Frenet-Serret Frame-based Decomposition for Part Segmentation of 3D Curvilinear Structures

Experiments on DenSpineEM Benchmark

Average Results (Mean ± Standard Deviation)

Model	Dataset	Spine IoU	Trunk IoU	Spine Dice	Trunk Dice	Spine Accuracy	Average Spine Recall
PointNet++	M50	0.6951 ± 0.0314	0.9484 ± 0.0223	0.8004 ± 0.0286	0.9724 ± 0.0132	0.8703 ± 0.0189	0.8644 ± 0.0150
PointNet++	M10	0.7329 ± 0.0217	0.8948 ± 0.0095	0.8428 ± 0.0147	0.9433 ± 0.0055	0.7866 ± 0.0318	0.8058 ± 0.0265
PointNet++	H10	0.6056 ± 0.0285	0.8985 ± 0.0120	0.7419 ± 0.0247	0.9454 ± 0.0067	0.6673 ± 0.0536	0.7417 ± 0.0329
PointNet++ w. FFD	M50	0.8260 ± 0.0409	0.9808 ± 0.0034	0.8928 ± 0.0283	0.9903 ± 0.0018	0.8992 ± 0.0212	0.8861 ± 0.0155
PointNet++ w. FFD	M10	0.8740 ± 0.0087	0.9566 ± 0.0030	0.9319 ± 0.0051	0.9777 ± 0.0016	0.8656 ± 0.0233	0.8546 ± 0.0210
PointNet++ w. FFD	H10	0.6829 ± 0.0208	0.9286 ± 0.0071	0.7927 ± 0.0202	0.9626 ± 0.0040	0.7850 ± 0.0240	0.8095 ± 0.0218
RandLA-Net	M50	0.1488 ± 0.0252	0.6397 ± 0.1040	0.2463 ± 0.0359	0.7660 ± 0.0840	0.4304 ± 0.1692	0.4840 ± 0.1647
RandLA-Net	M10	0.2433 ± 0.0332	0.4821 ± 0.0694	0.3794 ± 0.0419	0.6401 ± 0.0668	0.4885 ± 0.1266	0.5396 ± 0.1219
RandLA-Net	H10	0.2202 ± 0.0256	0.5597 ± 0.0768	0.3449 ± 0.0326	0.7078 ± 0.0631	0.4907 ± 0.1691	0.5382 ± 0.1632
RandLA-Net w. FFD	M50	0.3710 ± 0.1782	0.8665 ± 0.0487	0.4938 ± 0.1781	0.9252 ± 0.0288	0.4867 ± 0.2121	0.5524 ± 0.1807
RandLA-Net w. FFD	M10	0.4406 ± 0.1332	0.7857 ± 0.0521	0.5884 ± 0.1337	0.8762 ± 0.0337	0.3713 ± 0.1404	0.4847 ± 0.1242
RandLA-Net w. FFD	H10	0.3745 ± 0.1234	0.7900 ± 0.0505	0.5168 ± 0.1261	0.8796 ± 0.0312	0.4211 ± 0.1916	0.5299 ± 0.1626
PointTransformer	M50	0.8807 ± 0.0242	0.9829 ± 0.0027	0.9261 ± 0.0204	0.9912 ± 0.0015	0.9594 ± 0.0085	0.9464 ± 0.0087
PointTransformer	M10	0.8377 ± 0.0132	0.9337 ± 0.0052	0.9080 ± 0.0078	0.9650 ± 0.0028	0.9121 ± 0.0106	0.9020 ± 0.0088
PointTransformer	H10	0.7377 ± 0.0153	0.9282 ± 0.0051	0.8395 ± 0.0111	0.9618 ± 0.0030	0.8255 ± 0.0132	0.8478 ± 0.0104
PointTransformer w. FFD	M50	0.9074 ± 0.0250	0.9900 ± 0.0029	0.9443 ± 0.0211	0.9949 ± 0.0015	0.9545 ± 0.0138	0.9382 ± 0.0155
PointTransformer w. FFD	M10	0.9172 ± 0.0022	0.9721 ± 0.0008	0.9561 ± 0.0013	0.9858 ± 0.0004	0.9586 ± 0.0035	0.9303 ± 0.0039
PointTransformer w. FFD	H10	0.7757 ± 0.0130	0.9575 ± 0.0019	0.8663 ± 0.0098	0.9782 ± 0.0010	0.8368 ± 0.0148	0.8482 ± 0.0118

