What Does It Mean by Gradient / Divergence / Curl of a 2D Image $ g \left( x, y \right) $?
Original Image



Image Gradient

The gradient shows how quickly the color (or greyscale) changes from pixel to pixel. In very "busy" images, the gradient will change much. In areas of less color change, the gradient will be close to zero. 

In the image above, the petals don't change color very much so the gradient is close to zero (or small). At the edges of the petals where the color changes from purple to green, the gradient is large.



Image Divergent

In the sense of image processing, it is the inverse of gradient, this is a indicate of minor gray scale variation.In this aproach i used the channel Red and Green as vector field



Image Curl

Its a like a circular motion of variation of pixels. The curl operation measures the tendency of rotation around the point itself.