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(Nlog(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.

This paper addresses the problem of detecting features running along lines or piecewise constant curves. Our method is adapted either for common image features like edges or ridges as well as any kind of features that can be designed by a priori knowledge. The main contribution of this paper is to unify the well-known Beamlet transform, introduced by Donoho et al, with linear filtering technique in order to define what we call the feature-adapted Beamlet transform. If the desired feature is chosen to belong to the class of steerable filters, our method can be achieved in linear time and can be easily implemented on a parallel machine. We present some experimental results both on edge- and ridge-like features that demonstrate the substantial improvement over classical feature detectors.

This paper presents a new method for computing the feature-adapted Radon and beamlet transforms in a fast and accurate way. These two transforms can be used for detecting features running along lines or piecewise constant curves. The main contribution of this paper is to unify the fast slant stack method, introduced in [2], with linear filtering technique in order to define what we call the feature-adapted fast slant stack. If the desired feature is chosen to belong to the class of steerable filters, our method can be achieved in 0(N log(iV)), where N = n2is the number of pixels. This new method leads to an efficient implementation of both feature-adapted radon and beamlet transforms, that outperforms our previous works. Our method has been developed in the context of biological imaging to detect image features lying along curves like edges or ridges as well as any kind of features that can be designed by a priori knowledge.