DLT (Direct Linear Transform) algorithm

1. Definition of DLT

DLT is an algorithm for solving the least squares problem with scale problems.

The standard form of DLT problem solving is:

Another form of expression is:

Or

This model is often encountered in projection geometry.

For example, the pinhole camera projection model, 3D point to the image plane projection relationship;

The single-response matrix (homography) in two-view geometry;

2. DLT Solution

Because the scale exists, it cannot be solved directly by the linear homogeneous least squares method.

from (1) (2) The formula shows that the direction is the same, that is, the result of the fork is 0:

The (3) is represented by a cross-multiplication matrix:

For the (4) type, refer to: vector fork multiplication and cross multiplication matrix

A linear homogeneous least squares solution problem can be obtained by the variant of the (4) equation. Can refer to: least squares

3. Example

By formula (4):

Expand

Written in the form of a matrix:

which

DLT (Direct Linear Transform) algorithm