Quantization error in regular grids: triangular pixels

Quantization of the image plane into pixels results in the loss of the true location of features within pixels and introduces an error in any quantity computed from feature positions in the image. We derive closed-form, analytic expressions for the error distribution function, the mean absolute error (MAE), and the mean square error (MSE) due to triangular tessellation, for differentiable functions of an arbitrary number of independently quantized points, using a linear approximation of the function. These quantities are essential in examining the intrinsic sensitivity of image processing algorithms. Square and hexagonal pixels were treated in previous papers. An interesting result is that for all possible cases 0.99<D¯_T/D¯S<1.13, where D¯_T and D¯_S are the MAE in triangular and square tessellations