RNDr. Martin Bujk, PhD 
is the place where I'm pushing the state-of-the-art further...
Contact address:
Karlovo namesti 13, 121 35 Praha 2,
Czech Republic
Tel.: +420-224-355-732
Fax: +420-224-357-385
ICQ: 229-585-902
E-mail: bujnam1@cmp.felk.cvut.cz
Center for Machine Perception
Department of Cybernetics
Faculty of Electrical Engineering
Czech Technical University in Prague
Computational and Cognitive
Vision Systems: A Training
European Network
Research interests
My Phd thesis
My master thesis
About me

Research interests:
  • Camera pose estimation, Relative camera motion, Structure from motion
  • Methods for solving systems of polynomial equations
  • Shape from video, Stereo matching (wide/near baseline), Tracking
  • Real-time rendering, Image based rendering
  • Classification and recognition
My PhD thesis:

Algebraic solutions to absolute pose problems


Estimating internal and external camera calibration is a very basic element in many computer vision applications. Camera localization, structure from motion, scene reconstruction, object localization, tracking and recognition are just a few examples of such applications. This thesis focuses on minimal algorithms for estimating camera calibration, i.e. algorithms which use all possible constraints and minimal number of inputs, for example point correspondences between 2D and 3D space, to calculate the camera pose and other camera parameters such as unknown focal length or coefficients modeling lens distortion.
    In this work, we first study the absolute pose problem for a calibrated camera, which was an intensively studied problem in the past and many solutions were already developed. The problem itself can be formulated as a simple system of polynomial equations. Researches in the past focused on how to solve this problem, searched for different solutions, compared numerical stability, speed, or studied how to calculate the camera pose from more than three 2D-to-3D point correspondences. We review the state-of-the-art and present our own formulations to this problem based on the well known invariants and properties of the problem. We provide solutions to our formulations using different methods for solving system of polynomial equations. Next we provide solutions to the absolute pose for a camera without complete internal calibration or for a camera where some additional information about the scene is known. In particular, absolute pose of a camera calibrated up to an unknown focal length or a camera with unknown focal length and unknown radial distortion. Furthermore, we describe special cases when some of the scene or camera priors are known, for example, scene is planar, scene is non-planar or when vertical direction of a camera is known from a gyroscope or a vanishing point. The main contribution of this thesis is in finding minimal or finding optimal solutions to these problems. We formulate all studied problems, from very basic relations between 3D space and 2D measurements, show different formulations and how can different invariants be helpful in reducing the number of unknowns or to simplify the problem. All our formulations lead to systems of polynomial equations. We show how to solve these systems using methods for solving systems of polynomial equations, which we developed during our research. Solution the problems are evaluated with high level of detail and with focus on important properties such as numerical stability and resistance to noise in data. We compare our new solvers with the state-of-the-art on synthetic and real data.
    In this thesis we further present a general method which speeds up most of the presented solvers and can be also used to speed up other solvers based on eigenvalue computation. We have also found the connection between methods for converting basis of an ideal to a basis with respect to the lexicographic ordering and calculation of the characteristic polynomial of an action matrix.

