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## Quantization and Sampling

Abstract-Due to the important role that digitization error plays in the field of computer vision, a careful analysis of its impact on the computational approaches used in the field is necessary. In this paper we develop the mathematical tools for the computation of the average (or expected) error due to quantization. They can be used in estimating the actual error occurring in the implementation of a method. Also derived is the analytic expression for the probability density of error distribution of a function of an arbitrarily large number of indepen­ dently quantized variables. The probability of the error of the function to be within a given range can thus be obtained accurately. In analyz­ ing the applicability of an approach one must determine whether the approach is capable of withstanding the quantization error. If not, then regardless of the accuracy with which the experiments are carried out the approach will yield unacceptable results. The tools developed here can be used in the analysis of the applicability of a given algorithm, hence revealing the intrinsic limitations of the approach.