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.

Crime Económico Não Esquecendo Crime Clássico

Fala-se hoje em dia muito e bem no crime económico e social. Crime de colarinho branco. Também crime da ocupação, profissional ou amadora. Falamos sobre direito penal económico e social. Fraude fiscal, corrupção, branqueamento de capitais, crimes da bolsa, abuso de posição dominante, etc.. Contudo, isto não podemos esquecer o crime clássico, furtos, roubos, danos, ofensas à integridade física, violação, tortura, ameaças, ofensas à honra, injúria ou difamação, abuso sexual (não apenas de crianças), violação, homicídios domésticos ou entre estranhos, etc.. § There is talk nowadays long and hard in the economic and social crime. White collar crime. Also crime of occupation, professional or amateur. We talk about economic and social criminal law. Tax fraud, corruption, money laundering, stock crimes, abuse of dominant position, etc .. However, this can not forget the classic crime, theft, robbery, damage, bodily harm, rape, torture, threats, insults to honor, slander or defamation, sexual abuse (not just children), rape, domestic or among strangers murders, etc ..