Predictive (un)distortion model and 3-D reconstruction by biplane snakes

This paper is concerned with the three-dimensional (3-D) reconstruction of coronary vessel centerlines and with how distortion of X-ray angiographic images affects it. Angiographies suffer from pincushion and other geometrical distortions, caused by the peripheral concavity of the image intensifier (II) and the nonlinearity of electronic acquisition devices. In routine clinical practice, where a field-of-view (FOV) of 17-23 cm is commonly used for the acquisition of coronary vessels, this distortion introduces a positional error of up to 7 pixels for an image matrix size of 512 x 512 and an FOV of 17 cm. This error increases with the size of the FOV. Geometrical distortions have a significant effect on the validity of the 3-D reconstruction of vessels from these images. We show how this effect can be reduced by integrating a predictive model of (un)distortion into the biplane snakes formulation for 3-D reconstruction. First, we prove that the distortion can be accurately modeled using a polynomial for each view. Also, we show that the estimated polynomial is independent of focal length, but not of changes in anatomical angles, as the II is influenced by the earth's magnetic field. Thus, we decompose the polynomial into two components: the steady and the orientation-dependent component. We determine the optimal polynomial degree for each component, which is empirically determined to be five for the steady component and three for the orientation-dependent component. This fact simplifies the prediction of the orientation-dependent polynomial, since the number of polynomial coefficients to be predicted is lower. The integration of this model into the biplane snakes formulation enables us to avoid image unwarping, which deteriorates image quality and therefore complicates vessel centerline feature extraction. Moreover, we improve the biplane snake behavior when dealing with wavy vessels, by means of using generalized gradient vector flow. Our experiments show that the proposed methods in this paper decrease up to 88% the reconstruction error obtained when geometrical distortion effects are ignored. Tests on imaged phantoms and real cardiac images are presented as well.