How To Apply A Uniform Filter Using Scipy Image Where The Data Outside The Boundary Is Not Tallied?

I have spent lots of time on this, and I know how to manually do it by slicing and indexing the boundary rows/cols, but there has to be a simpler way with SciPy. I need to set the

Solution 1:

One simple approach is to use Normalized Convolution:

import numpy as np
from scipy import ndimage
m = np.reshape(np.arange(0,100),(10,10)).astype(np.float)

filter = ndimage.uniform_filter(m, size=3, mode='constant')    # normal filter result

weights = ndimage.uniform_filter(np.ones(m.shape), size=3, mode='constant')
filter = filter / weights    # normalized convolution resultprint(filter[1][1]) # equal to 11print(filter[9][9]) # equal to 93.49999999999994 -- rounding error! :)

We computed the result of the filter if all data points were 1 (weights). This shows how many data elements there are in each filter window, and returns a value of 1 everywhere except near the boundary, where this value decreases proportionally. By dividing the filtering result with these weights, we correct for the averaging taking zeros into account that were outside the data domain.

Solution 2:

This suggestion is less than ideal, because it will be slow compared to uniform_filter, but it will do what you want.

Using your idea of using nan for the constant value, you can implement the uniform filter by using ndimage.generic_filter instead of uniform_filter, with numpy.nanmean as the generic filter function.

For example, here's your sample array m:

In [102]: import numpy as np

In [103]: m = np.reshape(np.arange(0,100),(10,10)).astype(np.float)

Apply generic_filter, with numpy.nanmean as the function to be applied:

In [104]: from scipy.ndimage import generic_filter

In [105]: generic_filter(m, np.nanmean, mode='constant', cval=np.nan, size=3)
Out[105]: 
array([[ 5.5,  6. ,  7. ,  8. ,  9. , 10. , 11. , 12. , 13. , 13.5],
       [10.5, 11. , 12. , 13. , 14. , 15. , 16. , 17. , 18. , 18.5],
       [20.5, 21. , 22. , 23. , 24. , 25. , 26. , 27. , 28. , 28.5],
       [30.5, 31. , 32. , 33. , 34. , 35. , 36. , 37. , 38. , 38.5],
       [40.5, 41. , 42. , 43. , 44. , 45. , 46. , 47. , 48. , 48.5],
       [50.5, 51. , 52. , 53. , 54. , 55. , 56. , 57. , 58. , 58.5],
       [60.5, 61. , 62. , 63. , 64. , 65. , 66. , 67. , 68. , 68.5],
       [70.5, 71. , 72. , 73. , 74. , 75. , 76. , 77. , 78. , 78.5],
       [80.5, 81. , 82. , 83. , 84. , 85. , 86. , 87. , 88. , 88.5],
       [85.5, 86. , 87. , 88. , 89. , 90. , 91. , 92. , 93. , 93.5]])