Simulation and Visualization Research Group
3D registration through pseudo x-ray image generation

Introduction

Pre-operative planning for computer assisted surgery is generally based on information derived from CT and MR datasets.  The accuracy and usability of such an approach is largely dependent on the process of registering the pre-operative plan with the intra-operative position of the patient.  Many techniques have been previously investigated including digitisation of anatomical features, fiducial markers and image matching.

Image comparison based registration

A pseudo x-ray image is generated from a CT dataset absorber by a virtual image intensifier (II) using ray-tracing techniques.  The pseudo x-ray image is intra-operatively compared to a real fluoroscopic II image to determine a similarity measure.  The position and orientation of the virtual II is then refined on the basis of the similarity measure.  A registration solution is achieved when the position and orientation of the virtual II is located in a similar position, relative to the patient, as the real fluoroscopic II.

X-ray tracer based image generation

The x-ray tracer used in the generation of the pseudo x-ray image is very similar in principle to a visible light ray-tracer.  The significant difference is the replacement of the surface illumination model with an x-ray absorption model.  As rays pass through the scene, they may intersect one or more objects.  At each intersection the magnitude of the x-ray beam energy is reduced, based on the standard x-ray absorption equation with material characteristics and distance of penetration as parameters.  The intensity of an individual pixel on the pseudo x-ray image is proportional to the residual energy in the x-ray beam after traversing the scene.  The scene comprises a set of voxel objects that represent the CT dataset of the patient's anatomy.

Image comparison

The comparison of a real x-ray image with a pseudo x-ray image can be unreliable.  A novel approach has increased robustness and accuracy of the comparison with the addition of artefacts into the pseudo image including, image distortion, image noise and contrast variation.  The magnitude of each artefact has been carefully measured on a fluoroscopic II through rigorous experimentation.  The concept of a similarity value has been introduced to numerically describe the different between the real and pseudo images.  The similarity value is calculated as the mean difference of the two images.

Original x-ray

Before comparison

After comparison

Virtual II position model

The registration problem now reduces to the minimisation of a non-linear equation.  Where the equation takes N parameters that uniquely define the position and orientation of the virtual II and returns the similarity value for the real and pseudo images. The virtual II's position and orientation within the virtual world and its subsequent movement is described using a polar co-ordinate system based around a central virtual object.  At present this movement model is limited to 4 degrees of freedom: three angular and one radial.

Virtual II position realisation

Simulated annealing is used to ensure both a rapid convergence and a near optimal refinement of the virtual II's position and orientation.  Coupled with the annealing method is a hill descending strategy that performs a step based refinement of the virtual II's position and orientation in order to achieve a lower energy state.  The energy state is analogous to the similarity measure.

Experimental results

Firstly the algorithm was used to register the positions and orientations of a virtual II that generated two pseudo x-ray images from different viewpoints.  Artificial noise was added to both pseudo images.  The substitution of the pseudo image for the real image removed, from the equation, any noise, distortion or scaling effects caused by the real II.  This provided a means to assess the absolute accuracy that could be achieved, if the virtual II output was "tuned" exactly to match the output from the real II.  A worst-case mean angular error of 0.47° was achieved.

Secondly the algorithm was used to register a real and a pseudo x-ray image. Two real x-ray images of the scene were captured from different viewing angles.  The algorithm then registered the real II with the virtual II for each image.  The registration error was calculated as the difference between the view angles for the real and virtual II.  Positioning of the real II at a precise position is inherently inaccurate due to the absence of a suitable measuring device, consequently the scene rather than the real II was rotated between x-ray image capture. A worst-case mean angular error of 2.5° was achieved.

Calibration object

Discussion

The significant increase in error between the two sets of tests is thought to originate through imprecise "tuning" of the virtual II to match the output of the real II.  One particular factor that has not yet been incorporated into the virtual II is the blurring of the image caused by the fluoroscopic II during the horizontal scan of the image.

The advantage of this particular registration strategy over alternative approaches is that it is both non-invasive and non-user intensive, as fiducial markers and direct bone surface digitisation are both avoided.  Furthermore the approach does not require the segmentation of either the CT dataset or x-ray image, thus reducing a further source of inaccuracy.