Direct Linear Transformation (DLT) Algorithm

Problem

• Given 2D to 2D point correspondences {$x_i <=> x'_i$} Compute a 3x3 matrix $H$ such that

• The Number of required measurements

Degree-of-freedom: $dof(H) = 8$, a point-to-point correspondence => 2 constraints

To estimate Homography parameters, at least four point-to-point correspondences are required.

Equatinos from a point-to-point correspondences could be drived from:

Then, we could do Singular Value Decompostion to estimate $h$

This method is quite Simple, Linear and Fast.

But!!! Bad performance

So, people came up with better idea to estimate the parameters in terms of cost fuction (Geometric Interpretation of Reprojection Error)