To derive explicit expressions for the matrices *D* and *D*' in terms
of the fundamental matrix *F*, let us reconsider the above argument.
Let *F*=*UWV*^{t} be the Singular Value Decomposition of *F*. Here, *U*and *V* are orthogonal, and *W* is a diagonal matrix with diagonal
values *r*, *s*, 0. We can write this as follows:

Define

Hence,

Now explicitly compute the *d*_{ij} in order to use equation
(5.5). Decompose *A* and *A*' by rows:

Then,

We can write these equations directly in terms of the SVD of the fundamental matrix.

where is the

where is the

Our problem has five degrees of freedom. Each pair of images provides two independent constraints. From three images we can form three pairs which provide three pairs of constraints. This is enough to solve for all the variables in

The difficulty of such purely algebraic approaches explains why alternative approaches have been explored for self calibration. [10] provides one such alternative. In any case, an algebraic solution can only ever provide the essential first step for a more refined bundle adjustment (error minimization) process.