How would I go about showing that the following Mumford Shah functional is not convex?
$$E_{MS}(u,C)= \int_{\Omega} |u_{0}(x,y) -u(x,y)|^{2}\ dx\ dy + \mu \int_{\Omega \backslash C}|\nabla u(x,y)|^{2}\ dx\ dy + \nu \operatorname{Length}(C) $$
where $\mu,\nu >0$ are constants, $C$ is a smooth closed curve, $\Omega \subset \mathbb{R}^{2}$ is some image domain, and $u_{0}$ is an image, and $u$ is a piecewise smooth approximation to the image.
Not really sure where to begin here, any guidance would be much appreciated.