Epipolar Geometry
Projective Constraints and Spatial Reconstruction in Stereo Vision
Vol. I · Part 04
The Fundamental Constraint
The Fundamental Matrix F encapsulates the algebraic representation of epipolar geometry between two uncalibrated views. It relates corresponding points in stereo images through a rigorous projective constraint.
Given a point in the primary image plane, its correspondence in the secondary view is constrained to a singular Epipolar Line. This search-space reduction is the cornerstone of efficient stereo matching algorithms.
Awaiting Matrix Computation
Plate 4.1 — Visualization of Epipolar Line Constraints
Principles of Triangulation
To reconstruct the depth of a scene, we must reverse the projection process. Through Triangulation, we project rays from the optical centers through matching image coordinates. The intersection of these rays in Euclidean space defines the 3D position of the point.
Plate 4.2 — Ray Intersection and Coordinate Crystallization
Spatial Reconstruction via
When camera intrinsics are known, we employ the Essential Matrix E to recover the precise relative pose of the stereo pair. This enabling step allows for the generation of metric 3D point clouds.
Awaiting Stereo Epipolar Geometry
Plate 4.3 — Sparse 3D Point Cloud Generation