Showing papers by "Olivier Commowick published in 2006"

A log-euclidean framework for statistics on diffeomorphisms

Abstract: In this article, we focus on the computation of statistics of invertible geometrical deformations (i.e., diffeomorphisms), based on the generalization to this type of data of the notion of principal logarithm. Remarkably, this logarithm is a simple 3D vector field, and is well-defined for diffeomorphisms close enough to the identity. This allows to perform vectorial statistics on diffeomorphisms, while preserving the invertibility constraint, contrary to Euclidean statistics on displacement fields. We also present here two efficient algorithms to compute logarithms of diffeomorphisms and exponentials of vector fields, whose accuracy is studied on synthetic data. Finally, we apply these tools to compute the mean of a set of diffeomorphisms, in the context of a registration experiment between an atlas an a database of 9 T1 MR images of the human brain.

A log-euclidean polyaffine framework for locally rigid or affine registration

Abstract: In this article, we focus on the parameterization of non-rigid geometrical deformations with a small number of flexible degrees of freedom . In previous work, we proposed a general framework called polyaffine to parameterize deformations with a small number of rigid or affine components, while guaranteeing the invertibility of global deformations. However, this framework lacks some important properties: the inverse of a polyaffine transformation is not polyaffine in general, and the polyaffine fusion of affine components is not invariant with respect to a change of coordinate system. We present here a novel general framework, called Log-Euclidean polyaffine, which overcomes these defects. We also detail a simple algorithm, the Fast Polyaffine Transform, which allows to compute very efficiently Log-Euclidean polyaffine transformations and their inverses on a regular grid. The results presented here on real 3D locally affine registration suggest that our novel framework provides a general and efficient way of fusing local rigid or affine deformations into a global invertible transformation without introducing artifacts, independently of the way local deformations are first estimated.

Evaluation of Atlas Construction Strategies in the Context of Radiotherapy Planning

Abstract: Radiotherapy planning requires accurate delineations of the critical structures. Atlas-based segmentation has been shown to be very efficient to delineate brain structures. On other parts of the body, using an atlas built from one single image as for the brain does not seem adequate, since the structures to be delineated are not clearly defined. Using only one image may then introduce undesirable bias. Building an atlas from a set of segmented images address this issue, but it will then depend on the choice of the registration method used to fuse the images. This point is generally not addressed in the literature, and is the aim of this article. Since the atlas is designed to delineate structures, we will evaluate together both the registration method used to build the atlas, and the one used to deform the built atlas on an individual image. We illustrate our framework on the construction of an atlas of the head and neck area. Using atlasbased segmentation to delineate critical structures in this area seems indeed very interesting, as a large part of the cancers (7 %) arise there. We compare the results obtained using three different methods on a real dataset of manually segmented images.

Statistics on Diffeomorphisms in a Log-Euclidean Framework

Abstract: In this article, we focus on the computation of statistics of invertible geometrical deformations (i.e., diffeomorphisms), based on the generalization to this type of data of the notion of principal logarithm. Remarkably, this logarithm is a simple 3D vector field, and can be used for diffeomorphisms close enough to the identity. This allows to perform vectorial statistics on diffeomorphisms, while preserving the invertibility constraint, contrary to Euclidean statistics on displacement fields.

An efficient locally affine framework for the registration of anatomical structures

Abstract: Non-rigid image registration has been widely developed over the last years. However, many registration techniques do not take into account any a priori information on the structures in the images. We present in this article a general locally affine registration framework, which allows us to register local areas in the images using affine transformations having few degrees of freedom. Thanks to our novel polyaffine framework and Log-Euclidean regularization, we ensure a smooth, coherent and invertible transformation all over the image. Remarkably, this is achieved very efficiently, even in 3D. We illustrate our method with two applications: bone registration in the lower abdomen area and critical brain structures registration.