Vascular segmentation is often required in medical image analysis for various imaging modalities. Despite the rich literature in the field, the proposed methods need most of the time adaptation to the particular investigation and may sometimes lack the desired accuracy in terms of true positive and false positive detection rate. This paper proposes a general method for vascular segmentation based on locally connected filtering applied in a multiresolution scheme. The filtering scheme performs progressive detection and removal of the vessels from the image relief at each resolution level, by combining directional 2D-3D locally connected filters (LCF). An important property of the LCF is that it preserves (positive contrasted) structures in the image if they are topologically connected with other similar structures in their local environment. Vessels, which appear as curvilinear structures, can be filtered out by an appropriate LCF set-up which will minimally affect sheet-like structures. The implementation in a multiresolution framework allows dealing with different vessel sizes. The outcome of the proposed approach is illustrated on several image modalities including lung, liver and coronary arteries. It is shown that besides preserving high accuracy in detecting small vessels, the proposed technique is less sensitive with respect to noise and the presence of pathologies of positive-contrast appearance on the images. The detection accuracy is compared with a previously developed approach on the 20 patient database from the VESSEL12 challenge.