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While computing the regularized mean in medical image analysis, compensation for anatomical variation between different subjects is achieved by registering data with a standard template. In practice, template registration is never perfect and registration error (called jitter) can influence any statistic that is calculated using the template. This paper considers the design of regularizing filters which makes the effect of jitter harmless on the computed mean. The design is based on a new notion called jitter-resistant filtering. A regularizing kernel is jitter resistant if the effect of jitter on the regularized data is similar to a slight change in the scale of the kernel in the absence of jitter. Based on this notion, it is shown that the family of Gaussian filters is a jitter-resistant family of regularizing filters. Simulations in support of the theory are also presented.