Download (6.4MB pdf)  |  Introduction

Live & demo:
[[ Minimal problems in computer vision ]]
  • ( new ) Kukelova Z., Bujnak M., Heller J., Pajdla T., Singly-Bordered Block-Diagonal Form for Minimal Problem Solvers, ACCV 2014, Singapore, November, 2014. >> [pdf] <<
    Best Paper Honourable Mention
  • Kukelova Z., Bujnak M., Pajdla T., Real-time solution to the absolute pose problem with unknown radial distortion and focal length, ICCV 2013, Sydney, Australia, December, 2013. [pdf | code ]
  • Kukelova Z., Bujnak M., Pajdla T., Fast and stable algebraic solution to L2 three-view triangulation, 3DV 2013, Seattle, USA, June, 2013. [pdf | code ]
  • Bujnak M., Kukelova Z., Pajdla T., Making minimal solvers fast, CVPR 2012, Providence, USA, June 16-21, 2012. [pdf]
  • Bujnak M., Kukelova Z., and Pajdla T.. Efficient solutions to the absolute pose of cameras with unknown focal length and radial distortion by decomposition to planar and non-planar cases. IPSJ Transaction on Computer vision and Applications, 2012.
  • Kukelova Z., Bujnak M., Pajdla T., Polynomial Eigenvalue Solutions to Minimal Problems in Computer Vision. IEEE Trans. Pattern Analysis and Machine Intelligence, 2012, In Press, DOI: 10.1109/TPAMI.2011.230 [html] [pdf]
  • Bujnak M., Kukelova Z., Pajdla T., New efficient solution to the absolute pose problem for camera with unknown focal length and radial distortion, ACCV 2010, Queenstown, NZ, November 8-12, 2010. [pdf] [code]
  • Kukelova Z., Bujnak M., Pajdla T., Closed-form solutions to the minimal absolute pose problems with known vertical direction, ACCV 2010, Queenstown, NZ, November 8-12, 2010. [pdf] [code 2pt] [code 3pt]
  • Torri A., Kukelova Z., Bujnak M., Pajdla T., The six point algorithm revisited, Computer Vision in Vehicle Technology: From Earth to Mars, ACCV 2010 Workshop, Queenstown, NZ, November 8-12, 2010.
  • Bujnak M., Kukelova Z., and Pajdla T. 3D reconstruction from image collections with a single known focal length. ICCV 2009, Kyoto, Japan, September 29 - October 2, 2009. [pdf]
  • Bujnak M., Kukelova Z., and Pajdla T. Robust focal length estimation by voting in multiview scenes. ACCV 2009, Xi'an, China, September, 2009. [pdf]
  • Kukelova Z., Bujnak M., Pajdla T., Automatic Generator of Minimal Problem Solvers, ECCV 2008, Marseille, France, October 12-18, 2008. [pdf] [code]
  • Kukelova Z., Bujnak M., Pajdla T., Polynomial eigenvalue solutions to the 5-pt and 6-pt relative pose problems, BMVC 2008, Leeds, UK, September 1-4, 2008. [pdf] [5pt] [6pt]
  • Bujnak, M., Kukelova, Z., and Pajdla, T. A general solution to the p4p problem for camera with unknown focal length. CVPR 2008, Anchorage, Alaska, USA, June 2008. [pdf] [code]
  • Bujk, M., ra, R., An Efficient Deterministic Algorithm for The Sparse Correspondence, CVWW 2008
  • Bujk, M., ra, R., Randomized and Deterministic Approaches to The Sparse Correspondence Problem, PhD Thesis Proposal, August 2007
  • Bujk, M., ra, R., A Robust Graph-Based Method for The General Correspondence Problem Demonstrated on Image Stitching. ICCV 2007, Rio de Janeiro, Brazil, October 14-20, 2007. [pdf]
  • Bujk, M., ra, R.: An application of Strict Sub-Kernels in a Sparse Correspondence Problem, CMP Research report CTU-CMP-2007-18
  • Bujk, M., Dense reconstruction from uncalibrated video, Rigorous Thesis, Commenius university, Bratislava 2005 [pdf]
  • Bujk, M., Reconstructing 3D mesh from video sequence, MSc Thesis, Commenius university, Bratislava 2005 [web]
  • Bujk, M., Incremental method for structure and motion problem, SVK2005, FMFI UK, Bratislava 2005
  • Bujk, M., On-line structure from motion, in proc. of CESCG 2005
Expect people to be better than they are; it helps them to become better.
But don't be disappointed when they are not; it helps them to keep trying.

-- Merry Browne
About me:
  • 2005 - 2013 - PhD student at Center for Machine Perception, CVUT, Prague under VisionTrain project
  • 2005 Defense of Rigorous thesis at Faculty of Mathematics, Physics and Informatics, Comenius university in Bratislava, Computer science, specialization computer graphics, parallel computations.
  • 2000 2005 Faculty of Mathematics, Physics and Informatics, Comenius university in Bratislava, Computer science, specialization computer graphics, parallel computations.
  • 1996 2000 Juraj Hronec school, mathematical class

  • MS Visual C++ 2003/2005/2008, Delphi/Pascal, Java, SQL, HTML, PHP, JavaScript, X86 assembler, Visual Basic, C#, SmallTalk
  • .NET, COM+, MFC, ATL, GDI+, Win32Api, Open GL, DirectX
  • Matlab, Maple, Macaulay, Wincocoa, MathCad
  • 3D Studio Max, TrueSpace, AutoCAD, Cinema4D, Maya, Photoshop, Flash
  • office applications : Microsoft Office, TeX
  • driving license B (car).
Other activities / projects:

My journey at Microsoft, Live labs and Xbox, where I worked on projects related to photosynth and latter made XBox avatars to live out of the console.
Latest version of evi engine was integrated under comercial application Movis. Movis is successfully used for real-time visualizations of architecture / large scale projects.
Activities under corporation DataExpert ltd which I co-founded.
Before I've started my PhD study I was in a team developing a new generation of TrueSpace modeling and colaboration tool at Caligari Corporation.
LiteRay is a raytracer with addons like global illumination and ambient occlusions.
Computer graphics lecture project at FMFI-UK Bratislava.
Parallely communicating grammars used to generate 2D and 3D objects.
A project for Fractals and Procedural modeling lectures at FMFI-UK Bratislava.
A simple animation I did for Computer animation course at FMFI-UK Bratislava. I hope you will like it.
A simple multimedia project - flash game - for Multimedia and Flash course at FMFI-UK.
A 6-DOF Real-time rendering 3D engine with dynamic lights, shadows and rigid body physics.
Active X component implementation of evi engine for Micorosft Internet Explorer.
BDMspy (Background debug mode spy) is a tool for debugging Motorola's MCU in the BDM mode.
LiteTalk - is an untyped, interpreted scripting language, based on "C" syntax.
A simple RayTracer for SmalTalk object-oriented language.

by Martin Bujnak © 2013. All rights reserved.