Single View Geometry

Camera Calibration

Algorithm Camera Calibration

1. Prepare a calibration target/object, e.g. 2 orthogonal planes with a checkerboard pattern.
2. Position camera in front of target, capture image of the calibration target.
3. Find corners of the target in the image. Option1:
   • Detect edges with Canny detector.
   • Fit straight lines to detected linked edges (Hough).
   • Intersect lines to obtain 2D image coordinates
   • Match image corners & 3D target checkerboard corners.
   • Result: 2D–3D correspondences. Option2:
   • Apply a corner detector directly (Harris, Susan, FAST).
4. Derive constraints on camera matrix.

Attention

3D points cannot all be on the same plane.

Algorithm Direct Linear Transformation

Algorithm Normalised Direct Linear Transformation Objective: Given $n\ge 6$ 2D–3D point correspondences $\{{\mathbf{x}}_i\leftrightarrow {\mathbf{X}}_i\}$, determine the $3\times 4$ projection matrix $\mathbf{P}$ such that ${\mathbf{x}}_i\approx \mathbf{P}{\mathbf{X}}_i$.

1. Normalise 2D and 3D points: ${\tilde{\mathbf{x}}}_i=\mathbf{T}{\mathbf{x}}_i$, ${\tilde{\mathbf{X}}}_i=\mathbf{S}{\mathbf{X}}_i$.
2. Apply the DLT algorithm to $\{{\mathbf{x}}_i\leftrightarrow {\mathbf{X}}_i\}$.
3. Denormalize the recovered solution $\tilde{\mathbf{P}}$ using $\mathbf{P}={\mathbf{T}}^{-1}\tilde{\mathbf{P}}\mathbf{S}$.

Recovering The Camera Intrinsics