along the flagellum in 3-D is not a simple matter since it requires: 1) sophisticated fluorescence imaging techniques dealing with low intensity and signal to noise ratio (SNR) and 2) tracing the flagellum's centerline. Most of the algorithms proposed to trace tubular structures have been developed for multi-branch structures not being adequate for single tubular structures with low SNR. Taking into account the prior knowledge that the flagellum is constituted by a single tubular structure, we propose an automatic method to trace and track multiple single tubular structures from 3-D images. First, an algorithm based on one-class classification allows enhancement of the flagellum. This enhanced 3-D image permits guiding an iterative centerline algorithm toward the flagellum's centerline. Each sperm is assigned an ID to keep track of it in 3-D . Our algorithm was quantitatively evaluated using a ground truth 564 semi-manual traces (six 3-D image stacks) comparing them to those obtained from state-of-the-art tubular structure centerline extraction algorithms. The qualitative and quantitative results show that our algorithm is extracting similar traces as compared with ground truth, and it is more robust and accurate to trace the flagellum's centerline than multi-branch algorithms.

This paper presents a new version of the camera-space-manipulation method (CSM). The set of nonlinear view parameters of the classic CSM is replaced with a linear model. Simulations and experiments show a similar precision error for the two methods. However, the new approach is simpler to implement and is faster.