Weighted least squares for point-based registration in digital subtraction angiography (DSA)

Four main problems have to be solved for template matching based motion compensation in digital subtraction angiography. All the problems are concerned with the similarity measure that is the objective function to be optimized within the template matching procedure: 1) Due to the injection of contrast agent, mask and contrast image are dissimilar, which degrades the quality of some similarity measures. 2) Homogeneous areas in the fluoroscopic images lead to an insufficient quality of the similarity measure. 3) Shift invariant structures in fluoroscopic images (e.g. straight lines or edges) lead to a ridge-like objective function that potentially gives wrong results from the optimization procedure: If a ridge-like structure of the objective function is present movements along this direction cannot be detected. Therefore, the local accuracy of the estimated motion component parallel to these directions must be ranked low while the corresponding orthogonal direction must be ranked high. We here present a technique to obtain local, directional rankings from the shape of the objective function which especially improves the quality of DSA images obtained from peripheral areas like the shinbone. 4) Inhomogeneous movements inside a single template lead to ambiguous or even irrelevant optima of the objective function: This problem is out of the scope of the present paper and will therefore not be addressed here. The performance of the point-based registration using different weightings in the least squares procedure (equally, isotropic and anisotropic weighting) has been compared. The isotropic and anisotropic weighting turned out to be superior to the equally weighted least squares procedure.