Unknown Radial Distortion Centers in Multiple View Geometry Problems

The radial undistortion model proposed by Fitzgibbon and the radial fundamental matrix were early steps to extend classical epipolar geometry to distorted cameras. Later minimal solvers have been proposed to find relative pose and radial distortion, given point correspondences between images. However, a big drawback of all these approaches is that they require the distortion center to be exactly known. In this paper we show how the distortion center can be absorbed into a new radial fundamental matrix. This new formulation is much more practical in reality as it allows also digital zoom, cropped images and camera-lens systems where the distortion center does not exactly coincide with the image center. In particular we start from the setting where only one of the two images contains radial distortion, analyze the structure of the particular radial fundamental matrix and show that the technique also generalizes to other linear multi-view relationships like trifocal tensor and homography. For the new radial fundamental matrix we propose different estimation algorithms from 9,10 and 11 points. We show how to extract the epipoles and prove the practical applicability on several epipolar geometry image pairs with strong distortion that - to the best of our knowledge - no other existing algorithm can handle properly.

Dense motion field estimation from myocardial boundary displacements

Minimally invasive cardiovascular interventions guided by multiple imaging modalities are rapidly gaining clinical acceptance for the treatment of several cardiovascular diseases. These images are typically fused with richly detailed pre-operative scans through registration techniques, enhancing the intra-operative clinical data and easing the image-guided procedures. Nonetheless, rigid models have been used to align the different modalities, not taking into account the anatomical variations of the cardiac muscle throughout the cardiac cycle. In the current study, we present a novel strategy to compensate the beat-to-beat physiological adaptation of the myocardium. Hereto, we intend to prove that a complete myocardial motion field can be quickly recovered from the displacement field at the myocardial boundaries, therefore being an efficient strategy to locally deform the cardiac muscle. We address this hypothesis by comparing three different strategies to recover a dense myocardial motion field from a sparse one, namely, a diffusion-based approach, thin-plate splines, and multiquadric radial basis functions. Two experimental setups were used to validate the proposed strategy. First, an in silico validation was carried out on synthetic motion fields obtained from two realistic simulated ultrasound sequences. Then, 45 mid-ventricular 2D sequences of cine magnetic resonance imaging were processed to further evaluate the different approaches. The results showed that accurate boundary tracking combined with dense myocardial recovery via interpolation/ diffusion is a potentially viable solution to speed up dense myocardial motion field estimation and, consequently, to deform/compensate the myocardial wall throughout the cardiac cycle. Copyright © 2015 John Wiley & Sons, Ltd.