Statistics using SimpleITK

We can use Simple for extracting features from label images. For convenience reasons we use the napari-simpleitk-image-processing library.

import numpy as np
import pandas as pd
from skimage.io import imread
import pyclesperanto_prototype as cle
from napari_simpleitk_image_processing import watershed_otsu_labeling
from napari_simpleitk_image_processing import label_statistics

blobs = imread('../../data/blobs.tif')
cle.imshow(blobs)

Starting point: a segmented label image

labels = watershed_otsu_labeling(blobs)
cle.imshow(labels, labels=True)

Label statistics

statistics = label_statistics(blobs, labels, 
                              intensity=True, 
                              size=True, 
                              shape=True, 
                              perimeter=True, 
                              position=True,
                              moments=True)

df = pd.DataFrame(statistics)
df

	label	maximum	mean	median	minimum	sigma	sum	variance	bbox_0	bbox_1	...	number_of_pixels_on_border	perimeter	perimeter_on_border	perimeter_on_border_ratio	principal_axes0	principal_axes1	principal_axes2	principal_axes3	principal_moments0	principal_moments1
0	1	224.0	137.526132	136.0	112.0	13.360739	157880.0	178.509343	0	0	...	36	2461.579651	36.0	0.014625	-0.574118	-0.818773	0.818773	-0.574118	5063.911496	5560.184284
1	2	232.0	193.014354	200.0	128.0	28.559077	80680.0	815.620897	11	0	...	16	85.499572	16.0	0.187135	0.902494	0.430703	-0.430703	0.902494	17.056706	72.884853
2	3	224.0	179.846995	184.0	128.0	21.328889	32912.0	454.921516	53	0	...	21	53.456120	21.0	0.392846	-0.042759	-0.999085	0.999085	-0.042759	8.637199	27.432794
3	4	248.0	207.082171	216.0	120.0	27.772832	133568.0	771.330194	95	0	...	23	93.409370	23.0	0.246228	0.991601	0.129334	-0.129334	0.991601	48.975064	55.851742
4	5	248.0	223.146402	232.0	128.0	30.246515	89928.0	914.851647	144	0	...	19	74.218143	19.0	0.256002	0.974707	0.223487	-0.223487	0.974707	32.059800	33.765222
5	6	248.0	214.906725	224.0	128.0	26.386796	99072.0	696.263020	238	0	...	39	80.787183	40.0	0.495128	0.999408	0.034407	-0.034407	0.999408	23.320204	59.820502
6	7	248.0	211.565891	224.0	136.0	30.197236	54584.0	911.873073	189	7	...	0	57.938471	0.0	0.000000	0.932037	0.362364	-0.362364	0.932037	18.705896	22.720115
7	8	200.0	166.171429	168.0	136.0	16.466894	11632.0	271.158592	133	17	...	0	29.917295	0.0	0.000000	0.960385	0.278678	-0.278678	0.960385	4.741825	6.584094
8	9	224.0	176.932331	176.0	128.0	24.022064	47064.0	577.059555	211	17	...	0	59.834590	0.0	0.000000	0.997651	0.068495	-0.068495	0.997651	14.969363	30.395186
9	10	240.0	191.598174	200.0	128.0	28.239851	41960.0	797.489171	37	18	...	0	53.360835	0.0	0.000000	0.992904	0.118917	-0.118917	0.992904	15.331341	19.871929
10	11	232.0	190.962963	200.0	128.0	23.617106	92808.0	557.767698	162	21	...	0	79.485892	0.0	0.000000	0.950824	0.309732	-0.309732	0.950824	35.879673	42.001599
11	12	232.0	173.000000	176.0	128.0	19.441981	110720.0	377.990610	59	26	...	0	93.218800	0.0	0.000000	0.848443	0.529287	-0.529287	0.848443	38.069371	69.135089
12	13	200.0	168.351648	168.0	128.0	19.226356	15320.0	369.652747	3	39	...	0	35.050291	0.0	0.000000	0.945102	0.326774	-0.326774	0.945102	5.568379	9.510959
13	14	248.0	203.019608	208.0	128.0	32.682072	41416.0	1068.117840	226	39	...	0	51.464716	0.0	0.000000	0.999604	-0.028149	0.028149	0.999604	13.550254	19.604062
14	15	248.0	216.156863	224.0	136.0	28.644305	88192.0	820.496218	129	42	...	0	72.226739	0.0	0.000000	0.985169	-0.171585	0.171585	0.985169	26.472262	39.901074
