Using variable window ("kernel") size for raster processing in QGIS?

Input square window size raster:

Script:

import arcpy, os, traceback, sys, numpy
from arcpy import env
env.overwriteOutput = True

dem=r'D:\Scratch\demG'
wsize=r'D:\Scratch\wsize'
d=arcpy.Describe(dem)
try:
    def showPyMessage():
        arcpy.AddMessage(str(time.ctime()) + " - " + message)

    demArray = arcpy.RasterToNumPyArray(dem,"","","",-9999)
    sizeArray=arcpy.RasterToNumPyArray(wsize,"","","",-9999)
    blankArray=arcpy.RasterToNumPyArray(dem,"","","",-9999)
    d=arcpy.Describe(wsize)
    origin=d.extent.lowerLeft
    cSize=arcpy.Raster(wsize).meanCellHeight
    nRows,nCols=demArray.shape
    cellsTotal=nCols*nRows

#  main loop
    arcpy.SetProgressor("step", "", 0, nRows)
    for nRow in range (nRows):
            for nCol in range (nCols):
                S=sizeArray[nRow,nCol]
                shift=S/2
                top=max(0,nRow-shift)
                bottom=min(nRows-1,nRow+shift)
                rows=demArray[top:bottom+1]
                left=max(0,nCol-shift)
                right=min(nCols-1,nCol+shift)
                kernel=rows[:,range(left,right+1)]
                nR,nC=kernel.shape
                blankArray[nRow,nCol]=float(numpy.sum(kernel))/nR/nC
            arcpy.SetProgressorPosition()
    myRaster = arcpy.NumPyArrayToRaster(blankArray,origin,cSize,cSize)
    oneGrid=Con(myRaster<>-9999,myRaster)
    oneGrid.save(r'D:\Aerials\nztm\toriver')
    del demArray,blankArray,sizeArray
except:
    message = "\n*** PYTHON ERRORS *** "; showPyMessage()
    message = "Python Traceback Info: " + traceback.format_tb(sys.exc_info()[2])[0]; showPyMessage()
    message = "Python Error Info: " +  str(sys.exc_type)+ ": " + str(sys.exc_value) + "\n"; showPyMessage()        

Hillshade before:

and after