Essential Matrix and Pose
From F to E in calibrated coordinates, its decomposition into four motions, and the cheirality test.
Key Terms
Essential MatrixCalibrated CoordinatesE = [t]x RSVD DecompositionFour-Fold AmbiguityCheirality
Python Tools
OpenCVNumPyMatplotlib
Textbook Reference
Szeliski Ch.11Hartley & Zisserman Ch.9-11
Topics Covered
- 1Normalized image coordinates and the relation E = K'^T F K
- 2Structure of E: two equal singular values and E = [t]x R
- 3Decomposing E into four candidate rotation and translation pairs
- 4Cheirality check: selecting the solution with points in front of both cameras
- 5Relative pose from the essential matrix and degenerate motions
Learning Outcomes
- Relate the essential and fundamental matrices through the intrinsics
- Decompose E into rotation and translation up to scale
- Resolve the four-fold ambiguity using the cheirality condition
Lecture PDFs
Essential Matrix and Pose
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