The instantaneous coefficient of variation (ICOV) edge detector, based on normalized gradient and Laplacian operators, has been proposed for edge detection in ultrasound images. In this paper, the edge detection and localization performance of the ICOV-squared (ICOVS) detector are examined. First, a simplified version of the ICOVS detector, the normalized gradient magnitude squared, is scrutinized in order to reveal the statistical performance of edge detection and localization in speckled ultrasound imagery. Both the probability of detection and the probability of false alarm are evaluated for the detector. Edge localization is characterized by the position of the peak and the 3-dB width of the detector response. Then, the speckle-edge response of the ICOVS as applied to a realistic edge model is studied. Through theoretical analysis, we reveal the compensatory effects of the normalized Laplacian operator in the ICOV edge detector for edge-localization error. An ICOV-based edge-detection algorithm is implemented in which the ICOV detector is embedded in a diffusion coefficient in an anisotropic diffusion process. Experiments with real ultrasound images have shown that the proposed algorithm is effective in extracting edges in the presence of speckle. Quantitatively, the ICOVS provides a lower localization error, and qualitatively, a dramatic improvement in edge-detection performance over an existing edge-detection method for speckled imagery.