  Image segmentation is to separate an image into distinct homogeneous regions
belonging to different objects. It is an essential step in image analysis and
computer vision. This paper compares some segmentation technologies and
attempts to find an automated way to better determine the parameters for image
segmentation, especially the connectivity value of $\lambda$ in
$\lambda$-connected segmentation.
  Based on the theories on the maximum entropy method and Otsu's minimum
variance method, we propose:(1)maximum entropy connectedness determination: a
method that uses maximum entropy to determine the best $\lambda$ value in
$\lambda$-connected segmentation, and (2) minimum variance connectedness
determination: a method that uses the principle of minimum variance to
determine $\lambda$ value. Applying these optimization techniques in real
images, the experimental results have shown great promise in the development of
the new methods. In the end, we extend the above method to more general case in
order to compare it with the famous Mumford-Shah method that uses variational
principle and geometric measure.
