Radial Distortion Self-Calibration

In cameras with radial distortion, straight lines in space are in general mapped to curves in the image. Although epipolar geometry also gets distorted, there is a set of special epipolar lines that remain straight, namely those that go through the distortion center. By finding these straight epipolar lines in camera pairs we can obtain constraints on the distortion center(s) without any calibration object or plumbline assumptions in the scene. Although this holds for all radial distortion models we conceptually prove this idea using the division distortion model and the radial fundamental matrix which allow for a very simple closed form solution of the distortion center from two views (same distortion) or three views (different distortions). The non-iterative nature of our approach makes it immune to local minima and allows finding the distortion center also for cropped images or those where no good prior exists. Besides this, we give comprehensive relations between different undistortion models and discuss advantages and drawbacks.

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.

One-sided Radial-Fundamental Matrix Estimation

For modern consumer cameras often approximate calibration data is available, making applications such as 3D reconstruction or photo registration easier as compared to the pure uncalibrated setting. In this paper we address the setting with calibrateduncalibrated image pairs: for one image intrinsic parameters are assumed to be known, whereas the second view has unknown distortion and calibration parameters. This situation arises e.g. when one would like to register archive imagery to recently taken photos. A commonly adopted strategy for determining epipolar geometry is based on feature matching and minimal solvers inside a RANSAC framework. However, only very few existing solutions apply to the calibrated-uncalibrated setting. We propose a simple and numerically stable two-step scheme to first estimate radial distortion parameters and subsequently the focal length using novel solvers. We demonstrate the performance on synthetic and real datasets.

Targeting lactate transport suppresses in vivo breast tumour growth

Background: Most cancers, including breast cancer, have high rates of glucose consumption, associated with lactate production, a process referred as “Warburg effect”. Acidification of the tumour microenvironment by lactate extrusion, performed by lactate transporters (MCTs), is associated with higher cell proliferation, migration, invasion, angiogenesis and increased cell survival. Previously, we have described MCT1 up-regulation in breast carcinoma samples and demonstrated the importance of in vitro MCT inhibition. In this study, we performed siRNA knockdown of MCT1 and MCT4 in basal-like breast cancer cells in both normoxia and hypoxia conditions to validate the potential of lactate transport inhibition in breast cancer treatment. Results: The effect of MCT knockdown was evaluated on lactate efflux, proliferation, cell biomass, migration and invasion and induction of tumour xenografts in nude mice. MCT knockdown led to a decrease in in vitro tumour cell aggressiveness, with decreased lactate transport, cell proliferation, migration and invasion and, importantly, to an inhibition of in vivo tumour formation and growth. Conclusions: This work supports MCTs as promising targets in cancer therapy, demonstrates the contribution of MCTs to cancer cell aggressiveness and, more importantly, shows, for the first time, the disruption of in vivo breast tumour growth by targeting lactate transport.