difference between mean filter and order statistic filter
Quick Answer

The main difference of this filters is how it perform the operations.

Mean Filter

Brief Description

Mean filtering is a spatial filter, and it's a simple, intuitive and easy to implement method of smoothing images, i.e. reducing the amount of intensity variation between one pixel and the next.

How It Works

The idea of mean filtering is simply to replace each pixel value in an image with the mean (`average') value of its neighbors, including itself.
Mean filtering is usually thought of as a convolution filter and it's based around a kernel, which represents the shape and size of the neighborhood to be sampled when calculating the mean. Often a 3×3 square kernel is used like this
 $$
   K =
  \left[ {\begin{array}{cc}
                \frac{1}{9} &amp; \frac{1}{9} &amp; \frac{1}{9}\\  
                \frac{1}{9} &amp; \frac{1}{9} &amp; \frac{1}{9}\\  
                \frac{1}{9} &amp; \frac{1}{9} &amp; \frac{1}{9}\\  
              \end{array} } \right]
$$

Note: Check this link for more details in mean filtering.

Order Statistics Filter

Brief Description

This type of filter is based on estimators and  is based on "order", the sense of order is about some quatities like $\operatorname{min} $ (first order statistic), $\operatorname{max}$ (largest order statistic) and etc...

How It Works

Given $N$ observations $ X_{1}, X_{2}, X_{3}, \dots X_{N} $ of a random variable $X$, the order statistics are obtained by sorting the $\{X_{i}\}$ in ascending order. This produces $\{X_{(i)}\}$ satisfying: 

$$X_{(1)} \leq X_{(2)} \leq X_{(3)} \dots \leq X_{(N)}$$

where $\{X_{i}\}$ are the order statistics of the N observations.
So, an Order Statistic Filter (OSF) is a estimator $ F(X_{1}, X_{2}, X_{3}, \dots X_{N})$.

Some common filters which fit the order statistic filter framework are:


The linear average, which has coefficients:
  $$ \alpha_{i} = \frac{1}{N} $$
The median filter, which has coefficients: 
$$ \alpha_{i} = \left\{ \begin{array}{ll}
     1 &amp; i = (N+1)/2\\
     0 &amp; \text{otherwise} \end{array} \right.$$
The trimmed mean filter, which has coefficients:
$$ \alpha_{i} = \left\{ \begin{array}{ll}
     1/M &amp; (N - M + 1)/2 \leq i \leq (N + M + 1)/2 \\
     0 &amp; \text{otherwise} \end{array} \right.$$ 


Please check the references for more details in the Todd Veldhuizen web page.