In this paper, we present an entropic edge-detection method based on the Jensen-Shannon divergence, applied to grey level histograms obtained by sliding a window over an image. For every pixel in the image, we calculate the elements of a divergence matrix and a direction matrix, via spline approximation. Based on these estimated matrices, a new technique for thinning and linking unconnected edge pixels is also described. The global method is found to be an excellent technique for image segmentation. For example, it is very robust against noise, and it is especially appropriate in the interfacial tension measures obtained by means of contour images of liquid drops. Results show a better performance than others methods used in this field.