minor_axis_length for 1 pixel objects

[Phlya]

Description

When an object has a width of 1 pixel, minor_axis_length (from regionprops) equals 0, while I expected it to be 1. Same goes for major_axis_length, if the object is just one pixel.
I would expect to never get zero width, since if width equals 0 then there is no object... This is very annoying when checks like p.major_axis_length/p.minor_axis_length>1.5 raise a ZeroDivisionError.

a = np.zeros((5, 5))
a[2:4, 2] = 1
pr = regionprops(label(a))
print(pr[0].major_axis_length)
print(pr[0].minor_axis_length)
#Output:
2.0
0.0

skimage 0.13.0, python3, Ubuntu 16.04

[stefanv]

We should probably clip the result to 1, minimum, but also check carefully what happens for 2 pixels etc.

[rfezzani]

After some investigations, I found that this is due to the 'grid centered' (versus 'cell centered' paradigm) adopted in the skimage.measure._moments module.
In fact, minor_axis_length calls internally _moments.inertia_tensor_eigvals, with dependency to _moments.inertia_tensor, _moments.moments_central and finally _moments.centroid.

The output of this last function explains the behavior observed in this issue:

>>> from skimage.measure import _moments
>>> _moments.centroid(ones((1, )))
array([0.])
>>> _moments.centroid(ones((1, 1)))
array([0., 0.])
>>> _moments.centroid(ones((1, 2)))
array([0. , 0.5])
>>> _moments.centroid(ones((2, 1)))
array([0.5, 0. ])
>>> _moments.centroid(ones((2, 2)))
array([0.5, 0.5])

Clipping the the result to 1 as suggested by @stefanv in fact solves the problem, but what about enabling the cell centered paradigm?

[jni]

@rfezzani do you have a source that defends the little square model as effectively as Alvy Ray attacks it? =)

http://alvyray.com/Memos/CG/Microsoft/6_pixel.pdf

Almost every time I've looked, I've found that the continuous-space model is more self-consistent, and easier to program with and reason about.

[rfezzani]

Concerning this subject @jni, I liked this blog post.

I think that we all agree that images manipulates data positioned on a grid. The cell centered paradigm doesn't stipulate that a pixel is a little square, it stipulates that the sampled values are positioned at the center of the grid cells, while the grid centered paradigm stipulates that it lies on the intersection points of the grid.

Both paradigms are valid, depending on the context in which they are involved ;-).