# Interpreting Image Processing Math Equation

I am reading "Image Processing and Analysis" by Chan and Shen, c 2005 SIAM. They introduce some notation I'm not 100% sure how to interpret:

$$u_0(x)=u(x)+n(x), x=(x_1,x_2) \in \Omega$$

They state $$u_0$$ represents a noisy image, $$u$$ is the clean image and $$n$$ is Gaussian white noise. I assume that $$x=(x_1,x_2)$$ is meant to convey that x is a two-dimensional vector indexing both image height and width. I don't know how to interpret $$\Omega$$. Is it meant to denote the entire image index range?

• $$\Omega$$ is the image domain, it can be either discrete or continuous. No idea how it is defined in that particular book.
• $$x=(x_1, x_2)$$ are the 2D image coordinates
• $$u_0, u, n$$ are functions that return intensity values at the given location $$x$$.