Understanding the "Demon's Algorithm": 3D Non-rigid Registration by Gradient Descent

The "Demons Algorithm" in increasingly used for non-rigid registrationof 3D medical images. However, if it is fast an d usually accu- rate, the algorithm is based onin tuitive ideas about image registration and it is difficult to predict when it will fail and why. We show in this paper that this algorithm canbe considered as anapproximationof a sec- ond order gradient descent on the sum of square of intensity differences criterion. We also reformulate Gaussian and physical model regulariza- tions as minimization problems. Experimental results on synthetic and 3D Ultrasound images show that this formalization helps identifying the weak points of the algorithm and offers new research openings.