Time-lapse confocal fluorescence microscopy images from mouse embryonic stem cells (ESCs) carrying reporter genes, histone H2B-mCherry and Mvh-Venus, have been used to monitor dynamic changes in cellular/differentiation characteristics of live ESCs. Accurate cell nucleus segmentation is required to analyse the ESC dynamics and differentiation at a single cell resolution. Several methods used concavities on nucleus contours to segment overlapping cell nuclei. Our proposed method evaluates not only the concavities but also the size and shape of every 2D nucleus region to determine if any of the strait, extrusion, convexity and large diameter criteria is satisfied to segment overlapping nuclei inside the region. We then use a 3D segmentation method to reconstruct simple, convex, and reasonably sized 3D nuclei along the image stacking direction using the radius and centre of every segmented region in respective microscopy images. To avoid false concavities on nucleus boundaries, fluorescence images of the H2B-mCherry reporter are used for localisation of cell nuclei and Venus fluorescence images are used for determining the cell colony ranges. We use a series of image preprocessing procedures to remove noise outside and inside cell colonies, and in respective nuclei, and to smooth nucleus boundaries based on the colony ranges. We propose dynamic data structures to record every segmented nucleus region and solid in sets (volumes) of 3D confocal images. The experimental results show that the proposed image preprocessing method preserves the areas of mouse ESC nuclei on microscopy images and that the segmentation method effectively segment out every nucleus with a reasonable size and shape. All 3D nuclei in a set (volume) of confocal microscopy images can be accessed by the dynamic data structures for 3D reconstruction. The 3D nuclei in time-lapse confocal microscopy images can be tracked to calculate cell movement and proliferation in consecutive volumes for understanding the dynamics of the differentiation characteristics about ESCs. LAY DESCRIPTION: Embryonic stem cells (ESCs) are considered as an ideal source for basic cell biology study and producing medically useful cells in vitro. This study uses time-lapse confocal fluorescence microscopy images from mouse ESCs carrying reporter gene to monitor dynamic changes in cellular/differentiation characteristics of live ESCs. To automate analyses of ESC differentiation behaviours, accurate cell nucleus segmentation to distinguish respective cells are required. A series of image preprocessing procedures are implemented to remove noise in live-cell fluorescence images but yield overlapping cell nuclei. A segmentation method that evaluates boundary concavities and the size and shape of every nucleus is then used to determine if any of the strait, extrusion, convexity, large and local minimum diameter criteria satisfied to segment overlapping nuclei. We propose a dynamic data structure to record every newly segmented nucleus. The experimental results show that the proposed image preprocessing method preserves the areas of mouse ESC nuclei and that the segmentation method effectively detects overlapping nuclei. All segmented nuclei in confocal images can be accessed using the dynamic data structures to be visualised and manipulated for quantitative analyses of the ESC differentiation behaviours. The manipulation can be tracking of segmented 3D cell nuclei in time-lapse images to calculate their dynamics of differentiation characteristics.