  Image segmentation is an inherently ill-posed problem and thus requires
regularization in order to limit the search space to reasonable solutions. A
majority of segmentation methods integrates these regularization terms in one
way or the other in an energy functional using a balancing term. The tuning of
this parameter that either favours more the regularization or the data
conformity is critical and, unfortunately, the success of the optimization
process strongly depends on it. Often the optimal settings change from image to
image. In this paper we propose a novel general framework based on an adaptive
eigenspace that was first proposed for solving inverse problems. The resulting
method proves accurate and yields robust results, without the need for
optimization techniques or being sensitive to the parameter choice. In fact,
the method solves a symmetric positive definite sparse system and hence, uses
only a fraction of the computational cost. The method is very versatile and
does not need parameter-tuning, when segmenting objects from any kind of an
image or when segmenting different organs. As the adaptive eigenspace is
determined directly from the image to segment, the approach also does not need
a tedious training phase.
