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This paper presents a general method for detecting curvilinear structures, like filaments or edges, in noisy images. This method relies on a novel technique, the feature-adapted beamlet transform (FABT) which is the main contribution of this paper. It combines the well-known beamlet transform (BT), introduced by Donoho , with local filtering techniques in order to improve both detection performance and accuracy of the BT. Moreover, as the desired feature detector is chosen to belong to the class of steerable filters, our transform requires only O(N log(N)) operations, where N = n 2 is the number of pixels. Besides providing a fast implementation of the FABT on discrete grids, we present a statistically controlled method for curvilinear objects detection. To extract significant objects, we propose an algorithm in four steps: 1) compute the FABT, 2) normalize beamlet coefficients, 3) select meaningful beamlets thanks to a fast energy-based minimization, and 4) link beamlets together in order to get a list of objects. We present an evaluation on both synthetic and real data, and demonstrate substantial improvements of our method over classical feature detectors.