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Aligning Shapes

We now have our set of shapes in a common representation. However, we first have to remove the degrees of freedom corresponding to position, orientation, and scale, as mentioned above. The method most commonly used is Procrustes analysis. The generalised Procrustes procedure was developed in 1991. Procrustes analysis translates, rotates and scales each shape, so as to minimise the sum of squared distances between corresponding landmarks. Having aligned all the shapes, the mean shape is then obtained by simply averaging the position of each corresponding landmark across the whole set of shapes.

Figure: Landmark identification and mark-up in medical images