Section: New Results
Medical Image Analysis
Segmentation of anatomical structures of the lower abdomen for radiotherapy planning
This work is performed in the framework of the European project MAESTRO (Methods and Advanced Equipment for Simulation and Treatment in Radio Oncology), in collaboration with DOSIsoft SA, Cachan.
We are interested in the automatic delineation of anatomical structures of the lower abdomen in the frame of dose calculation for conformational radiotherapy. We approach the segmentation issue as a process of fitting a series of 3D deformable templates to the contours of anatomical structures.
Deformable models : Many deformable surface representations have been proposed for model–based segmentation of medical images. Among existing representations, we use the discrete simplex meshes for their simple geometry and their ability to define shape constraints in a computationally efficient manner.
Images : For our study, we rely on a database of tomodensitometric (CT) images of male patients' lower abdomens, and first apply this method to the segmentation of the bladder, which is one of the structures of interest.
The bladders in our database images are very heterogeneous: while some of them present an homogeneous intensity that is quite similar to that of the background, others show both high and low intensity zones due to the presence, to a smaller or greater degree, of a contrast agent. Since we need a fully automatic segmentation algorithm, we must be able to determine what type of bladder is present in each image and follow the necessary (and often different) steps in each of the cases.
Outline of the method
Initially, we perform some preliminary treatments (see  for more details) and compute a series of parameter values that describe the structure of interest for each patient. We determine whether the image shows the presence of a contrast agent or not, and whether the bladder's intensity is homogeneous or not.
A binary approximation of the structure is then computed in order to guide the preliminary stages of deformation (both local and global) of a simplex mesh. The model undergoes several deformations, guided by regularizing forces and also by image-derived forces, so that it can adjust to the structure's boundaries. Further details can be found at  .
The parameter values are then refined and used in a more precise step in the mesh deformation process. If the bladder was found to be non–homogeneous, the mesh is divided into zones that respond to different forces, in order to account for these intensity inhomogeneities.
It is now the image itself, and not the initial binary approximation, together with a histogram based force that we have devised to this end, that guide the model's last deformation stage.
If needed, the final automatic result may be manually improved by an expert.
In order to validate the approach, we use a set of CT images that have been segmented by medical experts. These handmade contours act as "ground truth", allowing for an objective evaluation of the performance of the algorithm.
Work in progress
We are now working on the joint segmentation of the bladder and the prostate by the competitive, simultaneous deformation of two simplex meshes.
Log-Euclidean Polyaffine Transformations
In 2003, we introduced a novel kind of geometrical transformations, named polyrigid and polyaffine. These transformations efficiently code for locally rigid or affine deformations with a small number of intuitive parameters. They can describe compactly large rigid or affine movements, unlike most free-form deformation classes. Very flexible, this tool can be readily adapted to a large variety of situations, simply by tuning the number of rigid or affine components and the number of parameters describing their regions of influence  .
This year, we presented a novel framework, called Log-Euclidean polyaffine , which drastically simplifies our previous framework and guarantees strong invariance properties. In particular, the inverse of a (Log-Euclidean) polyaffine transformation is polyaffine, and the (Log-Euclidean) polyaffine fusion of affine components is invariant with respect to a change of coordinate system. The nice mathematical properties of these transformations allow to compute them very efficiently as well as their inverses on regular grids. Details about the theory and the efficient numerical algorithms are available in  . Results were presented at the international workshop of Biomedical image Registration WBIR'06  , and used to design efficient non-linear registration algorithms such as  (see also Section 6.2.3 ).
Locally Affine Registration Framework for the Registration of Anatomical Structures
In collaboration with DOSIsoft SA, Cachan, Centre Antoine Lacassagne, Nice and Institut Gustave Roussy, Villejuif.
The planning of conformal radiotherapy requires accurate localizations of the tumor and the critical structures. In existing planning systems, the segmentation of brain structures is manual. An automatic segmentation algorithm of all the critical structures in a patient image is then an invaluable tool for radiotherapy.
In order to segment all these structures in a specific patient image, we use an anatomical atlas containing labels of the structures of the brain. The atlas was manually labeled from an artificial MR image (obtained from the BrainWeb). The first step of the general segmentation method is an affine matching between the atlas and the patient MRI (usually T1). The recovered transformation is then refined using non-rigid registration, and applied to the atlas labelization in order to obtain a segmentation of the patient image.
