Kroon 2009), a Quasi-Newton optimizer, to move the control points, in order to achieve the optimal registration between both images with minimal similarity error. The implemented B-Spline method can also performed rigid and affine transformations (section 2.3.).
The Demon algorithm is a non-rigid registration technique faster and rather simpler than the B-Spline. This algorithm was first described by (Thirion 1998) and followed by (Wang, Dong et al. 2005), and the methodology followed in the present study was developed by (Kroon 2008). For each pixel a velocity, or movement, is defined by this method, using the intensity differences and gradient information. The velocity matrix is smoothed by a Gaussian filter and iteratively applied to transform the moving image and register it onto the fixed image. The transformation is optimized by a limit memory BFGS optimizer (Liu and Nocedal 1989) in an iterative and multi-resolution way. The Demon algorithm also performs affine registration (section 2.3.).
In the second approach were also tested combinations of the previously described algorithms, starting with a rigid registration technique followed by a more accurate and computational demanding non-rigid registration algorithm, as performed in previous studies (Roberts, Magee et al. 2012).
In order to align all the images from the datasets available, two different registration models, the reference slice model and the pairwise model, were implemented for all the abovementioned registration methods, starting from the middle slice (in the datasets) since, generally, it is the section with most tissue (Roberts, Magee et al. 2012). Through the reference model the registration procedure is performed considering only as fixed image the middle slice from the image dataset, thus, being all the slices registered to reference section. The pairwise model is performed in a cascade process starting from the center slice and performing registration in pairs of slices (moving image becomes fixed image in the next alignment) in two directions - until the top slice in the first run and the first slice in the second run.
The workflow of the registration approach combined with the best suited pre-processing method is presented in Figure 24.