Live-cell imaging technology using fluorescent proteins (green fluorescent protein and its homologues) has revolutionized the study of cellular dynamics. But tools that can quantitatively analyse complex spatiotemporal processes in live cells remain lacking. Here we describe a new technique--fast multi-colour four-dimensional imaging combined with automated and quantitative time-space reconstruction--to fill this gap. As a proof of principle, we apply this method to study the re-formation of the nuclear envelope in live cells. Four-dimensional imaging of three spectrally distinct fluorescent proteins is used to simultaneously visualize three different cellular compartments at high speed and with high spatial resolution. The highly complex data, comprising several thousand images from a single cell, were quantitatively reconstructed in time-space by software developed in-house. This analysis reveals quantitative and qualitative insights into the highly ordered topology of nuclear envelope formation, in correlation with chromatin expansion - results that would have been impossible to achieve by manual inspection alone. Our new technique will greatly facilitate study of the highly ordered dynamic architecture of eukaryotic cells.