Errors in digital area measurement of regular 2D figures
Dennis Rosen · Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE · 1993
When an area is measured digitally, by the pixels it encloses or by the lattice points it overlaps, there is invariably an error in the recorded value. The determination of that error is a long-standing problem in the field of geometric probability and a relatively recent problem in applications of computer vision. This paper deals with the errors associated with the digital measurement of rectangles, including squares; it is presented as a contribution to digital geometry, but its relevance is to automated visual inspection. The results show that for a rectangle aligned on the co-ordinate lattice at a fixed angle, the error varies with size of rectangle according to a near-parabola function; and for a rectangle of fixed size rotated by a small amount about that initial angle, the error varies according to a near-sinc function.