Complete Signal Representation With Multiscale Edges

Whilst the greatest effort has been made to ensure the quality of this text, due to the historical nature of this content, in some rare cases there may be minor issues with legibility. We introduce the most important mathematical results in the text but leave the proofs in appendices. The transition between models based on functions of continuous variables to discrete computations is often delicate and can induce many errors. We tried to properly build this transi tion while leaving in appendices all the discrete algorithms.