Minimizing energy function to find disparity

I would like to find the disparity between a stereo pair by minimizing the following:

In latex:

In plain text:

E(d) = \int_{\Omega} |I_1(x+d)-I_0(x)|^2 dx + \nabla d

where Omega is the image space, d is the disparity between image0 and image1 and \nabla d is a regularizer that enforces local smoothness in the disparity d.

I am not sure how to implement this in Matlab

Can anyone give hints as to how I can start. Thanks!