OPEN ACCESS
In this paper, we generalize the gradient vector flow field to vector-valued images. We base our method on the definition of a structure tensor that is calculated according to a blind estimation of contrast in the different channels and that exploits the whole spatiospectral information, hence reducing sensitivity to noise and better defining orientations of the force field. The resulting field takes profit of both magnitude and direction of the vectorvalued gradient. Applied to biological volume delineation in 3D dynamic Positron Emission Tomography (PET) imaging, we validate our method on realistic Monte Carlo simulations of numerical phantoms and present results on real dynamic PET data. Performances observed on such images confirm the potential of the proposed active surface approach for vector-valued data.
Extended Abstract
Deformable models like snakes have become popular in the field of image segmentation over the past 25 years. By iteratively deforming an evolving object superimposed onto the image domain, such techniques enable to accurately delineate regions of interest and to guarantee the smoothness of the resulting contours. There are relatively few edge-based deformable models dedicated to vector-valued images in which the additional information provided by the extra dimension available is exploited (Sapiro, 1996; Xie, Mirmehdi, 2004; Yang et al., 2005). In these methods, the gradient magnitude is used to characterize vector edges and is derived from the eigenvalues of a structure tensor that embeds the local orientations of the image features. While improving single-channel approaches, such methods only make use of the scalar information embedded in the structure tensor. Moreover, the influence of each channel should be weighted to favor the ones bearing the most relevant information.
In this paper, we design a new gradient vector flow scheme tailored for segmentation of vector-valued images. In our approach, edge information in each channel is weighted according to its relevance as calculated from a blind estimator of contrast, favouring channels in which the features of interest can be better detected. The proposed weighting scheme makes the method well adapted to modalities in which the different channels are affected by varying noise levels. From local structure analysis, we obtain not only scalar, but also vectorial information for identifying and propagating directions of the vector gradient. By performing nonlinear diffusion of both directions and magnitudes of the vector gradient, we produce a robust external force field able to drive deformable models toward vector edges.
We validate the proposed method quantitatively over four state of the art approaches of the literature on synthetic images and realistic simulations of dynamic PET images. Results suggest that incorporating directional information contained in the structure tensor in the diffusion scheme can improve segmentation quality over approaches that consider vector edges in a scalar way. Applied to a real dynamic PET image of a rat brain, our approach accurately located an injured functional region, illustrating the potential of the proposed method for pre-clinical or clinical applications.
RÉSUMÉ
Danscetarticle,nousgénéralisonsleflotdevecteursgradients(GVF)pourlesimages à valeurs vectorielles. Nous basons notre méthode sur la définition d’un tenseur de structure multicomposante pondéré par une estimation aveugle du contraste, exploitant l’intégralité de l’information spatio-spectrale pour réduire la sensibilité au bruit et affiner les orientations du champ de forces dans l’image. Le champ de forces ainsi produit tire profit des directions et amplitudes du gradient déduites de l’analyse de la structure locale. Appliquée à la segmentation de volumes biologiques en imagerie par tomographie d’émission de positrons (TEP) 3D dynamique, nous validons notre méthode sur des simulations Monte Carlo réalistes d’images TEP de fantômes numériques et présentons des résultats sur des images TEP dynamiques réelles. Les performances obtenues sur ce type d’images confirment l’intérêt de l’approche multicomposante de surfaces actives proposée.
3D segmentation, deformable models, dynamic PET
MOTS-CLÉS
segmentation 3D, modèles déformables, TEP dynamique.
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