What is the meaning of D(x,l) or D(x,f(x)) in here?

Question

I was reading this paper https://arxiv.org/pdf/1312.6199.pdf and I couldn't understand what D(x,l) means.

My interpretation of the objective function is as follows.

r : noise
x : image
l : label

Minimize the noisy image r such that its addition to the image x results in the new image being classified as l. The following sentence then uses the term D(x,l) and I still don't get what it means after spending some time reading it.

Answer 1

I think I finally understood it. D(x,l) is the distortion function such that x is classified as l or intuitively, the intensity I need to add to each pixel such that the resulting image gets classified as l. That is why D(x,f(x)) = f(x) because the distortion function to have x be classified as f(x) is simply f(x)