Talks by Dr. Kukelova and Prof. Pajdla
April 27 (Fri.)
National Institute of Informatics
Room 1901/1902, 19th floor
Dr. Zuzana Kukelova (Dept. of Cybernetics Czech Technical University in Prague)
Fast Grobner basis solvers for computer vision problems
Many problems in computer vision, but also in other field such as robotics, control design or economics, can be formulated using systems of polynomial equations. For computer vision problems, general algorithms for solving polynomial systems cannot be efficiently applied. The reasons are twofold - computer vision and robotic applications usually require real time solutions, or they often solve systems of polynomial equations for millions of different instances. Several approaches based on algebraic geometry have been recently proposed for the design of very efficient algorithms (solvers) that solve specific classes of systems of polynomial equations. In this talk we will briefly discuss such method for creating efficient solvers of systems of polynomial equations. This method is based on Grobner bases and it uses the structure of the system of polynomial equations representing a particular problem to design an efficient specific solver for this problem. We will discuss several approaches for improving the efficiency of the final solvers. We will also introduce the automatic generator of Grobner basis solvers which could be used even by non-experts to efficiently solve problems resulting in systems of polynomial equations. Finally, we will demonstrate the usefulness of the approach by presenting new, efficient and numerical stable solutions to several important computer vision problems and problems from robotics.
Prof. Tomas Pajdla (Czech Institute of Informatics, Robotics and Cybernetics, Czech Technical University in Prague)
On the Two-View Geometry of Unsynchronized Cameras
We will present a method for simultaneously estimating camera geometry and time shift from video sequences from multiple unsynchronized cameras. We estimate fundamental matrices and homographies and the unknown time shift between images. We use minimal correspondence sets (eight for fundamental matrix and four and a half for homography), and hence our approach is suitable for robust estimation using RANSAC. Furthermore, we present an iterative algorithm that extends the applicability on sequences which are significantly unsynchronized, finding the correct time shift up to several seconds. We evaluate the methods on synthetic and wide range of real world datasets and the results show a broad applicability to the problem of camera synchronization.