Background

CAJAL takes a skeleton and selects N uniformly (?) sampled points. Here is an example for N of 50, 100, 200 and 500:

In their docs they suggest around 100 points - I'm not sure that's enough to describe the shape of this PN though. For the tests below, I ended up using N=200.

From there, CAJAL computes an intracellular distance matrix based on either the Euclidean or the geodesic distance between the sample points:

Both matrices capture the overall structure: dense proximal dendrite and less-branchy, far-away axon. Importantly, using geodesic distance means that our final distances are invariant to bending or flexing - i.e. the same neuron but bent differently in space would have a distance of 0.

As a testbed I took the ~130 uniglomerular PNs from the hemibrain and from one hemisphere of the FlyWire dataset and ran:

1. CAJAL's Gromov-Wasserstein distance based on the geodesic intracellular matrix
2. CAJAL's Gromov-Wasserstein distance based on the Euclidean intracellular matrix
3. Run of the mill NBLAST

Timings

Start to finish CAJAL took 2-3 minutes. NBLAST took just under 2 minutes of which 40s was the transform to a common brain space. With the low number of neurons in the test, the pairwise comparisons made up only a small fraction of the total time - so not sure how this scales to larger datasets.

Accuracy

To assess accuracy I simply asked: "How often is the top hit of the same cell type as the query?"

nblast_correct    0.912
euc_correct       0.200
geo_correct       0.208

At first glance this looks a bit bleak: NBLAST gets us the correct result for 91% of all neurons, CAJAL only in 20%. Maybe the CAJAL distance is at least high whenever the top hit is wrong? Alas, not really:

In some sense this is not very surprising: PNs all look somewhat similar. I also noticed that CAJAL tends to confuse neurons from adjacent glomeruli - e.g. DA4l_adPN instead of DA4m_adPN - which, again, is understandable given that it has no notion of absolute positioning.

What if we relax the conditions and ask "How often is the correct cell type among the top 5 hits?"

nblast_correct5    0.976
euc_correct5       0.432
geo_correct5       0.456

This looks better but NBLAST clearly still outperforms CAJAL in this (somewhat unfair) test. It's still important to acknowledge that NBLAST requires a spatial transform to align neurons while CAJAL doesn't which I think is a huge strength. An obvious scenario where CAJAL would likely do better than NBLAST would be in the visual system of the fly - or any system with repeated, columnar organisation for that matter. Should tune the tutorial accordingly!

Edit: increasing the number of points from 200 to 500 doesn't have any noticeable impact on the distances - it does increase the time to calculate them by a lot though.