Abstract. 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.
Abstract. In this article we merge point feature and intensity-based registration in a single algorithm to tackle the problem of multiple brain registration. Because of the high variability of the shape of the cortex across individuals, there exist geometrical ambiguities in the registration process that an intensity measure alone is unable to solve. This problem can be tackled using anatomical knowledge. First, we automatically segment and label the whole set of the cortical sulci, with a non-parametric approach that enables the capture of their highly variable shape and topology. Then, we develop a registration energy that merges intensity and feature point matching. Its minimization leads to a linear combination of a dense smooth vector field and radial basis functions. We use and process differently the bottom line of the sulci from its upper border, whose localization is even more variable across individuals. We show that the additional sulcal energy improves the registration of the cortical sulci, while still keeping the transformation smooth and one-to-one.
Abstract. Without any prior knowledge, the non-rigid registration of two images is a symmetric problem, i.e. we expect to find inverse results if we exchange these images. This symmetry is nonetheless broken in most of intensity-based algorithms. In this paper, we explain the reasons why most non-rigid registration algorithms are asymmetric. We show that the asymmetry of quadratic regularization energies causes an oversmoothing of expending regions relatively to shrinking regions, hampering in particular registration-based detection of evolving processes. We therefore propose to use an inversion-invariant energy to symmetrize the registration problem. To minimize this energy, two methods are used, depending on whether we compute the inverse transformation or not. Finally, we illustrate the interest of the theory using both synthetic and real data, in particular to improve the detection and segmentation of evolving lesions in MR images of patients suffering from multiple sclerosis.
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