Background: Due to the large amount of data produced by advanced microscopy, automated image analysis is crucial in modern biology. Most applications require reliable cell nuclei segmentation. However, in many biological specimens cell nuclei are densely packed and appear to touch one another in the images. Therefore, a major difficulty of three-dimensional cell nuclei segmentation is the decomposition of cell nuclei that apparently touch each other. Current methods are highly adapted to a certain biological specimen or a specific microscope. They do not ensure similarly accurate segmentation performance, i.e. their robustness for different datasets is not guaranteed. Hence, these methods require elaborate adjustments to each dataset. Results: We present an advanced three-dimensional cell nuclei segmentation algorithm that is accurate and robust. Our approach combines local adaptive pre-processing with decomposition based on Lines-of-Sight (LoS) to separate apparently touching cell nuclei into approximately convex parts. We demonstrate the superior performance of our algorithm using data from different specimens recorded with different microscopes. The three-dimensional images were recorded with confocal and light sheet-based fluorescence microscopes. The specimens are an early mouse embryo and two different cellular spheroids. We compared the segmentation accuracy of our algorithm with ground truth data for the test images and results from state-of-the-art methods. The analysis shows that our method is accurate throughout all test datasets (mean F-measure: 91 %) whereas the other methods each failed for at least one dataset (F-measure ≤ 69 %). Furthermore, nuclei volume measurements are improved for LoS decomposition. The state-of-the-art methods required laborious adjustments of parameter values to achieve these results. Our LoS algorithm did not require parameter value adjustments. The accurate performance was achieved with one fixed set of parameter values. Conclusion: We developed a novel and fully automated three-dimensional cell nuclei segmentation method incorporating LoS decomposition. LoS are easily accessible features that ensure correct splitting of apparently touching cell nuclei independent of their shape, size or intensity. Our method showed superior performance compared to state-of-the-art methods, performing accurately for a variety of test images. Hence, our LoS approach can be readily applied to quantitative evaluation in drug testing, developmental and cell biology.