Energy function

The energy function currently used by Seamstress is an approximate measure of the gradient parallel to the x and y axes of a slightly blurred version of the input image.

If $\mathbf{I}$ is the original image, then the energy of that image can be defined as

$$E(\mathbf{I}) = \vert\frac{\partial\mathbf{I}^\prime}{\partial{x}}\vert + \vert\frac{\partial\mathbf{I}^\prime}{\partial{y}}\vert$$

where $\mathbf{I}$ is the result of the convolution

$$\mathbf{I}^\prime = c e^\frac{-(x^2+y^2)}{\sigma^2} \ast \mathbf{I}$$

with $\sigma=1$ and $c$ is a normalizing constant.