Fold 0

Model	Dataset	Spine IoU	Trunk IoU	Spine Dice	Trunk Dice	Spine Accuracy	Average Spine Recall
PointNet++	M50	0.6685	0.9071	0.7897	0.9475	0.8877	0.8866
PointNet++	M10	0.7384	0.9006	0.8464	0.9468	0.8153	0.8263
PointNet++	H10	0.5515	0.8747	0.6960	0.9321	0.7508	0.7990
PointNet++ w. FFD	M50	0.8166	0.9760	0.8768	0.9878	0.9130	0.9022
PointNet++ w. FFD	M10	0.8785	0.9596	0.9343	0.9793	0.9013	0.8846
PointNet++ w. FFD	H10	0.6738	0.9236	0.7817	0.9599	0.8255	0.8451
RandLA-Net	M50	0.1914	0.4588	0.3042	0.6193	0.7089	0.7582
RandLA-Net	M10	0.2877	0.3538	0.4289	0.5128	0.7134	0.7580
RandLA-Net	H10	0.2618	0.4404	0.3986	0.6052	0.7668	0.8047
RandLA-Net w. FFD	M50	0.6432	0.9409	0.7565	0.9686	0.6772	0.7015
RandLA-Net w. FFD	M10	0.6174	0.8491	0.7535	0.9144	0.4586	0.5505
RandLA-Net w. FFD	H10	0.5934	0.8881	0.7398	0.9396	0.5974	0.6682
PointTransformer	M50	0.8976	0.9801	0.9426	0.9897	0.9503	0.9467
PointTransformer	M10	0.8151	0.9249	0.8945	0.9602	0.9013	0.8928
PointTransformer	H10	0.7087	0.9192	0.8190	0.9564	0.8255	0.8406
PointTransformer w. FFD	M50	0.9013	0.9916	0.9434	0.9958	0.9637	0.9484
PointTransformer w. FFD	M10	0.9144	0.9714	0.9544	0.9854	0.9650	0.9327
PointTransformer w. FFD	H10	0.7630	0.9545	0.8580	0.9766	0.8505	0.8637

Fold 1

Model	Dataset	Spine IoU	Trunk IoU	Spine Dice	Trunk Dice	Spine Accuracy	Average Spine Recall
PointNet++	M50	0.6829	0.9449	0.7963	0.9713	0.8758	0.8729
PointNet++	M10	0.7120	0.8790	0.8294	0.9340	0.8280	0.8430
PointNet++	H10	0.6188	0.9069	0.7499	0.9502	0.6636	0.7276
PointNet++ w. FFD	M50	0.8179	0.9812	0.8849	0.9905	0.9088	0.8938
PointNet++ w. FFD	M10	0.8752	0.9571	0.9328	0.9780	0.8758	0.8599
PointNet++ w. FFD	H10	0.6801	0.9276	0.7892	0.9621	0.7882	0.8116
RandLA-Net	M50	0.1607	0.6032	0.2677	0.7350	0.4462	0.5090
RandLA-Net	M10	0.2561	0.5579	0.4019	0.7047	0.4650	0.5203
RandLA-Net	H10	0.2108	0.5573	0.3314	0.7094	0.4760	0.5158
RandLA-Net w. FFD	M50	0.1880	0.7935	0.3046	0.8827	0.2297	0.3421
RandLA-Net w. FFD	M10	0.2446	0.6991	0.3809	0.8183	0.2006	0.3192
RandLA-Net w. FFD	H10	0.2377	0.7547	0.3746	0.8558	0.2236	0.3420
PointTransformer	M50	0.9173	0.9861	0.9560	0.9930	0.9714	0.9583
PointTransformer	M10	0.8410	0.9349	0.9091	0.9655	0.9140	0.9032
PointTransformer	H10	0.7433	0.9294	0.8444	0.9625	0.8162	0.8406
PointTransformer w. FFD	M50	0.9421	0.9938	0.9696	0.9969	0.9563	0.9477
PointTransformer w. FFD	M10	0.9200	0.9734	0.9577	0.9865	0.9586	0.9363
PointTransformer w. FFD	H10	0.7973	0.9602	0.8820	0.9796	0.8505	0.8590

Fold 2

Model	Dataset	Spine IoU	Trunk IoU	Spine Dice	Trunk Dice	Spine Accuracy	Average Spine Recall
PointNet++	M50	0.6595	0.9706	0.7543	0.9850	0.8474	0.8455
PointNet++	M10	0.7724	0.9076	0.8697	0.9504	0.7866	0.8058
PointNet++	H10	0.6048	0.9022	0.7400	0.9477	0.6978	0.7558
PointNet++ w. FFD	M50	0.7597	0.9799	0.8536	0.9898	0.8571	0.8567
PointNet++ w. FFD	M10	0.8862	0.9596	0.9393	0.9793	0.8694	0.8655
PointNet++ w. FFD	H10	0.6605	0.9201	0.7709	0.9578	0.7788	0.8164
RandLA-Net	M50	0.1382	0.7089	0.2290	0.8201	0.4675	0.4947
RandLA-Net	M10	0.2576	0.4986	0.3989	0.6585	0.4968	0.5383
RandLA-Net	H10	0.2342	0.5452	0.3615	0.6999	0.5272	0.5684
RandLA-Net w. FFD	M50	0.2062	0.8690	0.3166	0.9284	0.3182	0.3916
RandLA-Net w. FFD	M10	0.3388	0.7604	0.4948	0.8619	0.2611	0.3876
RandLA-Net w. FFD	H10	0.2941	0.7754	0.4350	0.8720	0.2556	0.3944
PointTransformer	M50	0.8477	0.9833	0.8994	0.9915	0.9676	0.9525
PointTransformer	M10	0.8327	0.9317	0.9052	0.9640	0.9013	0.8938
PointTransformer	H10	0.7504	0.9301	0.8501	0.9629	0.8069	0.8378
PointTransformer w. FFD	M50	0.8712	0.9852	0.9083	0.9925	0.9525	0.9312
PointTransformer w. FFD	M10	0.9152	0.9711	0.9550	0.9852	0.9554	0.9256
PointTransformer w. FFD	H10	0.7820	0.9586	0.8718	0.9788	0.8380	0.8417

