Estimation of Volume and Mass of Axi-Symmetric Fruits Using Image Processing Technique

Figures & data

FIGURE 1 Steps involved in the proposed method.

FIGURE 2 Steps in extraction of contour.

FIGURE 3 Boundary points of apple.

TABLE 1 Criteria for shape models

Eccentricity	b/a Ratio	Position of ED with respect to mid. of PD	Shape models
<0.3	0.95–1.05	± 5% of PD	Circular
0.3–0.7	0.7–0.95	± 5% of PD	Elliptical
−	−	>5% of PD	Parabolic

TABLE 2 Estimated and actual values of volume and mass of apple, sweet-lime, lemon, and orange fruits with % deviation

Fruit no.	Est. vol. (cm^3)	Act. vol. (cm^3)	% vol Dev	Est. mass (g)	Act. mass (g)	% Mass dev	Fruit no.	Est. vol. (cm^3)	Act. vol. (cm^3)	% Vol dev	Est. mass (g)	Act. mass (g)	% Mass dev
Apple fruit samples
1	199.96	195	2.54	160.52	154	4.23	11	190.28	195	−2.42	153.89	155	−0.72
2	173.84	175	−0.67	142.62	144	−0.96	12	173.52	180	−3.6	140.54	145	−3.07
3	178.15	185	−3.71	145.57	146	−0.30	13	204.40	210	−2.67	163.57	169	−3.22
4	212.82	215	−1.01	169.34	172	−1.55	14	182.54	190	−3.93	148.58	152	−2.25
5	159.28	160	−0.45	132.64	134	−1.02	15	193.31	200	−3.35	155.96	169	−7.72
6	171.63	165	4.02	141.10	137	2.99	16	201.38	200	0.69	161.50	158	2.21
7	166.19	170	−2.24	137.38	136	1.01	17	186.41	190	−1.89	151.23	155	−2.43
8	162.71	165	−1.39	134.99	138	−2.18	18	258.46	245	5.50	200.62	189	6.15
9	204.41	210	−2.66	163.57	167	−2.05	19	210.06	210	0.03	167.44	170	−1.51
10	189.78	185	2.58	153.54	155	−0.94	20	206.51	215	−3.95	165.01	170	−2.93
Sweet-lime fruit samples
1	203.80	200	1.90	183.02	184	−0.53	19	189.07	190	−0.49	171.35	167	2.61
2	214.59	215	−0.19	191.57	187	2.44	20	164.38	165	−0.38	151.78	156	−2.71
3	194.25	200	−2.87	175.46	182	−3.60	21	214.39	220	−2.55	191.41	199	−3.81
4	163.47	170	−3.84	151.06	157	−3.78	22	157.32	160	−1.68	146.18	139	5.17
5	187.05	190	−1.55	169.75	173	−1.88	23	165.44	175	−5.46	152.62	160	−4.61
6	147.58	150	−1.62	138.46	148	−6.44	24	182.48	180	1.38	166.13	171	−2.85
7	140.21	145	−3.30	132.62	133	−0.28	25	191.52	190	0.80	173.29	174	−0.41
8	190.37	190	0.20	172.38	179	−3.70	26	132.45	140	−5.39	126.48	135	−6.31
9	178.56	185	−3.48	163.02	168	−2.97	27	148.86	150	−0.76	139.48	137	1.81
10	190.31	190	0.16	172.33	168	2.58	28	186.60	200	−6.70	169.39	173	−2.08
11	235.33	230	2.32	208.01	202	2.97	29	209.90	205	2.39	187.86	185	1.54
12	209.42	200	4.71	187.48	183	2.45	30	197.87	200	−1.07	178.32	180	−0.93
13	189.54	200	−5.23	171.72	177	−2.98	31	148.59	160	−7.13	139.26	146	−4.61
14	174.06	185	−5.92	159.45	166	−3.95	32	136.39	130	4.91	129.60	130	−0.31
15	200.41	200	0.20	180.33	187	−3.57	33	166.00	175	−5.14	149.10	158	−5.63
16	190.55	200	−4.73	172.52	177	−2.53	34	177.57	175	1.47	162.23	160	1.40
17	171.73	175	−1.87	157.61	157	0.39	35	159.76	170	−6.03	144.15	152	−5.16
18	144.28	155	−6.91	135.85	143	−5.00	36	228.51	220	3.87	202.61	200	1.30
Lemon fruit samples
1	54.49	55	−0.92	49.05	48	2.19	11	37.38	35	6.80	34.98	33	6.00
2	52.82	50	5.63	47.62	45	5.82	12	32.98	35	−5.78	30.72	29	5.91
3	35.07	35	0.19	32.50	31	4.83	13	37.08	35	5.95	35.07	34	3.14
4	75.84	71	6.82	67.24	63	6.73	14	35.27	33	6.87	34.37	32	7.41
5	71.96	70	2.80	63.94	60	6.56	15	53.37	50	6.74	49.80	47	5.95
6	56.13	55	2.06	50.45	50	0.89	16	51.00	50	1.99	46.07	46	0.15
7	42.63	40	6.57	38.94	37	5.24	17	44.36	45	−1.43	40.41	38	6.35
8	46.91	44	6.61	42.59	40	6.47	18	46.72	50	−6.55	42.43	41	3.49
9	48.15	45	7.01	43.65	42	3.92	19	46.73	45	3.85	42.44	42	1.04
10	47.94	45	6.53	44.32	42	5.52	20	39.10	40	−2.24	35.94	34	5.69
Orange fruit samples
1	361.49	350	3.28	262.51	248	5.85	21	177.04	165	7.30	153.75	144	6.77
2	290.03	305	−4.91	220.38	235	−6.22	22	154.20	160	−3.63	117.88	113	4.32
3	206.33	220	−6.21	168.08	180	−6.62	23	182.36	175	4.21	156.89	164	−4.34
4	273.24	275	−0.64	210.47	196	7.38	24	253.77	275	−7.72	204.00	220	−7.27
5	277.96	300	−7.35	212.08	229	−7.39	25	299.80	300	−0.07	226.14	225	0.51
6	210.05	225	−6.64	175.50	190	−7.63	26	219.99	235	−6.39	179.08	194	−7.69
7	282.17	285	−0.99	215.74	225	−4.12	27	196.11	210	−6.61	164.10	176	−6.76
8	187.61	200	−6.2	155.86	159	−1.98	28	316.29	320	−1.16	235.86	219	7.70
9	194.41	210	−7.42	161.05	161	0.03	29	293.29	295	−0.58	222.30	228	−2.50
10	166.06	160	3.79	147.28	137	7.50	30	259.44	250	3.78	202.34	198	2.19
11	291.72	290	0.59	221.37	225	−1.61	31	218.79	235	−6.90	178.37	193	−7.58
12	204.78	220	−6.92	170.11	182	−6.53	32	287.62	275	4.59	215.95	202	6.91
13	182.59	195	−6.36	157.03	156	0.66	33	240.38	255	−5.73	191.10	204	−6.32
14	160.14	165	−2.94	143.79	147	−2.18	34	190.11	200	−4.94	161.46	170	−5.02
15	143.44	150	−4.37	133.94	136	−1.51	35	297.81	285	4.49	224.96	211	6.62
16	178.09	165	7.93	154.37	150	2.91	36	187.06	195	−4.07	159.66	152	5.04
17	184.04	190	−3.13	167.88	177	−5.15	37	241.81	255	−5.17	194.94	211	−7.61
18	145.86	150	−2.76	135.37	139	−2.61	38	272.75	255	6.96	210.18	196	7.24
19	187.29	195	−3.95	169.80	181	−6.19	39	189.57	195	−2.78	161.14	165	−2.34
20	143.58	150	−4.28	134.03	136	−1.45	40	232.32	220	5.60	186.35	185	0.73

