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 = n² is 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.