1. An image processing method; the method operating on image data, the image data defining an image that includes a first number of locations, the image having an image characteristic relative to each of the locations; the method measuring the image characteristic for the image to a degree of statistical significance; the method comprising steps of: for each of a second number of locations in the image, operating on the image data to obtain respective sample result data, each location's sample result data measuring the image characteristic relative to the location; each location's sample result data indicating a measurement in a direction extending from the location; the direction being the same for each location; each of the second number of locations being selected by: randomly obtaining location data indicating one of the locations in the first number of locations; the location data being randomly obtained in a way that can obtain data indicating any of the first number of locations and that would, over a sufficiently large group of locations, indicate locations evenly distributed among the first number of locations; and applying a criterion to the image data to determine whether to select the location indicated by the location data as one of the second number of locations; and combining the respective sample result data of the second number of locations to obtain image result data for the direction; the second number being smaller than the first number but sufficient that the image result data measure the image characteristic for the image to the degree of statistical significance.