On quantization errors in computer vision

The author considers the error resulting in the computation of multivariable functions h(X₁, X, . . ., X_n), where all the X_is are only available in the quantized form. In image processing and computer vision problems, the variables are typically a mixture of the spatial coordinates and the intensity levels of objects in an image. A method is introduced using a first-order Taylor series expansion together with a periodic extension of the resulting expression and its Fourier series representation so that the moments and the probability distribution function of the error can be computed in closed form. This method only requires that the joint probability density function of X_i s be known and makes no assumption on the behavior on the quantization errors of the variables. Examples are also given where these results are applied