The notion of tangential cover, based on maximal segments, is a well-known tool to study the geometrical characteristics of a discrete curve. However, it is not adapted to noisy digital contours. In this paper, we propose a new notion, named Adaptive Tangential Cover, to study noisy digital contours. It relies on the meaningful thickness, calculated at each point of the contour, which permits to locally estimate the noise level. The Adaptive Tangential Cover is then composed of maximal blurred segments with appropriate widths, deduced from the noise level estimation. We present a parameter-free algorithm for computing the Adaptive Tangential Cover. Moreover an application to dominant point detection is proposed. The experimental results demonstrate the efficiency of this new notion.