Cell migration is a key feature for living organisms. Image analysis tools are useful in studying cell migration in three-dimensional (3-D) in vitro environments. We consider angiogenic vessels formed in 3-D microfluidic devices (MFDs) and develop an image analysis system to extract cell behaviors from experimental phase-contrast microscopy image sequences. The proposed system initializes tracks with the end-point confocal nuclei coordinates. We apply convolutional neural networks to detect cell candidates and combine backward Kalman filtering with multiple hypothesis tracking to link the cell candidates at each time step. These hypotheses incorporate prior knowledge on vessel formation and cell proliferation rates. The association accuracy reaches 86.4% for the proposed algorithm, indicating that the proposed system is able to associate cells more accurately than existing approaches. Cell culture experiments in 3-D MFDs have shown considerable promise for improving biology research. The proposed system is expected to be a useful quantitative tool for potential microscopy problems of MFDs.