In the medical field, image registration is used for diagnostic purposes when images of the same anatomical structure must be superimposed on each other. Registration methods are used for combining computer tomography (CT) and magnetic resonance imaging (MRI) data to obtain more complete information about the patient, for monitoring tumor growth, for treatment verification, for comparison of the patient’s data with anatomical atlases [1]. Image registration is often a necessary procedure. It is used to merge images from different imaging modalities and different examination dates and therefore it is useful for diagnosis and assessment of disease progression or remission. Different imaging modalities provide complementary information and when the images are aligned and merged, this information is added to give a more clinically useful result. In another type of application, the progression of a disease over time can be assessed by registering images of the same patient from two different examination dates. For example, after registration, measurements of a tumor growth can be made.

The majority of image registration methods are based on the use of a similarity/disparity criterion which, when the two images are brought to register, is maximized/minimized. Numerical analysis techniques are used to maximize/minimize the similarity/disparity criterion. There are many different criteria, with mutual information (MI) being the standard since it is quite accurate for rigid body registration and does not require any image segmentation prior to registration.

Image registration is an active research field and in recent years image registration methods have evolved from the research setting, to being incorporated into clinically useful software tools [2]. The image registration methods can be in general divided into rigid and non-rigid. Rigid registration techniques adjust for rotations and translations only (six parameters for the 3D case). This is the case with rigid brain scans. Non-rigid techniques assume a nonlinear transformation model and can adjust for image warping. Warping occurs usually due to the soft tissue deformations of the body organs between different scans [2]. Medical image registration techniques are also categorized according to the type of features they use for registration. Surface-based techniques rely on the characteristics of the surface of the registrable objects while volume-based techniques use the full volume information. West et al. [3] define as volume-based “any technique which performs registration by making use of a relationship between voxel intensities within the images and as surface-based, any technique which works by minimizing a distance measure between two corresponding surfaces in the images to be matched”. According to Slomka et al. [2] volume- or voxel-based techniques are more robust and accurate because they do not rely on the preprocessing of the images for being accurate. This is especially the case for the MI methods. These methods rely on maximizing the amount of information sharing between the two images to be registered. According to Bardera [4], “MI methods have become a standard reference due to their accuracy and robustness.” In Liao et al. [5] surface matching and MI methods are compared and the conclusion is that the surface matching registration algorithms could be followed by a few iterations of a MI algorithm for better accuracy. Improvement of the standard MI algorithms is an active research field and the effort is to use a combined approach that does not rely on voxel values only, but incorporates geometrical or regional features for computation of the MI [4, 6–9].

The type of problem which is solved by the registration algorithm is another categorization criterion. The methods may be suitable for image-to-image space registration (3D–3D, 2D–3D) or physical to image space registration. 3D–3D methods register image volumes to image volumes (MR-MR, CT-MR, (positron emission tomography) PET-MR, Ultrasound-MR) [2, 3, 10]. 2D–3D registration techniques register, for example, one or more intraoperative X-ray projections of the patient and the preoperative 3D volume [11, 12]. Physical to image space registration is similar to 2D–3D registration but may use interventional techniques like bone-implanted markers for patient to image registration [13].

In this paper, we follow a novel approach to the medical image registration problem. We propose, test and compare to the standard MI methods a method which uses binary projections of the 2D or 3D images for the computation of the registration function.

Several techniques for signal-intensity projection-based image registration have been developed [14–16]. The most relevant work to this report is the method presented in Khamene et al. [14]. In this work, the registration problem is analyzed into the sub-problems of registering, using signal-intensity-based algorithms and criteria, the rendering projections of the two volumes along the three axes and adjusting the two volumes according to the projection-based computed registration parameters. In this work, we use a different similarity/disparity measure and a different iteration loop which have been shown to be very accurate and robust for volume-based registration [17]. The similarity/disparity measure allows us to use binary (shadowing) projections and not renderings simplifying the hardware limitations for projection computation presented in Khamene et al. [14].

Another projection-based technique for 3D–3D vascular registration is presented in Chan et al. [15]. In this technique, the 3D–3D registration problem is transformed into multiple 2D–3D vascular registration problems. The 2D images are the maximum intensity projection (MIP) images (gray-scale signal-intensity images) which are first generated for the reference volume along the three axes. At each iteration, three binary projections from the segmented binary floating volume are compared and registered to the corresponding MIPs. The similarity measure used is the sum-of-squared-differences.

