Fit a plane to a depth image

I have a depth image which I can visualize using the surf function as below.

Image = double(imread('Image.png'));
surf(Image, 'EdgeColor', 'none');

Here, the image dimension is 200X300; so it has 200 rows and 300 columns. This is the output of the surf.

View-1:

View-2

View-3 (I would like to have a fitted plane like this gray plane)

Since the value of the pixels are quite scattered, I would like to fit a plane (similar to the gray rectangle shown on view-3) to this image. I tried to use the fit function, but didn't work. What should I do fit the image points to a plane. Any suggestions?