Understanding the "Demon's Algorithm": 3D non-rigid registration by gradient descent

The "Demons Algorithm" in increasingly used for non-rigid registration of 3D medical images. However, if it is fast and usually accurate, the algorithm is based on intuitive ideas about image registration and it is difficult to predict when it will fail and why. We show in this paper that this algorithm can be considered as an approximation of a second order gradient descent on the sum of square of intensity differences criterion. We also reformulate Gaussian and physical model regularizations 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.