Fold 3

Model	Dataset	Spine IoU	Trunk IoU	Spine Dice	Trunk Dice	Spine Accuracy	Average Spine Recall
PointNet++	M50	0.7303	0.9573	0.8314	0.9778	0.8487	0.8504
PointNet++	M10	0.7173	0.8934	0.8312	0.9426	0.7580	0.7828
PointNet++	H10	0.6325	0.9053	0.7680	0.9492	0.5981	0.7065
PointNet++ w. FFD	M50	0.8799	0.9867	0.9325	0.9933	0.9117	0.8884
PointNet++ w. FFD	M10	0.8696	0.9551	0.9295	0.9769	0.8344	0.8377
PointNet++ w. FFD	H10	0.6782	0.9311	0.7913	0.9641	0.7819	0.7926
RandLA-Net	M50	0.1180	0.7601	0.2007	0.8608	0.1972	0.2528
RandLA-Net	M10	0.1900	0.5217	0.3086	0.6794	0.3248	0.3832
RandLA-Net	H10	0.1875	0.6816	0.3032	0.8031	0.2396	0.2934
RandLA-Net w. FFD	M50	0.3062	0.8426	0.4533	0.9083	0.4217	0.5114
RandLA-Net w. FFD	M10	0.4758	0.8214	0.6332	0.9003	0.3439	0.4921
RandLA-Net w. FFD	H10	0.3344	0.7818	0.4794	0.8764	0.3291	0.4770
PointTransformer	M50	0.8709	0.9794	0.9169	0.9894	0.9541	0.9412
PointTransformer	M10	0.8469	0.9372	0.9141	0.9670	0.9299	0.9173
PointTransformer	H10	0.7368	0.9273	0.8372	0.9613	0.8442	0.8644
PointTransformer w. FFD	M50	0.9276	0.9900	0.9606	0.9949	0.9703	0.9528
PointTransformer w. FFD	M10	0.9171	0.9721	0.9560	0.9858	0.9586	0.9297
PointTransformer w. FFD	H10	0.7623	0.9574	0.8549	0.9782	0.8349	0.8457

Fold 4

Model	Dataset	Spine IoU	Trunk IoU	Spine Dice	Trunk Dice	Spine Accuracy	Average Spine Recall
PointNet++	M50	0.7345	0.9622	0.8301	0.9806	0.8919	0.8665
PointNet++	M10	0.7242	0.8933	0.8373	0.9425	0.7452	0.7714
PointNet++	H10	0.6206	0.9032	0.7558	0.9477	0.6262	0.7195
PointNet++ w. FFD	M50	0.8560	0.9804	0.9164	0.9900	0.9054	0.8894
PointNet++ w. FFD	M10	0.8603	0.9517	0.9238	0.9750	0.8471	0.8251
PointNet++ w. FFD	H10	0.7221	0.9409	0.8304	0.9693	0.7508	0.7818
RandLA-Net	M50	0.1360	0.6677	0.2299	0.7951	0.3324	0.4052
RandLA-Net	M10	0.2251	0.4786	0.3589	0.6448	0.4427	0.4982
RandLA-Net	H10	0.2065	0.5741	0.3300	0.7214	0.4441	0.5087
RandLA-Net w. FFD	M50	0.5117	0.8864	0.6381	0.9381	0.7865	0.8156
RandLA-Net w. FFD	M10	0.5266	0.7987	0.6796	0.8858	0.5924	0.6742
RandLA-Net w. FFD	H10	0.4126	0.7500	0.5551	0.8543	0.6997	0.7677
PointTransformer	M50	0.8701	0.9854	0.9154	0.9926	0.9535	0.9334
PointTransformer	M10	0.8531	0.9400	0.9170	0.9684	0.9140	0.9028
PointTransformer	H10	0.7494	0.9349	0.8469	0.9656	0.8349	0.8554
PointTransformer w. FFD	M50	0.8947	0.9892	0.9396	0.9945	0.9297	0.9108
PointTransformer w. FFD	M10	0.9193	0.9723	0.9574	0.9859	0.9554	0.9271
PointTransformer w. FFD	H10	0.7737	0.9569	0.8648	0.9779	0.8100	0.8311