How to detect, using matlab, the center of the biggest circle?
Would the built-in function imfindcircles work for you?  The radius and center are both returned. The examples are included in the same page. The function is based on Hough transform so it might be an overkill.

Another much faster method is regionprops. You may use this function only after binarizing the image first, and that means there must be a contrast difference between the region inside and outside the circle. You may try something like this (copied from this post):

st = regionprops( ~BW, 'Area', 'Centroid', 'PixelIdxList' );

sel = [st.Area] &gt; numel(BW)*0.5; % exclude the small regions
st = st(sel);

cntr = .5 * [size(BW,2) size(BW,1)]; % Compute region distance to center of image
d = sqrt( sum( bsxfun(@minus,vertcat( st.Centroid ), cntr ).^2, 2 ) );

[mn idx] = min(d); % pick the region closest to center

res = false(size(BW)); 
res( st(idx).PixelIdxList ) = true; % the region outside the circle is 
                                      set to false, thus excluded


Note that in the code above, cntr = .5 * [size(BW,2) size(BW,1)]; assumes the circle is in the center of the whole image. You need to estimate the rough position of the circle in your case as a prior knowledge and change this line. 

Several assumptions mentioned above make the regionprops option more tricky than imfindcircles.