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Abstract

The central difference along a selected axis through a point (u, v) of a rectangularly-sampled luminance field and at an arbitrary angle .alpha. is computed by interpolation. The octant in which the selected axis lies is identified, and first and second pixels through which the lines that limit the identified octant .Iadd.extend .Iaddend.are identified. The first and second pixels are adjacent each other in the luminance field array and lie on a common ordinate or a common abscissa. .[.The difference between the luminance values of the first and second pixels is calculated..]. Third and fourth pixels, which are symmetrically disposed with respect to the first and second pixels respectively about the point (u, v), are identified.[., and the.]..Iadd.. The .Iaddend.difference in luminance values of the .Iadd.first and .Iaddend.third .[.and fourth.]. pixels is calculated.Iadd., and the difference in luminance values of the second and fourth pixels is calculated.Iaddend.. The central difference along the selected axis is calculated by applying the MIX operator to the two difference values and a mix ratio coefficient which is the tangent of an angle which is related to .alpha. and multiplying the result by a factor proportional to the cosine of that angle.

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