notesum.ai

Published at November 12

Leonardo vindicated: Pythagorean trees for minimal reconstruction of the natural branching structures

cs.AI

cs.LG

68U05, 68T45, 92C80, 28A80

I.3.5; I.2.10; I.4.8; I.5.1; J.2

Released Date: November 12, 2024

Authors: Dymitr Ruta¹, Corrado Mio¹, Ernesto Damiani¹

Aff.: ¹Not specified

Arxiv: http://arxiv.org/abs/2411.08024v1

Refer to caption

type	e	b	$\alpha$	$v$	p(tree)	class1	class2	class3	p(class1)	p(class2)	p(class3)
ftree	5.0000	1.5000	90	1.1000	0.9897	tree	leaf	grapes	0.9897	0.0053	0.0021
ftree	5.0000	2.0000	90	1.0000	0.9890	tree	leaf	palm tree	0.9890	0.0064	0.0016
ftree	5.0000	2.0000	60	1.0000	0.9855	tree	vase	house plant	0.9855	0.0050	0.0019
pytree	5.0000	2.0000	90	1.0000	0.9717	tree	broom	leaf	0.9717	0.0120	0.0098
pytree	2.0000	1.5000	90	1.0000	0.9710	tree	broccoli	grapes	0.9710	0.0201	0.0063
pytree	2.0000	2.0000	90	1.0000	0.9568	tree	vase	house plant	0.9568	0.0167	0.0085
ftree	5.0000	1.5000	120	1.0000	0.9483	tree	palm tree	house plant	0.9483	0.0428	0.0032
ftree	5.0000	1.5000	60	0.9000	0.9182	tree	map	giraffe	0.9182	0.0182	0.0119
ftree	5.0000	1.5000	90	1.0000	0.8896	tree	broccoli	map	0.8896	0.0216	0.0121
ftree	5.0000	1.5000	150	1.2500	0.8324	tree	palm tree	house plant	0.8324	0.1632	0.0013
ftree	5.0000	1.5000	120	0.9000	0.8164	tree	palm tree	house plant	0.8164	0.1403	0.0396
ftree	5.0000	1.5000	60	1.0000	0.8112	tree	grapes	broccoli	0.8112	0.1476	0.0188
ftree	5.0000	2.0000	60	0.9000	0.7926	tree	vase	broom	0.7926	0.1661	0.0180
ftree	5.0000	1.5000	120	1.1000	0.7746	tree	house plant	palm tree	0.7746	0.1193	0.0977
ftree	5.0000	1.5000	120	1.2500	0.7717	tree	leaf	bush	0.7717	0.1099	0.0929
ftree	5.0000	1.2500	120	1.2500	0.7491	tree	grapes	leaf	0.7491	0.0374	0.0353
ftree	5.0000	1.5000	60	1.2500	0.7107	tree	leaf	carrot	0.7107	0.0639	0.0593
pytree	1.0000	1.5000	90	1.0000	0.7085	tree	grapes	broccoli	0.7085	0.1120	0.0742
pytree	5.0000	1.5000	90	1.0000	0.6269	tree	map	grapes	0.6269	0.3218	0.0164
ftree	5.0000	1.5000	60	1.1000	0.6203	tree	map	grapes	0.6203	0.2278	0.0899
ftree	5.0000	2.0000	120	1.0000	0.6152	tree	palm tree	house plant	0.6152	0.3708	0.0093
pytree	0.5000	2.0000	90	1.0000	0.5329	tree	house plant	palm tree	0.5329	0.1134	0.0593
ftree	5.0000	1.5000	90	0.9000	0.4676	tree	vase	giraffe	0.4676	0.1497	0.1120
ftree	5.0000	2.0000	90	0.9000	0.4184	tree	hurricane	palm tree	0.4184	0.2104	0.1333
ftree	5.0000	1.2500	120	1.1000	0.3207	broccoli	tree	garden	0.3712	0.3207	0.0910
pytree	1.0000	2.0000	90	1.0000	0.3184	tree	flower	garden	0.3184	0.2753	0.1662
ftree	5.0000	2.0000	120	1.1000	0.2475	palm tree	tree	leaf	0.6613	0.2475	0.0761
ftree	5.0000	1.5000	150	1.1000	0.2430	palm tree	tree	house plant	0.7533	0.2430	0.0036
ftree	5.0000	2.0000	120	0.9000	0.2387	palm tree	tree	house plant	0.7376	0.2387	0.0200
ftree	5.0000	1.2500	150	1.2500	0.2055	palm tree	tree	house plant	0.7930	0.2055	0.0006
ftree	5.0000	2.0000	120	1.2500	0.2023	palm tree	leaf	tree	0.5469	0.2351	0.2023
pytree	10.0000	1.5000	90	1.0000	0.1436	map	tree	hurricane	0.4329	0.1436	0.1246
pytree	0.2000	1.5000	90	1.0000	0.1381	roller coaster	tree	garden	0.7478	0.1381	0.0334
ftree	5.0000	2.0000	60	1.2500	0.1245	leaf	tree	palm tree	0.7466	0.1245	0.1019
pytree	2.0000	1.0000	90	1.0000	0.1030	bowtie	hexagon	boomerang	0.3392	0.2240	0.1279
pytree	2.0000	5.0000	90	1.0000	0.0952	leaf	string bean	tree	0.4812	0.2999	0.0952
ftree	5.0000	2.0000	90	1.1000	0.0674	leaf	palm tree	tree	0.6264	0.1513	0.0674
