I am a Ph.D. student advised by Tomas Pajdla at CIIRC, the intitute of the Czech Technical University in Prague. Currently, I work on application of techniques from semidefinite programming to polynomial optimization problems arising from computer vision and robotics.
Previously, I have received my master degree from Czech Technical University in Prague by defending the thesis Semidefinite Programming for Geometric Problems in Computer Vision. I have spent two summers in France. The first at LAAS-CNRS in Toulouse with Didier Henrion and the second in Willow team at INRIA in Paris with Josef Sivic.
The IMPACT project focuses on fundamental and applied research in computer vision, machine learning and robotics to develop machines that learn to perceive, reason, navigate and interact with complex dynamic environments.
We build a fully integrated software for 3D reconstruction, photomodeling and camera tracking. We aim to provide a strong software basis with state-of-the-art computer vision algorithms that can be tested, analyzed and reused. Links between academia and industry is a requirement to provide cutting-edge algorithms with the robustness and the quality required all along the visual effects and shooting process.
A Python package for modelling and solving moment LMI relaxations of polynomial optimization problems. The semidefinite solver is a stand-alone basic implementation of a primal interior-point method.
Automatic generator of Groebner basis solvers.
An implementation of the F4 Algorithm in Maple.
We will explain some fundamental notions appearing in advanced robotics. We shall, e.g., learn how to solve the inverse kinematics task of a general serial manipulator with 6 degrees of freedom. There is a general solution to this problem but it can't easily be obtained by elementary methods. We shall present some more advanced algebraic tools for solving algebraic equations. We will also pay special attention to representing and parameterizing rotations and motions in 3D space. We will solve simulated problems as well as problems with real data in labs and assignments.
We will explain the basics of Euclidean, Affine and Projective geometry and show how to measure distances and angles in a scene from its images. We will introduce a model of the perspective camera, explain how images change when moving a camera and show how to find the camera pose from images. We will demonstrate the theory in practical tasks of panorama construction, finding the camera pose, adding a virtual object to a real scene and reconstructing a 3D model of a scene from its images.
Research in deep learning for algebraic geometry:
Investigation how deep neural networks could be used to train fast solvers (i.e. mappings of input coefficients to output solutions) for multi-view geometry problems.
Generating examples by simulations and use slow algebraic solvers to obtain data that would be efficiently "remembered and interpolated" by Neural Networks.
Validating the proposed method on synthetic and real data.