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Automatic segmentation of cell nuclei is an essential step in image cytometry and histometry. Despite substantial progress, there is a need to improve accuracy, speed, level of automation, and adaptability to new applications. This paper presents a robust and accurate novel method for segmenting cell nuclei using a combination of ideas. The image foreground is extracted automatically using a graph-cuts-based binarization. Next, nuclear seed points are detected by a novel method combining multiscale Laplacian-of-Gaussian filtering constrained by distance-map-based adaptive scale selection. These points are used to perform an initial segmentation that is refined using a second graph-cuts-based algorithm incorporating the method of alpha expansions and graph coloring to reduce computational complexity. Nuclear segmentation results were manually validated over 25 representative images (15 in vitro images and 10 in vivo images, containing more than 7400 nuclei) drawn from diverse cancer histopathology studies, and four types of segmentation errors were investigated. The overall accuracy of the proposed segmentation algorithm exceeded 86%. The accuracy was found to exceed 94% when only over- and undersegmentation errors were considered. The confounding image characteristics that led to most detection/segmentation errors were high cell density, high degree of clustering, poor image contrast and noisy background, damaged/irregular nuclei, and poor edge information. We present an efficient semiautomated approach to editing automated segmentation results that requires two mouse clicks per operation.