Prevent singular estimates

[axelpale]

Let the domain be [[-1,0],[1,0]] and the range [[0,-1],[0,1]]. The in other words the plane rotates 90 degrees.

Let us apply TS estimator. The estimate becomes { a: 0, b: 0, x: 1, y: 0 } which means that all points map to [1,0].

This is optimal behavior in a sense that it maps the domain as close to the range as possible. However, is this desired behavior? The singularity causes information loss. It maps the whole space to a point and therefore it is not anymore an affine transformation but an affine map. Should we promise that the estimates are always true affine transformations?

An approach that would satisfy the requirement is to fall back to translation if the linear transformation becomes singular. However, this causes a discontinuity at rotation angles near 90 degrees.

Another approach would always estimate a TSR and then extract the required part, TS.

[axelpale]

Maybe it is enough to document that S and TS are able to produce singular transformations.