The common way to study microtubule dynamics in microscopy image sequences is to track the growing ends of microtubules. However, this strategy may fail for dense microtubules due to numerous ambiguities in point association. We suggest that detecting and tracking full length microtules, instead of tracking their extremities only, would provide substantial information to resolve these ambiguities. In this paper, we propose a first part toward that end by introducting a fully automated detection method of full length microtubules, with a statistical control of false detections. It is based on the Feature-adapted Beamlet transform which has been successfully used for filament detection [1]. We provide three improvements to our previous work: i) a normalization of beamlet coefficients, ii) a scale-dependent thresholding of beamlets and iii) a novel beamlet chaining algorithm, adapted to microtubules images.