Regularization in Image Non-Rigid Registration: I. Trade-off between Smoothness and Intensity Similarity

In this report, we first propose a new classification of non-rigid registratio- n algorithms into three main categories: in one hand, the geometric algorithms- , and in the other hand, intensity based methods that we split here into standard intensity-based (SIB) and pair-and-smooth (P&S) algorithms. We then focus on the subset of SIB and P&S algorithms that are competitive, i.e. that use a regularization energy which is minimized together with the intensity similarity energy. In SIB algorithms, these two energies are combined in a weighted sum, and thus the trade-off between them is direct. P&S algorithms alternates their respective minimization, leading to the characteristic two steps: pairing of points, and smoothing. We theoretically compare the behavior of SIB and P&S algorithms, and more precisely, we explain why in practice the smoothness of the transforms estimated by SIB algorithms is non-uniform, thus difficult to control, while P&S algorithms estimate a motion that is more uniformly smooth. We give an example illustrating this behavior. Very few P&S algorithms minimize a global energy. We therefore propose a new image registration energy whose minimization leads to a \PAS algorithm. This energy is general, and can use any existing similarity or regularization energy. Its behavior is also compared to the previous SIB and \PAS algorithms. This new energy allows uniformly smooth solutions, as for our previous P&S algorithm, while preventing registration of non-informative, noisy areas, as for SIB algorithms

Recalage non rigide d'images médicales volumiques : contributions aux approches iconiques et géométriques

Non-rigid image registration is a classical problem in computer vision that consists in deforming one image so that it follows the geometry of another image. Registration techniques are very numerous, and are generally classified according to the kind of features they use in the images to deform them. On one hand, intensity-based algorithms use the intensity of the images. On the other hand, geometric algorithms use geometric features segmented from the images, such as object boundaries. In this thesis, we first show that this classification is not fine enough to explain some fundamental differences between some registration algorithms. We propose to part the intensity-based algorithms in two classes : we distinguish between the standard intensity based (SIB) algorithms, and the intensity feature based (IFB) algorithms. We introduce a general registration energy for iconic feature registration; then, we develop particular instances of this energy with special properties according to the application : additional geometric constraints obtained from a segmentatio- n, non uniform bias invariance, vectorial regularization with cross-effects between coordinates, invariance by exchange of the images to be registered. We give applications of our algorithm in brain tracking in volumetric ultrasound image sequences, in inter-subject brain registration using magnetic resonance imaging, and in shape-and-intensity interpolation.Le recalage non rigide d'images est un problème classique en vision par ordinateur qui revient à déformer une image afin qu'elle ressemble à une autre. Les techniques existantes, très nombreuses, sont généralement répertoriées selon l'information utilisée pour le recalage. D'un côté les algorithmes iconiques utilisent l'intensité des images. De l'autre, les algorithmes géométiques utilisent des amers géométriques extraits des images, comme les bords d'un objet. Dans cette thèse, nous montrons d'abord que cette classification n'est pas assez fine pour expliquer certaines différences fondamentales dans le comportement de certains algorithmes. Nous proposons de ce fait de diviser la classe des algorithmes iconiques en deux : nous distinguons d'une part les algorithmes iconiques standard, et d'autre part les algorithmes de recalage d'amers iconiques. Nous introduisons une énergie générale de recalage d'amers iconiques, puis nous développons des instances particulières de cette énergie ayant des propriétés spéciales selon l'application visée : ajout de contraintes géométriques supplémentaires, invariance au biais non uniforme, régularisation vectorielle avec des effets croisés, invariance par échange des images. Nous montrons des applications de nos algorithmes en suivi du mouvement dans des séquences échographiques tridimensionnelles, en relage intersujet de cerveaux, et en interpolation de formes et d'intensités

How to trade off between Regularization and Image Similarity in Non-rigid Registration?

International audienceno abstrac

Regularization in Image Non-Rigid Registration: I. Trade-off between Smoothness and Intensity Similarity

In this report, we #rst propose a new classi#cation of non-rigid registration algorithms into three main categories: in one hand, the geometric algorithms, and in the other hand, intensity based methods that we split here into standard intensity-based #SIB# and pairand -smooth #P&S# algorithms

Isotropic energies, filters and splines for vectorial regularization

International audienceno abstrac

Regularization in Image Non-Rigid Registration: I. Trade-off between Smoothness and Intensity Similarity

In this report, we first propose a new classification of non-rigid registration algorithms into three main categories: in one hand, the geometric algorithms, and in the other hand, intensity based methods that we split here into standard intensity-based (SIB) and pair-and-smooth (P&S) algorithms. We then focus on the subset of SIB and P&S..

Symmetrization of the Non-Rigid Registration Problem using Inversion-Invariant Energies: Application to Multiple Sclerosis

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

Symmetrization of the Non-Rigid Registration Probem using Inversion-Invariant Energies: Application to Multiple Sclerosis

International audienceno abstrac