A projection-based 2D-2D image registration technique in the presence of fixed pattern noise is presented in Cain et al. [16]. In this method, the 1D projections along the two axes are computed by accumulating pixels along the two main axes of the 2D image. The horizontal and vertical components of the shift are then computed using 1D cross-correlation. They show that the method is very robust in the presence of temporal and spatial noise and computationally efficient compared to the 2D correlation based shift estimator.

The goal of this work is to develop and test a registration solution that will be able to address different forms of the registration problem using a common registration logic. The common logic is to use a simple registration criterion which utilizes minimal information. We also implement a novel and easy to understand iteration loop which, in comparison to other minimization techniques, makes it easier to register images with less information used. In this context, the motivation is the need to produce a well-engineered registration system of methods for 3D–3D rigid body registration (volume- and projection-based), 2D–3D registration and non-rigid body registration. By well-engineered, we mean that we will be able to address the main registration algorithm problems which are accuracy and convergence. We want to research the goodness of the registration algorithm convergence criterion in relation to the accuracy desired and the data set used. For example, we want to find out how many iterations have to be taken for the registration algorithm to converge.

The main steps of the method are:

For 2D registration using 1D projections, the scans correspond to 3D studies and the ones used were randomly selected from the cases of acute stroke, multiple embolic infarctions, multiple sclerosis and vascular dementia. One additional scan pair consists of T1/T2 interleaved study scans from the database of the Cleveland Clinic Foundation.

The preprocessing of the 2D scans was performed using the Bioimage Suite Software of Yale University [22]. Preprocessing consists of the following steps:

The effort in the preprocessing step was to introduce minimum non-registrable areas which affect the registration accuracy.

Figure 1 shows the scan pairs for the five cases and the areas of non-overlap after preprocessing:

The 2D registration method works in the following way:

Another form of the 2D registration method incorporates multiple projections for rotational adjustment into the iteration loop. In order to incorporate multiple projections a decision has to be made at each iteration about the best projection. It was found that this decision cannot be projection-based. The reason for this is that the projection-based sequential execution of the full algorithm is based on selecting the final best result after visual inspection of all the final results. For the automated form of the algorithm [17] the full area-based criterion was found to be robust and accurate. This criterion was used for the incorporation of multiple projections into the iteration loop.

The implementation of the incorporated projections method uses two sets of projections with each rotational iteration, one at 40–50° and one at −50 to −40°. The best result from these two sets is kept as the correct result.

The algorithms used are:

Algorithm 1 2D image registration using binary projections and repetitive execution

Algorithm 2 2D image registration using binary projections with inclusion of theta selection in the iteration loop

Figure 2 shows an example of one projection used for the computation of the registration function for the 2D registration case.

The basic characteristics of the 3D registration method are:

Algorithm 3 3D registration algorithm using 2D binary projections

One of the two scans was used as the reference scan. The other scan was considered to be the reslice scan. The latter was rotated and translated using a standard set of 20 2D geometric transformations and then registered to the reference scan, giving 20 registration experiments per case. For this reason, these experiments are referred to as “20 displacements” experiments. The geometric transformations parameters were randomly selected using a random number generator in the range [−45, 45°] for the xy rotation and [−30, 30] mm for x and y translations. The 2D geometric transformation set is shown in Table 1.

Table 2 shows the average errors for the 20-displacements experiments for each of the five cases.

The processing time of the method is 1–2 s on a HP A6240 Intel Quad Core 2.4 GHz PC with 2 Gbyte RAM. Of course the method can be implemented in parallel and give processing time less than 1 s.

For the 2D case, the accuracy of the method is better than 1° and 1 pixel. In most cases, the error is less than 0.5° and 0.5 pixels. The preprocessing of the images must be careful not to produce non-registrable areas in the contours to be registered (avoid for example repetitive median filtering in one of the two images). No interpolation is necessary for 2D registration with the use of binary projections. The registration function is not dependent on signal-intensity distributions. The method is directly applicable to binary images and contours. The method is fast with a typical time of 1–2 s running on an HP A6240 Intel Quad Core 2.4 GHz PC with 2 Gbyte RAM.

The first results of a 3D projection-based method have been given in this report. The accuracy of the method is better than 0.5° for rotations and 0.5 voxels for translations. Compared to the full volume method [17], the method takes more steps to converge towards the correct registration position but remains as accurate. Minimal preprocessing of the images prior to registration is needed. The method is more accurate and robust than standard MI methods. It converges to stable final positions independent of the initial misregistration.