scipy.ndimage.label: include error margin

After reading an interesting topic on scipy.ndimage.label (Variable area threshold for identifying objects - python), I'd like to include an 'error margin' in the labelling.

In the above linked discussion: How can the blue dot on top be included, too (let's say it is wrongly disconnected from the orange, biggest, object)?

I found the structure attribute, which should be able to include that dot by changing the array (from np.ones(3,3,3) to anything more than that (I'd like it to be 3D). However, adjusting the 'structure' attribute to a larger array does not seem to work, unfortunately. It either gives an error of dimensions (RuntimeError: structure and input must have equal rank ) or it does not change anything..

Thanks!

this is the code:

labels, nshapes = ndimage.label(a, structure=np.ones((3,3,3)))

in which a is a 3D array.

Solution

Here's a possible approach that uses scipy.ndimage.binary_dilation. It is easier to see what is going on in a 2D example, but I'll show how to generalize to 3D at the end.

In [103]: a
Out[103]: 
array([[0, 0, 0, 1, 0, 0, 0],
       [0, 0, 0, 0, 0, 0, 0],
       [1, 1, 0, 0, 1, 0, 0],
       [1, 1, 0, 0, 0, 1, 1],
       [0, 0, 0, 0, 0, 1, 1],
       [1, 1, 1, 0, 0, 0, 0]])

In [104]: from scipy.ndimage import label, binary_dilation

Extend each "shape" by one pixel down and to the right:

In [105]: b = binary_dilation(a, structure=np.array([[0, 0, 0], [0, 1, 1], [0, 1, 1]])).astype(int)

In [106]: b
Out[106]: 
array([[0, 0, 0, 1, 1, 0, 0],
       [0, 0, 0, 1, 1, 0, 0],
       [1, 1, 1, 0, 1, 1, 0],
       [1, 1, 1, 0, 1, 1, 1],
       [1, 1, 1, 0, 0, 1, 1],
       [1, 1, 1, 1, 0, 1, 1]])

Apply label to the padded array:

In [107]: labels, numlabels = label(b)

In [108]: numlabels
Out[108]: 2

In [109]: labels
Out[109]: 
array([[0, 0, 0, 1, 1, 0, 0],
       [0, 0, 0, 1, 1, 0, 0],
       [2, 2, 2, 0, 1, 1, 0],
       [2, 2, 2, 0, 1, 1, 1],
       [2, 2, 2, 0, 0, 1, 1],
       [2, 2, 2, 2, 0, 1, 1]], dtype=int32)

By multiplying a by labels, we get the desired array of labels of a:

In [110]: alab = labels*a

In [111]: alab
Out[111]: 
array([[0, 0, 0, 1, 0, 0, 0],
       [0, 0, 0, 0, 0, 0, 0],
       [2, 2, 0, 0, 1, 0, 0],
       [2, 2, 0, 0, 0, 1, 1],
       [0, 0, 0, 0, 0, 1, 1],
       [2, 2, 2, 0, 0, 0, 0]])

(This assumes that the values in a are 0 or 1. If they are not, you can use alab = labels * (a > 0).)

For a 3D input, you have to change the structure argument to binary_dilation:

struct = np.zeros((3, 3, 3), dtype=int)
struct[1:, 1:, 1:] = 1
b = binary_dilation(a, structure=struct).astype(int)