Conventional deterministic algorithms (i.e., skeletonization and edge-detection) lack robustness and sensitivity to reliably detect the neurite elongation and branching of low signal-to-noise-ratio microscopy images. Neurite outgrowth experiments produce an enormous number of images that require automated measurement; however, the tracking of neurites is easily lost in the automated process due to the intrinsic variability of neurites (either axon or dendrite) under stimuli. We have developed a stochastic random-reaction-seed (RRS) method to identify neurite elongation and branching accurately and automatically. The random-seeding algorithm of RRS is based on the hidden-Markov-model (HMM) to offer a robust enough way for tracing arbitrary neurite structures, while the reaction-seeding algorithm of RRS secures the efficiency of random seeding. It is noteworthy that RRS is capable of tracing a whole neurite branch by only one initial seed, so that RRS is proficient at quantifying extensive amounts of neurite outgrowth images with noisy background in microfluidic devices of biomedical engineering fields. The method also showed notable performance for reconstructing of net-like structures, and thus is expected to be proficient for biomedical feature extractions in a wide range of applications, such as retinal vessel segmentation and cell membrane profiling in spurious-edge-tissues.