I want to extract an elliptical region from an image (a portion of a face portion from an image) preferably in MATLAB: 

For example, in this image, I want to extract the region within red boundary.
Can anyone help me with this ? 

 Answers:

Cropping is easy, all you have to do is apply a proper mask. The trick is to create such a mask.

Assuming A is your image, try this: 

%# Create an ellipse shaped mask
c = fix(size(A) / 2);   %# Ellipse center point (y, x)
r_sq = [76, 100] .^ 2;  %# Ellipse radii squared (y-axis, x-axis)
[X, Y] = meshgrid(1:size(A, 2), 1:size(A, 1));
ellipse_mask = (r_sq(2) * (X - c(2)) .^ 2 + ...
    r_sq(1) * (Y - c(1)) .^ 2 <= prod(r_sq));

%# Apply the mask to the image
A_cropped = bsxfun(@times, A, uint8(ellipse_mask));

The cropped image will be stored in A_cropped. Play with the coordinates of the center and the values of the radii until you get the desired result.

EDIT: I extended the solution for RGB images (if matrix A is 3-D).