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

Suppose, a 2D image is represented by g(x,y).

Then, what does it mean by "Gradient of g(x,y)", "Divergence of g(x,y)" and "Curl of g(x,y)"?

Please, avoid formal math for explanations.

Please, use layman's terms and informal discussions.

• The deleted answer was a perfect answer to your question. If you want to know something else, you should formulate your question in a way that people here can actually understand what it is that you need to know. Nobody wants to waste time on answering a badly formulated question. – Matt L. Mar 19 '16 at 12:43
• @MattL., I updated my question. – user18425 Mar 19 '16 at 12:49

## Original Image

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.

• Bro, no offence, but, your formal texts are already available in DIP books. I am here to have some informal knowledge. – user18425 Mar 19 '16 at 12:26
• Great answer! If you could elaborate and add intuition, it will be perfect. Especially the practical meaning of each symbol. – Royi Apr 15 '16 at 8:27