The majority of machine vision systems derive their input data by digitising an image to produce a square grid of sampled points. However, other sampling techniques can represent equal picture information in a smaller number of samples, with a consequent reduction in data rate. Several workers have looked at regular hexagonal sampling of images which produces optimum data rates for a given information content. Previous work on hexagonal sampling by the authors and others, has shown that image processing operators are computationally more efficient, and as accurate, as their square counterparts. Historically, one factor which has lead to the predominance of square sampling in vision systems, is that this produces images which are more visually pleasing to human observers. This paper describes an investigation of machine vision systems performing industrial inspection tasks, which suggests that in such applications, hexagonal systems out-perform square systems. In particular hexagonal operators can follow tight curves more accurately, allowing better surface defect detection. A surprising observation of this work was that with such images, hexagonal sampling also gave images which were more visually pleasing to human operators. The paper presents a study of sampling point geometry and operator design. Details are given of an implementation of a set of hexagonal, grey-scale operators for use in pipeline or other image processing systems, and a comparison of square and hexagonal techniques has been made. Results of operations on real and simulated surface defect images are given for both sampling systems and the requirement for a defect detection figure of merit identified.