Based on the assumptions of uniformity in scaling wrt. both axes and that sampling is taken at equal intervals of θ, changes in size of a shape result in changes in the amplitude values of the corresponding signature.
One way to normalize this is to scale all functions so that they always span the same range of values. e.g [0,1]
Main advantage is simplicity but serious disadvantage is that scaling of the entire function depends upon only two values: maximum & minimum.
If the shapes are noisy, error can occur.