A satellite-image registration routine corrects for a change in the camera's…

PHYSICS · Multi-part · Fermi University Physics · Mathematical Methods for Physics · Linear algebra and vector spaces · Linear algebra and vector spaces

Mathematical Methods for Physics, Ch Matrices, determinants and systems of linear equations

Problem

A satellite-image registration routine corrects for a change in the camera's orientation between two passes over the same ground. It reports that a reference square with corners at the origin,

(1.0, 0)\,\mathrm{km}

(1.0, 1.0)\,\mathrm{km}

and

(0, 1.0)\,\mathrm{km}

is carried, with the origin fixed, so that the point originally at

(1.0, 0)\,\mathrm{km}

moves to

(0.60, 0.80)\,\mathrm{km}

and the point originally at

(0, 1.0)\,\mathrm{km}

moves to

(-0.80, 0.60)\,\mathrm{km}

. ((a)) Write the correction as a matrix

\mathsf{A}

, using the two reported image points. ((b)) Evaluate

\det\mathsf{A}

and say what it implies about the area of the ground patch after correction. ((c)) Decide whether

\mathsf{A}

is orthogonal, and say what that tells you about the nature of the correction the routine has found.

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