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.

A-scan ultrasound system for real-time puncture safety assessment during percutaneous nephrolithotomy

Background: Kidney stone is a major universal health problem, affecting 10% of the population worldwide. Percutaneous nephrolithotomy is a first-line and established procedure for disintegration and removal of renal stones. Its surgical success depends on the precise needle puncture of renal calyces, which remains the most challenging task for surgeons. This work describes and tests a new ultrasound based system to alert the surgeon when undesirable anatomical structures are in between the puncture path defined through a tracked needle. Methods: Two circular ultrasound transducers were built with a single 3.3-MHz piezoelectric ceramic PZT SN8, 25.4 mm of radius and resin-epoxy matching and backing layers. One matching layer was designed with a concave curvature to work as an acoustic lens with long focusing. The A-scan signals were filtered and processed to automatically detect reflected echoes. Results: The transducers were mapped in water tank and tested in a study involving 45 phantoms. Each phantom mimics different needle insertion trajectories with a percutaneous path length between 80 and 150 mm. Results showed that the beam cross-sectional area oscillates around the ceramics radius and it was possible to automatically detect echo signals in phantoms with length higher than 80 mm. Conclusions: This new solution may alert the surgeon about anatomical tissues changes during needle insertion, which may decrease the need of X-Ray radiation exposure and ultrasound image evaluation during percutaneous puncture.