Geometry for Computer Vision 2014 (6hp)
The course topics are representations for various types of geometric objects in geometry (such as points, lines, transformations, constraints) and how to estimatimate these representations from measurments in images, typically of point coordinates.
The course starts with two lectures on basic projective, and epipolar geometry. The remaining six lectures cover a selection of more recent techniques and methods that are widely used in the Computer Vision community. These six lectures are each accompanied by a scientific paper that should be read by the participants before the lecture.
- [IREG] "Introduction to Representations and Estimation in Geometry" by Klas Nordberg.
- [HZ] "Multiple View Geometry in Computer Vision" by Hartley and Zisserman . If you are on campus you can use this link to browse the electronic version
The first lecture is on Tuesday April 29, 10:15 - 12:00 in Seminar room Signalen (Buidling B, map). The subsequent lectures will be one per week, on Tuesday 10:15 - 12:00, in Signalen, except on Tuesday June 3 when the lecture is in Algoritmen.
|1||Introduction to projective spaces, homogeneous coordinates in 2D+3D, points, lines, planes, transformations, homographies, camera matrices. Klas||
ch 1 - 7
HZ: ch 2, 3, 4, 6
|2||Epipolar geometry: fundamental matrix, triangulation, rectification, degeneracies from planes, transfer. Klas||
HZ: ch 9
|3||Estimation theory: DLT, data normalization, algebraic & geometric errors, Maximum-likelihood, RANSAC, Generalized Hough Transform, Mean-shift. Klas||
ch 10 - 15
HZ: ch 4, 11
Camera calibration: Zhang's calibration plane, self-calibration. Oriented epipolar geometry.
Chum, Werner, Matas
|Affine geometry, multi-body factorization, LCV. Klas|
Mutli-view and multi-point geometry. Trifocal tensor. 6-point geometry.
ch 15 - 7
|Calibrated multi-view geometry: 5-point problem, bundle adjustment. Per-Erik||
ch 14.3, 17
HZ: ch 9
Triggs et al.
Relative pose, estimation of rigid transformations, Procrustes. PnP, P3P.
Kneip, Scaramuzza, Siegwart
|Sample consensus strategies: LO-RANSAC, preemptive RANSAC, PROSAC & DEGENSAC. Per-Erik|
Representations of 3D rotations: exp of so(3), quaternions, Rodrigues.
HZ: ch A4.3
|Smoothing of SO(3) and SE(3). SLeRP, and splines on SO(3). Per-Erik|
|8||Rolling shutter and push-broom cameras: geometry and calibration. Per-Erik||Ringaby&Forssén|
- Short question seminars on the literature after lectures 4-8.
- Short (<2h) written examination on concepts from the lectures. See this old exam for an example of what type of questions to expect.
- Small programming project (2hp) at the end of the course. Own or proposed projects.
Last updated: 2014-10-22