A method of processing images in images comprising curvilinear structures comprises, in parallel, a step of filtering said images and a decision step intended to select the pixels of the images pertaining to a curvilinear structure, the method comprising, in parallel, a sub-step of estimating the direction of each image pixel, as well as a sub-step of analyzing the connectivity of neighboring pixels based on their directions at the end of the sub-step of estimating the direction of each image pixel, and a sub-step of selecting groups of pixels as a function of the result of the sub-step of analyzing the connectivity of neighboring pixels based on their directions, at the end of the step of filtering. Such a method allows selection of curvilinear structures which are fine structures such as a catheter in a medical image, or thicker structures such as a tree-like structure of blood vessels. This method may be used, for example, in medical scanning apparatus for detecting artery anomalies such as stenosis or a diffuse coronary disease.