ftree	5.0000	1.2500	90	1.0000	0.0646	broccoli	map	brain	0.3342	0.1671	0.1553
pytree	0.5000	1.5000	90	1.0000	0.0570	broccoli	leaf	flower	0.4511	0.1738	0.1135
ftree	5.0000	1.5000	90	1.2500	0.0527	leaf	carrot	flower	0.5632	0.1312	0.0683
pytree	10.0000	2.0000	90	1.0000	0.0444	map	tree	hurricane	0.8606	0.0444	0.0228
ftree	5.0000	2.0000	60	1.1000	0.0438	leaf	tree	map	0.8871	0.0438	0.0297
ftree	5.0000	1.2500	90	1.1000	0.0400	broccoli	map	tree	0.6310	0.2804	0.0400
pytree	1.0000	5.0000	90	1.0000	0.0377	scorpion	leaf	tree	0.7230	0.0467	0.0377
ftree	5.0000	1.2500	120	1.0000	0.0361	palm tree	tree	fork	0.8003	0.0361	0.0312
ftree	5.0000	1.5000	150	0.9000	0.0337	palm tree	tree	house plant	0.9659	0.0337	0.0002
ftree	5.0000	1.2500	90	0.9000	0.0161	brain	cow	fence	0.4656	0.2073	0.0826
pytree	0.1000	2.0000	90	1.0000	0.0097	rake	palm tree	roller coaster	0.3822	0.2686	0.2253
pytree	10.0000	5.0000	90	1.0000	0.0075	leaf	palm tree	broom	0.6861	0.2151	0.0291
ftree	5.0000	2.0000	150	1.2500	0.0068	palm tree	leaf	house plant	0.9484	0.0226	0.0088
ftree	5.0000	1.2500	150	1.1000	0.0063	palm tree	tree	house plant	0.9936	0.0063	0.0001
ftree	5.0000	1.2500	150	1.0000	0.0054	palm tree	tree	broom	0.9944	0.0054	0.0000
pytree	0.2000	2.0000	90	1.0000	0.0052	roller coaster	palm tree	fence	0.7792	0.0986	0.0331
pytree	5.0000	5.0000	90	1.0000	0.0037	leaf	bird	dragon	0.8446	0.0334	0.0211
ftree	5.0000	1.2500	90	1.2500	0.0025	broccoli	leaf	map	0.5153	0.3316	0.0433
pytree	0.2000	1.0000	90	1.0000	0.0022	bicycle	octagon	boomerang	0.6009	0.1402	0.0714
ftree	5.0000	2.0000	150	0.9000	0.0019	palm tree	tree	house plant	0.9964	0.0019	0.0018
ftree	5.0000	1.5000	150	1.0000	0.0015	palm tree	tree	house plant	0.9983	0.0015	0.0002
ftree	5.0000	1.0000	150	1.0000	0.0012	palm tree	parachute	rake	0.4800	0.3600	0.0465
ftree	5.0000	2.0000	90	1.2500	0.0009	leaf	palm tree	bush	0.9604	0.0261	0.0042
pytree	1.0000	1.0000	90	1.0000	0.0008	hexagon	octagon	zigzag	0.2076	0.2073	0.1122
ftree	5.0000	1.2500	60	1.0000	0.0008	hexagon	map	brain	0.9427	0.0366	0.0116
ftree	5.0000	1.2500	60	0.9000	0.0006	brain	boomerang	map	0.3458	0.2721	0.2014
ftree	5.0000	1.2500	150	0.9000	0.0006	palm tree	vase	broom	0.9873	0.0099	0.0008
ftree	5.0000	1.0000	150	0.9000	0.0005	palm tree	parachute	rake	0.4050	0.3542	0.1138
ftree	5.0000	2.0000	150	1.1000	0.0004	palm tree	house plant	tree	0.9978	0.0014	0.0004
ftree	5.0000	1.2500	120	0.9000	0.0004	palm tree	brain	leg	0.8486	0.0693	0.0208
pytree	0.1000	1.0000	90	1.0000	0.0004	bicycle	eiffel tower	triangle	0.3852	0.1549	0.1367
pytree	1.0000	10.0000	90	1.0000	0.0004	zigzag	garden hose	string bean	0.3320	0.1536	0.1004
ftree	5.0000	1.0000	150	1.2500	0.0003	parachute	palm tree	rake	0.4385	0.2488	0.1410
ftree	5.0000	1.0000	150	1.1000	0.0003	parachute	palm tree	brain	0.8565	0.0800	0.0158
ftree	5.0000	1.2500	60	1.1000	0.0002	map	hexagon	leaf	0.9558	0.0325	0.0035
pytree	2.0000	10.0000	90	1.0000	0.0002	zigzag	boomerang	garden hose	0.1834	0.1501	0.1260
pytree	0.1000	1.5000	90	1.0000	0.0002	roller coaster	tree	bridge	0.9991	0.0002	0.0002
ftree	5.0000	1.2500	60	1.2500	0.0002	leaf	parrot	map	0.9440	0.0198	0.0086
ftree	5.0000	2.0000	150	1.0000	0.0002	palm tree	house plant	tree	0.9995	0.0003	0.0002
ftree	5.0000	1.0000	90	1.1000	0.0002	brain	leaf	map	0.6582	0.2208	0.0577
ftree	5.0000	1.0000	90	1.2500	0.0001	brain	leaf	pear	0.9778	0.0163	0.0024
pytree	0.5000	1.0000	90	1.0000	0.0001	octagon	zigzag	boomerang	0.3738	0.1488	0.1268