How Much Confidence Do We Have in a MRI Tractography Experiment?

When performing a tractography experiment it is essential to know whether a reconstructed tract results from the diffusion signal itself or from some random effect or noise. In this study, we introduce a way to associate to every connection a confidence level. The reason why the latter greatly varies with the length of the tract is analyzed. We use this method to filter out the connections likely to be the result of noise and show the effect on the connectivity of the human visual system

A Variational Model for Object Segmentation Using Boundary Information, Statistical Shape Prior and the Mumford-Shah Functional

In this paper, we propose a variational model to segment an object belonging to a given scale space using the active contour method, a geometric shape prior and the Mumford-Shah functional. We define an energy functional composed by three complementary terms. The first one detects object boundaries from image gradients. The second term constrains the active contour to get a shape compatible with a statistical shape model of the shape of interest. And the third part drives globally the shape prior and the active contour towards a homogeneous intensity region. The segmentation of the object of interest is given by the minimum of our energy functional. This minimum is computed with the calculus of variations and the gradient descent method that provide a system of evolution equations solved with the well-known level set method. We also prove the existence of this minimum in the space of functions with bounded variation. Applications of the proposed model are presented on synthetic and medical images

Geometric Moments in Scale-Spaces

In this paper we present a generalization of geometric moments in scale-spaces derived from the general heat diffusion equation, with a particular interest for th

Affine invariant Matching Pursuit-based shape representation and recognition using scale-space

In this paper, we propose an analytical low-level representation of images, obtained by a decomposition process, here the matching pursuit (MP) algorithm, as a new way of describing objects through a general continuous description using an affine invariant dictionary of basis functions. This description is used to recognize objects in images. In the learning phase, a template object is decomposed, and the extracted subset of basis functions, called meta-atom, gives the description of our object. We then extend naturally this description into the linear scale-space using the definition of our basis functions, and thus bringing a more general representation of our object. We use this enhanced description as a predefined dictionary of the object to conduct an MP-based shape recognition (MPSR) task into the linear scale-space. The introduction of the scale-space approach improves the robustness of our method, and permits to avoid local minima problems encountered when minimizing a non-convex energy function. We show results for the detection of complex synthetic shapes, as well as natural (aerial and medical) images

Laplacian Operator, Diffusion Flow and Active Contour on non-Euclidean Images

We propose here some basic approaches to direct processing of the $360^o$-images as we take into consideration the geometry of each one. Obviously, the geometry of each of these images is a consequence of the geometry of the sensor's mirror used. This technical report is organized as follows: In the first section we develop the Laplacian operator on non-Euclidean manifolds. First we start by derivation of Laplacian operator on Riemannian manifolds and than we derive it explicitly for each of the non-Euclidean manifolds of our interest, i.e. hyperboloid, sphere and paraboloid. This allows us to implement the gradient and diffusion flow on hyperbolic and spherical image. For testing this techniques, a synthetic and a real image was used in the case of hyperboloid and sphere respectively. Then we demonstrate the active contour on non-Euclidean images. First it was derived by directly minimizing the energy functional where the specific geometry of the non-Euclidean image was taken into account. Then the same was proofed through Polyakov action. We give some examples in each of the cases and so derive conclusions about the influence of the geometry for each particular case