The transformations obtained using dense registration algorithms such as  are however often noisy, leading to irregular contours. These do not reflect the shapes expected for the structures. To overcome this problem, we have introduced in  a locally affine registration framework allowing to use an a priori on the structures we want to register. This is done by using a transformation parameterized by local affine transformations defined on regions. Thanks to the use of a Log-Euclidean regularization and of the fast polyaffine framework  , we ensure a smooth and invertible transformation, while using an efficient optimization scheme.
Thanks to this method, we obtain results that are much smoother than with a classical dense registration method (see images (c) and (d) on figure 6 ). The structures have indeed shapes corresponding to the ones expected by the clinicians. The algorithm is also much more robust to local perturbations in the images (see the eyes on figure 6 ). Finally, this work is currently being validated in clinical conditions at Institut Gustave Roussy  ,  .
Evaluation of Atlas Construction Strategies for Head and Neck Atlas Construction
In collaboration with DOSIsoft SA, Cachan and Université Catholique de Louvain
Atlas-based segmentation has been shown to be very efficient to delineate brain structures. A major localization of cancers is the head and neck region (7 % of all cancers). It would then be of great interest to use an anatomical atlas of this area to help the clinicians with the therapy planning.
However, on this part 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 an 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.
Since the atlas is designed to delineate structures, we have presented in  a framework based on the evaluation of the automatic delineations obtained from the constructed atlas. This allows us to evaluate both the registration method used to build the atlas, and the one used to deform it on an individual image. This is obtained by first leaving one image out of the dataset used to build the atlas. Then, using the manual delineations of this image and the automatic segmentations obtained by the atlas registration, we can compute quantitative measures (sensitivity and specificity) of the atlas quality.
Thanks to this method, we have developed an anatomical atlas of the head and neck region, illustrated on figure 7 , images (a), (b) and (c). We obtain good segmentation results (see images (d), (e), (f) in figure 7 for a qualitative view) thanks to the use of a constrained transformation (locally affine) followed by a dense registration method.
Evaluation of skull-stripping methods and atrophy measurements on magnetic resonance images
This work finds a direct application in the Qualicore project (evaluation of cognitive troubles and quality of life of multiple sclerosis patients) and is performed in close collaboration with Christine Lebrun (Neurology Department), at Pasteur Hospital, Nice.
Our previous work aimed at detecting lesion in MRI images  . However, the lesion load is not correlated to the pathology evolution, and the cerebral atrophy seems to be a better indicator. We have therefore developed tools to measure this atrophy independently in the cortex, the cerebellum and the brain stem. Our method relies on the previous classification results into Gray Matter (GM), White Matter (WM), Cerebro Spinal Fluid (CSF) and lesions  . It has appeared that the classification step as well as the atrophy measurements, are very sensitive to a preliminary step, called skull stripping, which aimed at isolating the brain in the image. Using the Staple probabilistic framework  , a comparative study of five skull stripping methods has been done in the case of relapsing remitting multiple sclerosis  . Methods were run on 30 sets of MRI sequences (T1, T2 FSE, PD). From these five segmentations, the Staple algorithm was used to give a probabilistic reference segmentation for each set. This segmentation was visually validated by an expert and compared with manual delineation when possible.
The Staple framework allowed to assess any segmentation method, by its sensitivity and its specificity. All methods and method combinations have been tested. A method combination binary segmentation was obtained by an automatic optimized thresholding of the corresponding Staple probabilistic segmentation.
The (sensitivity-specificity) measurement ranges from (0.838-0.763) to (0.985-0.993) for all methods and combination of methods. Considering additional information (average execution time, software installation facility, robustness... ), the best segmentation is a combination of only three methods with (0.980-0.951). This new method has been tested and validated by an expert on all database sets.
Thanks to  and morphological operations, the last step was to divide the mask given by this skull stripping method in three regions of interest : cortex, cerebellum and brain stem.
Using the previous classification results, we compute brain atrophy. Future works will study the sensitivity of this measure and compare atrophy measurements obtained on the study database subjects with atrophy measurements available in the literature.