15	16	232.0	181.963255	184.0	120.0	24.411574	69328.0	595.924962	185	43	...	0	81.382011	0.0	0.000000	0.925427	0.378925	-0.378925	0.925427	12.588614	76.471615
16	17	248.0	197.333333	200.0	120.0	26.311828	97088.0	692.312288	17	44	...	0	79.485892	0.0	0.000000	0.949997	0.312260	-0.312260	0.949997	33.707850	45.675040
17	18	248.0	200.160401	208.0	128.0	27.596051	79864.0	761.542046	90	60	...	0	72.782100	0.0	0.000000	0.959680	0.281094	-0.281094	0.959680	21.950618	46.037485
18	19	248.0	205.943775	216.0	136.0	30.086114	51280.0	905.174245	207	61	...	0	57.153073	0.0	0.000000	0.954815	0.297199	-0.297199	0.954815	14.780837	26.562206
19	20	232.0	192.235988	200.0	120.0	25.416595	65168.0	646.003316	235	63	...	11	66.863705	11.0	0.164514	-0.593398	-0.804909	0.804909	-0.593398	22.740379	32.242766
20	21	224.0	189.577465	200.0	136.0	24.291178	26920.0	590.061333	162	66	...	0	42.864805	0.0	0.000000	0.946821	0.321762	-0.321762	0.946821	9.729421	13.167326
21	22	224.0	187.870324	192.0	128.0	24.658125	75336.0	608.023142	53	73	...	0	71.996702	0.0	0.000000	0.993149	-0.116857	0.116857	0.993149	28.718371	35.697584
22	23	248.0	208.960836	216.0	128.0	30.936449	80032.0	957.063907	117	76	...	0	79.485892	0.0	0.000000	-0.249601	-0.968349	0.968349	-0.249601	17.353521	61.813901
23	24	240.0	182.081301	184.0	128.0	26.433619	44792.0	698.736220	26	77	...	0	56.597713	0.0	0.000000	0.999988	-0.004899	0.004899	0.999988	16.419754	23.402458
24	25	248.0	199.629032	200.0	128.0	27.426587	99016.0	752.217660	0	82	...	29	84.484136	29.0	0.343260	0.998757	-0.049841	0.049841	0.998757	24.491079	67.691848
25	26	240.0	192.449438	192.0	120.0	26.732458	51384.0	714.624314	214	86	...	0	58.493832	0.0	0.000000	0.929427	0.369006	-0.369006	0.929427	18.770857	24.067028
26	27	240.0	202.691706	208.0	128.0	24.550960	129520.0	602.749633	158	88	...	0	97.891721	0.0	0.000000	0.252109	-0.967699	0.967699	0.252109	34.790068	80.474893
27	28	232.0	200.641975	208.0	136.0	22.958406	32504.0	527.088413	245	95	...	20	51.004641	20.0	0.392121	0.999016	0.044348	-0.044348	0.999016	7.500566	24.475429
28	29	232.0	201.661721	208.0	136.0	24.593688	67960.0	604.849513	92	102	...	0	66.308345	0.0	0.000000	0.159256	-0.987237	0.987237	0.159256	22.243114	32.490995
29	30	240.0	202.541910	208.0	136.0	26.036533	103904.0	677.901072	26	108	...	0	82.167409	0.0	0.000000	0.989629	0.143647	-0.143647	0.989629	32.933086	51.101812
30	31	232.0	192.649396	200.0	120.0	25.700290	111544.0	660.504892	113	109	...	0	105.610950	0.0	0.000000	0.903873	0.427801	-0.427801	0.903873	18.013291	134.834719
31	32	248.0	195.953871	200.0	120.0	30.668210	118944.0	940.539123	151	114	...	0	99.692555	0.0	0.000000	0.830015	-0.557742	0.557742	0.830015	25.231170	101.168109
32	33	232.0	184.131148	192.0	128.0	26.165665	33696.0	684.642046	56	115	...	0	49.568597	0.0	0.000000	0.991750	-0.128190	0.128190	0.991750	12.926033	16.531401
33	34	248.0	215.125448	224.0	128.0	30.288772	120040.0	917.409728	211	115	...	0	85.174249	0.0	0.000000	0.220924	-0.975291	0.975291	0.220924	40.823045	48.505271
34	35	176.0	151.529412	152.0	136.0	15.091875	2576.0	227.764706	251	124	...	2	14.843629	2.0	0.134738	-0.163228	-0.986588	0.986588	-0.163228	1.046852	1.755916
35	36	232.0	191.224806	200.0	120.0	25.409101	49336.0	645.622417	0	130	...	13	57.153073	13.0	0.227459	0.970628	0.240586	-0.240586	0.970628	16.246640	26.130982
36	37	248.0	201.665497	200.0	128.0	28.167372	172424.0	793.400857	76	137	...	0	121.660584	0.0	0.000000	0.975948	0.218005	-0.218005	0.975948	27.394927	179.878327
37	38	248.0	208.017467	208.0	128.0	29.009010	95272.0	841.522670	233	137	...	23	83.278130	23.0	0.276183	0.844799	0.535083	-0.535083	0.844799	21.736051	65.950501
