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.

«Corruption» and social and economic criminal law: criminology, criminal policy, political science and law&economics - a new idea about criminal liability of legal entities

Abstract: If we think there is a significant number of legal offshore in the globalized world, then there is not even a global consensus about what «corruption» is. The «illegal corruption» in a country may be legal in another. Moreover, the great global corruption is above the law or above democratic States. And not all democratic States are «Rule of Law». Therefore, the solution is global earlier in time and space law, democratic, free and true law. While the human being does not reach a consensus of what «corruption» really is, the discussion will not go further than a caricature. One of the other problems about «corruption» is that it is very difficult to establish the imputation of crimes, including «corruption» (v.g. Portugal) on some «companies», corporations. We have a juridical problem in the composition of the art. 11. of the Portuguese Penal Code.