The authors consider the properties of putative \(C^1\) solutions of the Perona-Malik equation (which arises in computer vision). They argue that the formation of discontinuities observed in numerical computations is merely gradual and that the solution should approach a minimum of a relaxed functional. However, (i) the Perona-Malik equation does not have \(C^1\) solutions for general \(C^1\) data; (ii) discontinuities are essential in the application to computer vision, because they are related to enhanced edges; (iii) the relaxed functional in this case is identically zero; (iv) jump discontinuities do appear immediately and not gradually in practice.