38	39	232.0	197.419355	208.0	128.0	28.666250	42840.0	821.753883	60	138	...	0	52.805475	0.0	0.000000	0.986995	0.160753	-0.160753	0.986995	14.052349	21.247148
39	40	232.0	191.774648	200.0	136.0	24.532044	27232.0	601.821197	183	149	...	0	42.309444	0.0	0.000000	0.965804	0.259275	-0.259275	0.965804	9.197500	13.952669
40	41	232.0	180.952381	184.0	128.0	24.471401	72200.0	598.849486	125	152	...	0	72.226739	0.0	0.000000	-0.653319	-0.757082	0.757082	-0.653319	22.888892	44.383172
41	42	248.0	204.708333	216.0	120.0	28.500531	78608.0	812.280244	6	157	...	0	70.100583	0.0	0.000000	0.904586	0.426291	-0.426291	0.904586	25.066435	37.439939
42	43	248.0	191.221239	192.0	128.0	26.451712	43216.0	699.693058	206	158	...	0	53.916196	0.0	0.000000	0.977778	0.209643	-0.209643	0.977778	15.830580	20.544723
43	44	240.0	200.091691	208.0	136.0	27.115603	69832.0	735.255937	36	160	...	0	66.863705	0.0	0.000000	0.999560	-0.029663	0.029663	0.999560	21.238298	36.355055
44	45	240.0	204.294599	216.0	128.0	28.702058	124824.0	823.808151	167	167	...	0	88.736449	0.0	0.000000	0.984212	-0.176992	0.176992	0.984212	44.044878	54.215343
45	46	248.0	215.719298	224.0	136.0	32.074924	73776.0	1028.800741	223	174	...	0	65.752985	0.0	0.000000	0.756607	0.653870	-0.653870	0.756607	24.162673	30.794348
46	47	240.0	205.387454	216.0	136.0	24.250565	111320.0	588.089898	117	185	...	0	83.833491	0.0	0.000000	0.116985	-0.993134	0.993134	0.116985	41.327753	45.322011
47	48	232.0	194.711864	200.0	136.0	29.510402	11488.0	870.863822	251	193	...	15	33.479495	15.0	0.448035	0.999821	0.018944	-0.018944	0.999821	1.690956	14.325132
48	49	232.0	186.684211	192.0	128.0	25.196557	28376.0	634.866504	200	195	...	0	44.435601	0.0	0.000000	0.980620	0.195921	-0.195921	0.980620	9.610562	15.277380
49	50	232.0	168.875000	168.0	120.0	25.410148	75656.0	645.675615	18	200	...	0	82.262694	0.0	0.000000	0.958423	-0.285352	0.285352	0.958423	17.922660	72.404250
50	51	248.0	229.430657	248.0	144.0	26.958373	125728.0	726.753866	90	200	...	0	85.078964	0.0	0.000000	0.774700	-0.632329	0.632329	0.774700	31.162401	61.364008
51	52	216.0	191.100952	200.0	128.0	22.709233	100328.0	515.709255	51	203	...	0	83.278130	0.0	0.000000	0.957483	-0.288491	0.288491	0.957483	31.380235	55.869804
52	53	240.0	206.313514	216.0	144.0	26.433038	38168.0	698.705523	0	214	...	24	56.137637	24.0	0.427521	0.999497	-0.031726	0.031726	0.999497	6.941190	35.497670
53	54	248.0	224.251473	240.0	144.0	29.542436	114144.0	872.755534	221	215	...	0	80.826651	0.0	0.000000	0.327038	-0.945011	0.945011	0.327038	37.923490	43.556039
54	55	248.0	200.145985	208.0	128.0	27.374216	164520.0	749.347724	161	217	...	0	108.157714	0.0	0.000000	0.119267	-0.992862	0.992862	0.119267	41.764270	104.664511
55	56	232.0	195.920949	200.0	128.0	25.860310	49568.0	668.755631	131	224	...	0	56.597713	0.0	0.000000	0.998990	-0.044926	0.044926	0.998990	15.823917	25.661186
56	57	224.0	188.994924	192.0	136.0	24.472912	37232.0	598.923443	40	232	...	0	50.123958	0.0	0.000000	0.989524	0.144369	-0.144369	0.989524	11.684511	21.090000
57	58	216.0	184.761905	192.0	136.0	23.153557	15520.0	536.087206	118	249	...	21	44.856208	21.0	0.468163	0.006588	-0.999978	0.999978	0.006588	1.724907	28.033313
58	59	248.0	191.314286	184.0	144.0	30.233652	13392.0	914.073706	171	249	...	17	37.271733	17.0	0.456110	-0.007722	-0.999970	0.999970	-0.007722	1.757346	18.883470
59	60	248.0	204.600000	208.0	152.0	29.429446	8184.0	866.092308	228	250	...	12	27.005740	12.0	0.444350	-0.034966	-0.999388	0.999388	-0.034966	1.150116	9.234259