FIGURE 4(a) Comparison of estimated and actual volume of apples.

FIGURE 4(b) Comparison of estimated and actual volume of sweet-limes.

FIGURE 4(c) Comparison of estimated and actual volume of lemons.

FIGURE 4(d) Comparison of estimated and actual volume of oranges.

FIGURE 5(a) Comparison of estimated and actual mass of apples.

FIGURE 5(b) Comparison of estimated and actual mass of sweet-limes.

FIGURE 5(c) Comparison of estimated and actual mass of lemons.

FIGURE 5(d) Comparison of estimated and actual mass of oranges.

FIGURE 6(a) 2–σ plots for the difference in volume (estimated volume–actual volume) of apples.

FIGURE 6(b) 2–σ plots for the difference in volume (estimated volume–actual volume) of sweet-limes.

FIGURE 6(c) 2–σ plots for the difference in volume (estimated volume–actual volume) of lemons.

FIGURE 6(d) 2–σ plots for the difference in volume (estimated volume–actual volume) of oranges.

FIGURE 7(a) 2–σ plots for the difference in mass (estimated mass–actual mass) of apples.

FIGURE 7(b) 2–σ plots for the difference in mass (estimated mass–actual mass) of sweet-limes.

FIGURE 7(c) 2–σ plots for the difference in mass (estimated mass–actual mass) of lemons.

FIGURE 7(d) 2–σ plots for the difference in mass (estimated mass–actual mass) of oranges.

TABLE 3 Correlation data of fruit samples

	Coefficient of determination (R^2)
Fruit	Volume	Mass
Apples	0.925	0.887
Sweet-lime	0.943	0.947
Lemon	0.910	0.986
Orange	0.947	0.861