Colour Constant Image Sharpening

In this paper, we introduce a new sharpening method which guarantees colour constancy and resolves the problem of equiluminance colours. The algorithm is similar to unsharp masking in that the gradients are calculated at different scales by blurring the original with a variable size kernel. The main difference is in the blurring stage where we calculate the average of an n times n neighborhood by projecting each colour vector onto the space of the center pixel before averaging. Thus starting with the center pixel we define a projection matrix onto the space of that vector. Each neighboring colour is then projected onto the center and the result is summed up. The projection step results in an average vector which shares the direction of the original center pixel. The difference between the center pixel and the average is by definition a vector which is scalar away from the center pixel. Thus adding the average to the center pixel is guaranteed not to result in colour shifts. This projection step is also shown to remedy the problem of equiluminance colours and can be used for $m$-dimensional data. Finally, the results indicate that the new sharpening method results in better sharpening than that achieved using unsharp masking with noticeably less halos around strong edges. The latter aspect of the algorithm is believed to be due to the asymmetric nature of the projection step.