60 rows × 33 columns

These are all columns that are available:

print(statistics.keys())

Index(['label', 'maximum', 'mean', 'median', 'minimum', 'sigma', 'sum',
       'variance', 'bbox_0', 'bbox_1', 'bbox_2', 'bbox_3', 'centroid_0',
       'centroid_1', 'elongation', 'feret_diameter', 'flatness', 'roundness',
       'equivalent_ellipsoid_diameter_0', 'equivalent_ellipsoid_diameter_1',
       'equivalent_spherical_perimeter', 'equivalent_spherical_radius',
       'number_of_pixels', 'number_of_pixels_on_border', 'perimeter',
       'perimeter_on_border', 'perimeter_on_border_ratio', 'principal_axes0',
       'principal_axes1', 'principal_axes2', 'principal_axes3',
       'principal_moments0', 'principal_moments1'],
      dtype='object')

df.describe()

	label	maximum	mean	median	minimum	sigma	sum	variance	bbox_0	bbox_1	...	number_of_pixels_on_border	perimeter	perimeter_on_border	perimeter_on_border_ratio	principal_axes0	principal_axes1	principal_axes2	principal_axes3	principal_moments0	principal_moments1
count	60.000000	60.000000	60.000000	60.000000	60.000000	60.000000	60.000000	60.000000	60.000000	60.000000	...	60.000000	60.000000	60.000000	60.000000	60.000000	60.000000	60.000000	60.000000	60.000000	60.000000
mean	30.500000	236.000000	194.966598	200.800000	130.000000	26.069709	71696.933333	693.962389	123.516667	110.200000	...	5.683333	107.224145	5.700000	0.089574	0.696028	-0.138186	0.138186	0.696028	104.628848	134.931776
std	17.464249	14.012101	16.394414	19.579304	7.456086	3.817798	41465.329504	183.657670	81.460709	76.672493	...	10.255204	309.846236	10.310929	0.161164	0.476871	0.526743	0.526743	0.476871	651.200133	712.958883
min	1.000000	176.000000	137.526132	136.000000	112.000000	13.360739	2576.000000	178.509343	0.000000	0.000000	...	0.000000	14.843629	0.000000	0.000000	-0.653319	-0.999978	-0.653870	-0.653319	1.046852	1.755916
25%	15.750000	232.000000	188.713774	192.000000	128.000000	24.472535	40604.000000	598.904954	52.500000	42.750000	...	0.000000	53.221995	0.000000	0.000000	0.649215	-0.663517	-0.279282	0.649215	12.841678	22.351873
50%	30.500000	240.000000	195.937410	200.000000	128.000000	26.409917	71016.000000	697.484271	127.000000	108.500000	...	0.000000	68.482144	0.000000	0.000000	0.952820	0.026675	-0.026675	0.952820	18.738377	35.597627
75%	45.250000	248.000000	204.627083	210.000000	136.000000	28.649791	99386.000000	820.810634	201.500000	168.750000	...	11.250000	83.278130	11.250000	0.142182	0.989550	0.279282	0.663517	0.989550	29.329379	56.857478
max	60.000000	248.000000	229.430657	248.000000	152.000000	32.682072	172424.000000	1068.117840	251.000000	250.000000	...	39.000000	2461.579651	40.000000	0.495128	0.999988	0.653870	0.999978	0.999988	5063.911496	5560.184284

8 rows × 33 columns

Specific measures

SimpleITK offers some non-standard measurements which deserve additional documentation

perimeter_on_border_ratio

In this context, the SimpleITK documentation points to a publication which mentiones “‘SizeOnBorder’ is the number of pixels in the objects which are on the border of the image.” While the documentation is wage, the perimeter_on_border_ratio may be related.

First, we check its range on the above example image.

perimeter_on_border_ratio = df['perimeter_on_border_ratio'].tolist()

np.min(perimeter_on_border_ratio), np.max(perimeter_on_border_ratio)

(0.0, 0.4951280471249033)

Next, we visualize the measurement in space.

perimeter_on_border_ratio_map = cle.replace_intensities(labels, [0] + perimeter_on_border_ratio)
perimeter_on_border_ratio_map

cle._ image shape (254, 256) dtype float32 size 254.0 kB min 0.0 max 0.49512804

The visualization substantiates our presumption that the perimeter_on_border_ratio indeed is related to the amount the object touches the image border.