The 3D reconstruction of neuronal morphology is a powerful technique for investigating nervous systems. Due to the noises in optical microscopic images, the automated reconstruction of neuronal morphology has been a challenging problem. We propose a novel automatic neuron reconstruction algorithm, Rivulet, to target the challenges raised by the poor quality of the optical microscopic images. After the neuron images being de-noised with an anisotropic filter, the Rivulet algorithm combines multi-stencils fast-marching and iterative back-tracking from the geodesic farthest point on the segmented foreground. The neuron segments are dumped or merged according to a set of criteria at the end of each iteration. The proposed Rivulet tracing algorithm is evaluated with data provided from the BigNeuron Project. The experimental results demonstrate that Rivulet outperforms the compared state-of-the-art tracing methods when the images are of poor quality.