Automated thresholding approaches have normally been applied to gray-level intensity images to differentiate between objects and the background in the image. This paper investigates the use of an entropy-based thresholding approach for determining a reasonable threshold value for an intensity gradient in an edge tracking algorithm and a threshold value for the lengths of edges extracted from an image. The histograms of the intensity gradient of an edge and the lengths of edges generally peak very quickly at low values and quickly drop as their values increase. The entropy-based thresholding technique is adequate for determining a reasonable threshold value for these type of histograms, particularly since it computes the point at which the information content of the two sides of the histogram is a maximum. The paper also demonstrates the importance of reapplying the threshold determination algorithm on different parts of the image, since the threshold value is relative to the distribution in a region of interest. The effects of sparse data on the computation of the threshold are investigated and an example is presented demonstrated the strong impact that sparse data can have.