Based on this post, we could create sliding windows to get a 2D array of such windows being set as rows in it. These windows would merely be views into the data array, so no memory consumption and thus would be pretty efficient. Then, we would simply use those ufuncs along each row axis=1.

Thus, for example sliding-median` could be computed like so -

Copynp.median(strided_app(data, window_len,1),axis=1)

For the other ufuncs, just use the respective ufunc names there : np.min, np.max & np.mean. Please note this is meant to give a generic solution to use ufunc supported functionality.

For the best performance, one must still look into specific functions that are built for those purposes. For the four requested functions, we have the builtins, like so -

Median : scipy.signal.medfilt.

Max : scipy.ndimage.filters.maximum_filter1d.

Min : scipy.ndimage.filters.minimum_filter1d.

Mean : scipy.ndimage.filters.uniform_filter1d

It looks like you're trying to implement a two-dimensional median filter. The straightforward way to implement such a filter is to have four nested loops: two outer loops over the x and y coordinates of the whole image, and two inner loops over the neighborhood of the center pixel.

It's perhaps easier to describe this in code than in text, so here's some Python-esque pseudocode to illustrate:

# assumptions:
#  * image is a height x width array containing source pixel values
#  * filtered is a height x width array to store result pixel values in
#  * size is an odd number giving the diameter of the filter region

radius = (size - 1) / 2   # size = 3 -> radius = 1

for y from 0 to height-1:
    top = max(y - radius, 0)
    bottom = min(y + radius, height-1)

    for x from 0 to width-1:
        left = max(x - radius, 0)
        right = min(x + radius, width-1) 
        values = new list

        for v from top to bottom:
            for u from left to right:
                add image[v][u] to values

        filtered[y][x] = median(values)

Translating this code into C is left as an exercise.

It's also possible to optimize this code by noting that the neighborhoods of adjacent array cells overlap significantly, so that the values of those neighboring cells can be reused across successive iterations of the outer loops. Since the performance of this algorithm on modern CPUs is essentially limited by RAM access latency, such reuse can provide a significant speedup, especially for large filter sizes.

Try this:

from scipy.ndimage import median_filter
aFiltered=median_filter(a,size=(1,101))

Try this: Rolling median in C - Turlach implementation

http://ideone.com/8VVEa

Usage:

Mediator* m = MediatorNew(9);
for (...)
{
      MediatorInsert(m, value);
      median = MediatorMedian(m);
}

I believe this is the same as the R algo, but cleaner (amazingly so, in fact).

You can either wrap this, or port it and use Numba (or Cython). I think I'd recommend Numba over Cython, if nothing else because it is plain old python code.

I suggest adding this to scikits, if it runs faster than the one in scikits already :)

Code review

Peilonrays points out a mixup with the out-of-bounds testing that is valid. The statement if j ... must be within the loop for k .... One of the results is that you add a different number of elements to temp depending on which boundary you're at. But there are better ways to avoid out-of-bounds indexing, see below.

Your biggest bug, however, is that you write the result of the filter into the image you are processing. Median filtering cannot be done in-place. When you update data[i][j], you'll be reading the updated value to compute data[i][j+1]. You need to allocate a new image, and write the result there.

I would suggest not adding zeros for out-of-bounds pixels at all, because it introduces a bias to the output pixels near the boundary. The clearest example is for the pixels close to any of the corners. At the corner pixel, with a 3x3 kernel, you'll have 4 image pixels covered by the kernel. Adding 5 zeros for the out-of-bounds pixels guarantees that the output will be 0. For larger kernels this happens in more pixels of course. Instead, it is easy to simply remove the temp.append(0) statements, leading to a non-biased result. Other options are to read values from elsewhere in the image, for example mirroring the image at the boundary or extending the image by extrapolation. For median filtering this has little effect, IMO.

You set temp = [] at the very beginning of your function, then reset it when you're done using it, in preparation for the next loop. Instead, initialize it once inside the main double-loop over the pixels:

for i in range(len(data)):
   for j in range(len(data[0])):
      temp = []
      # ...

You're looping over i and j as image indices, then over z and c or k for filter kernel indices. c and k have the same function in two different loops, I would suggest using the same variable for that. z doesn't really fit in with either c or k. I would pick two names that are related in the way that i and j are, such as m and n. The choice of variable names is always very limited if it's just one letter. Using longer names would make this code clearer: for example img_column, img_row, kernel_column, kernel_row.

Out-of-bounds checking

This concludes my comments on your code. Now I'd like to offer some alternatives for out-of-bounds checking. These tests are rather expensive when performed for every pixel -- it's a test that is done \$n k\$ times (with \$n\$ pixels in the image and \$k\$ pixels in the kernel). Maybe in Python the added cost is relatively small, it's an interpreted language after all, but for a compiled language these tests can easily amount to doubling processing time. There are 3 common alternatives that I know of. I will use border = filter_size // 2, and presume filter_size is odd. It is possible to adjust all 3 methods to even-sized filters.

Separate loops for image border pixels

The idea here is that the loop over the first and last border pixels along each dimension are handled separately from the loop over the core of the image. This avoids all tests. But it does require some code duplication (all in the name of speed!).

for i in range(border):
   # here we loop over the kernel from -i to border+1
for i in range(border, len(data)-border):
   # here we loop over the full kernel
for i in range(len(data)-border, len(data)):
   # here we loop over the kernel from -border to len(data)-i

Of course, within each of those loops, a similar set of 3 loops is necessary to loop over j. The filter logic is thus repeated 9 times. In a compiled language, where this is the most efficient method, code duplication can be avoided with inlined functions or macros. I don't know how a Python function call compares to a bunch of tests for out-of-bounds access, so can't comment on the usefulness of this method in Python.

A separate code path for border pixels

The idea here is to do out-of-bounds checking only for those pixels that are close to the image boundary. For pixels within the border, you use a version of the filtering logic with out-of-bounds checking. For the pixels in the core of the image (which is the big majority of pixels), you use a second version of the logic without out-of-bounds checking.

for i in range(len(data)):
   i_border = i < border or i >= len(data)-border
   for j in range(len(data[0])):
      j_border = j < border or j >= len(data)-border
      if i_border or j_border:
         # filtering with bounds checking
      else:
         # filtering without bounds checking

Padding the image

The simplest solution, and also the most flexible one, is to create a temporary image that is larger than the input image by 2*border along each dimension, and copy the input image into it. The "new" pixels can be filled with zeros (to replicate what OP intended to do), or with values taken from the input image (for example by mirroring the image at the boundary or extrapolating in some other way).

The filter now never needs to check for out-of-bounds reads. When the filtering kernel is placed over any of the input image pixels, all samples fall within the padded image.

Since for this type of filtering it is necessary to create a new output image anyway (it is not possible to compute it in-place, as I mentioned before), this is not a huge cost: the original input image can now be re-used as output image.

This solution leads to the simplest code, allows for all sorts of boundary extension methods without complicating the filtering code, and often results in the fastest code too.

yeah, is easy with numpy. the image will be stored as img a 2D numpy array, then make a mask mask = (img == special_value).astype(int) so that's a 1/0 binary 2D array, then apply your filter using the mask img[mask]

you can use matplotlib to load the image import matplotlib.pyplot as plt, img = plt.imread(file_path)