How can one implement the fisheye lens effect illustrated in that image:

One can us
Just for the record:
This effect is a type of radial distortion called "barrel distortion".
For more information please see:
http: //en.wikipedia.org/wiki/Distortion_(optics)
Here is a different method to apply an effect similar to barrel distortion using texture mapping (adapted from MATLAB Documentation):
[I,map] = imread('logo.gif');
[h,w] = size(I);
sphere;
hS = findobj('Type','surface');
hemisphere = [ones(h,w),I,ones(h,w)];
set(hS,'CData',flipud(hemisphere),...
'FaceColor','texturemap',...
'EdgeColor','none')
colormap(map)
colordef black
axis equal
grid off
set(gca,'xtick',[],'ztick',[],'ytick',[],'box','on')
view([90 0])
This will give you the circular frame you are looking for but the aliasing artifacts might be too much to deal with.