Yaqing Ding presents Homography Decomposition Revisited
On 2026-05-25 11:00:00 at G205, Karlovo náměstí 13, Praha 2
**This seminar was postponed from May 19th to May 25th**
Homography refers to a specific type of transformation that relates two images
of the same planar surface taken from different perspectives. Recovering motion
parameters from a homography matrix is a classic problem in computer vision. It
is important to derive a fast and stable solution to homography decomposition,
since it forms a critical component of many vision systems, e.g., in
Structure-from-Motion and visual localization. The current state-of-the-art
solvers can be categorized into two types of methods: numerical procedures
based on singular value decomposition (SVD), and closed-form solutions.
SVD-based methods are generally stable but computationally expensive, while
existing
closed-form solutions are faster but may suffer from numerical instability.
In this talk, we first revisit the homography decomposition problem from a
different viewpoint. In contrast to existing methods that mainly exploit
algebraic properties of the homography matrix itself, we discuss an alternative
formulation based on a small set of point correspondences, which leads to a
conceptually simple closed-form solution with clear geometric interpretation.
We further analyze the configurations in which closed-form methods may become
unstable, and discuss practical strategies for balancing efficiency and
robustness in homography decomposition.
Paper link: https://link.springer.com/article/10.1007/s11263-025-02680-4
Secondly, we will briefly introduce the other topic related to solving
polynomial in computer vision. Specifically, we show that eliminating monomials
in the quaternion can lead to a more computationally efficient solution.
Paper link: https://ieeexplore.ieee.org/abstract/document/11062722
Homography refers to a specific type of transformation that relates two images
of the same planar surface taken from different perspectives. Recovering motion
parameters from a homography matrix is a classic problem in computer vision. It
is important to derive a fast and stable solution to homography decomposition,
since it forms a critical component of many vision systems, e.g., in
Structure-from-Motion and visual localization. The current state-of-the-art
solvers can be categorized into two types of methods: numerical procedures
based on singular value decomposition (SVD), and closed-form solutions.
SVD-based methods are generally stable but computationally expensive, while
existing
closed-form solutions are faster but may suffer from numerical instability.
In this talk, we first revisit the homography decomposition problem from a
different viewpoint. In contrast to existing methods that mainly exploit
algebraic properties of the homography matrix itself, we discuss an alternative
formulation based on a small set of point correspondences, which leads to a
conceptually simple closed-form solution with clear geometric interpretation.
We further analyze the configurations in which closed-form methods may become
unstable, and discuss practical strategies for balancing efficiency and
robustness in homography decomposition.
Paper link: https://link.springer.com/article/10.1007/s11263-025-02680-4
Secondly, we will briefly introduce the other topic related to solving
polynomial in computer vision. Specifically, we show that eliminating monomials
in the quaternion can lead to a more computationally efficient solution.
Paper link: https://ieeexplore.ieee.org/abstract/document/11062722