Benoit Tremblais

A fast multi-scale edge detection algorithm

In this paper we present a new explicit numerical scheme to approximate the solution of the linear diffusion filtering. This scheme is fast, stable, easy to program, applicable to arbitrary dimensions, and preserves the discontinuities of the objects. Experimental results support the efficiency of the proposed approach for the multi-scale detection of edges in greyscale, and color images.

A fast multiscale edge detection algorithm based on a new edge preserving PDE resolution scheme

In this communication we present a new explicit numerical scheme to approximate the solution of the linear diffusion filtering. It allows to introduce a new edge preserving scheme which is fast, stable, easy to program and applicable to any dimensions. Our diffusion scheme is then put into a simple and original multi-scale edge detection algorithm. Some experimental results of the proposed approach for the multi-scale detection of edges in grey scale images are presented, as well as a comparison with other diffusion filtering schemes.

A multiscale approach for the extraction of vessels

In this communication we propose a new and automatic strategy for the multiscale centerlines detection of vessels. So we wish to obtain a good representation of the vessels, that is a precise characterization of their centerlines and their diameters. The adopted solution requires the generation of an image scale-space in which the various levels of details allow to treat arteries of any diameter. The method proposed here is implemented using the Partial Differential Equations (PDE) formalism and those of differential geometry. The differential geometry permits by the computation of a new measure of valley to characterize locally the centerlines of vessels as the image surface bottom lines of valleys. The informations given by the centerlines and valley measure scale spaces are used to obtain the 2D multiscale centerlines of the coronary arteries. In that purpose we construct a multiscale adjacency graph which permits to keep the K strongest (according to the valley measure) detections. Then the obtained detection is coded as an attributed graph. So the medical practitioner can act and choose the most interesting arteries for the future 3D reconstruction. Finally, we test our process on several digital coronary arteriograms, and some retinal angiographies.

Vector Fields Modelization Using Basis of Polynomials: Application to the Analysis of Simple Face Movements

In this communication we present an original and general model for the approximation of vector fields and especially displacement vector fields. The proposed method uses the orthonormal multivariate polynomials framework to approximate vector fields as combinations of these particular functions. Then we demonstrate the noise robustness of our model. And finally we show that the model can efficiently be used for the recognition of simple face movement in a Webcam acquired sequence

A fast n-dimensional nonlinear filter

In this communication, we propose an original approach for the diffusion paradigm in image processing. Our starting point is the iterative resolution of partial differential equations (PDE) according to the explicit resolution scheme. We simply consider that this iterative process is nothing but a fixed point search. So we obtain a convergence condition which applies to a large set of image processing PDE. That allows to introduce a new smoothing process with strong abilities to preserve any structure of interest in the images. As an example we choose a linear isotropic diffusion for the denoising performances. Thus while resolving the equation of isotropic diffusion and by using an adaptive resolution parameter, we obtain a filtering process which can preserve arbitrary dimension object edges as one-dimensional signals, gray level images, color images, volumes, films, etc. We show the edge localization preserving property of the process. And we compare the complexity of the process with the Perona and Malik explicit scheme, and the Weickert AOS scheme. We establish that the computational effort of our scheme is lower than this of the two others. For illustration, we apply this new process to denoising of different kinds of medical images.

Multivalue image curvatures: application to color image denoising and feature detecting

In the present work we modelize multi-values 2D images as surfaces embbeded in space-features space. Using the differential geometric framework we then introduce an original definition of multi-values image curvatures. First we use these curvatures to detect valleys and ridges in color images. Then we generate a new non-linear color scale space based on a mean curvature flow. It leads to a powerful tool for denoising color images.

A multiscale medial axis detection of coronary arteries in X-rays angiographies

In the present work we are concerned with the assistance to the diagnostic of coronaries stenosis from X-rays angiography modality. We are treating here the problem of the 2D multiscale medial axis segmentation.

PDE-based approach for medial axis detection in x-ray angiographies

In the present work we deal with the assistance to the diagnostic of coronaries stenosis from X-rays angiographies. Our goal is a 3D-reconstruction of the coronarian tree, therefore the extraction of some 2D characteristics is necessary. Here, we treat the problem of the 2D vessels medial axis extraction. The vessels geometry looks like valleys embedded in the image surface. Using differential geometry we can locally characterize medial axis as bottom lines of valleys. However, we have to calculate the image local derivatives, which is an ill-posed and noise sensitive problem. To overcome this drawback, we use a PDE based approach. We first consider the PDEs numerical scheme as an iterative method known as fixed point search. So, we obtain a new method which assure the stability of the resolution process. The combinaison of this method an appropriate PDE generates a scale-space where we can detect arteries of various diameters. We use then the eigenvalues and eigenvectors of the Weingarten endomorphism to define a new valley-ness measure. We have tested this technique on several angiographies, where the medial axis have well been extracted, even in presence of strong stenosis. Furthermore, the extracted axis are one pixel large and quite continuous.