About LRA calculation about riconv2

[cszyzhang]

1. LRA is much more robust than the LRF of SHOT. Please check Fig. 8 of our IJCV paper which clearly shows this.
2. Sign ambiguity cannot be removed in many cases especially when the local shape is like a disk or lacking sufficient geometric features. Moreover, the noise can further deteriorate this. Thus, we proposed LRA which has no sign ambiguity problem.

[granadet17]

Thanks for the reply.
I understand now.

I would like to ask one more question about implementation.

riconv2/models/riconv2_utils.py

Lines 216 to 241 in 134122e

	def order_index(xyz, new_xyz, new_norm, idx):
	B, S, C = new_xyz.shape
	nsample = idx.shape[2]
	grouped_xyz = index_points(xyz, idx)
	grouped_xyz_local = grouped_xyz - new_xyz.view(B, S, 1, C) # centered
	# project and order
	dist_plane = torch.matmul(grouped_xyz_local, new_norm)
	proj_xyz = grouped_xyz_local - dist_plane*new_norm.view(B, S, 1, C)
	proj_xyz_length = torch.norm(proj_xyz, dim=-1, keepdim=True)
	projected_xyz_unit = proj_xyz / proj_xyz_length
	projected_xyz_unit[projected_xyz_unit != projected_xyz_unit] = 0 # set nan to zero
	length_max_idx = torch.argmax(proj_xyz_length, dim=2)
	vec_ref = projected_xyz_unit.gather(2, length_max_idx.unsqueeze(-1).repeat(1,1,1,3)) # corresponds to the largest length
	dots = torch.matmul(projected_xyz_unit, vec_ref.view(B, S, C, 1))
	sign = torch.cross(projected_xyz_unit, vec_ref.view(B, S, 1, C).repeat(1, 1, nsample, 1))
	sign = torch.matmul(sign, new_norm)
	sign = torch.sign(sign)
	sign[:, :, 0, 0] = 1. # the first is the vec_ref itself, should be 1.
	dots = sign*dots - (1-sign)
	dots_sorted, indices = torch.sort(dots, dim=2, descending=True)
	idx_ordered = idx.gather(2, indices.squeeze_(-1))
	return dots_sorted, idx_ordered

In this function, you wrote

riconv2/models/riconv2_utils.py

Line 236 in 134122e

sign[:, :, 0, 0] = 1. # the first is the vec_ref itself, should be 1.

but, I think the first is not the vec_ref.

[cszyzhang]

Thanks for reporting that line of comment. Yes. the first is not the vec_ref. The vec_ref is the one with largest distance from the center point, while the first one is the center point by itself whose vec is always [0,0,0]. So, we force its sign to 1 to avoid two identical dots after sign operation (Line 237). Otherwise, the 1st dot value and the ref dot value will become identical. I have updated that line of comment. Hope this clarifies.

[granadet17]

Thank you.
Shouldn't you set the sign of vec_ref manually since the cross product of vec_ref and vec_ref is also [0, 0, 0].

[cszyzhang]

So, set one of them to differentiate it from the other.

[granadet17]

I'm sorry, I misunderstood.

Thank you.