# In-Orchard Sizing of Mango Fruit: 2. Forward Estimation of Size at Harvest

^{*}

## Abstract

**:**

^{2}of 0.99, RMSE of 29.9 g and slope of 0.5472 g/cm

^{3}, while the linear correlation of fruit mass to $L(\frac{\left(W+T\right)}{2}$)

^{2}, mimicking what can be measured by machine vision of fruit on tree, was characterized by a R

^{2}of 0.97, RMSE of 25.0 g and slope of 0.5439 g/cm

^{3}. A procedure was established for the prediction of fruit size at harvest based on measurements made five and four or four and three weeks prior to harvest (approx. 514 and 422 GDD, before harvest, respectively). Linear regression models on weekly increase in fruit mass estimated from lineal measurements were characterized by an R

^{2}> 0.88 for all populations, with an average slope (rate of increase) of 19.6 ± 7.1 g/week, depending on cultivar, season and site. The mean absolute percentage error for predicted mass compared to harvested fruit weight for estimates based on measurements of the earlier and later intervals was 16.3 ± 1.3% and 4.5 ± 2.4%, respectively. Measurement at the later interval allowed better accuracy on prediction of fruit tray size distribution. A recommendation was made for forecast of fruit mass at harvest based on in-field measurements at approximately 400 to 450 GDD units before harvest GDD and one week later.

## 1. Introduction

^{2}= 0.97, RMSE = 28.7 g) by Anderson et al. [5] and Spreer and Muller [3].

^{2}. Wang et al. [4] reported use of a Kinect v2 depth camera mounted on an imaging platform with a LED floodlight used to perform orchard imaging at night for mango fruit load estimation (as used by Anderson et al. [2]. The depth camera allowed measurement of camera to fruit distance and estimation of the actual size of detected and localized fruit using the thin lens formula. A subset of imaged fruit was considered, being those fruit considered to be un-occluded based on eccentricity of an ellipse fitted to the object bounding box. A RMSE of 4.9 and 4.3 mm was reported for fruit L and apparent W, respectively. With the Kinect v2 discontinued from production, Neupane et al. [8] undertook a comparison of seven commercially available depth cameras, recommending the Azure Kinect camera for this fruit sizing application, based on the RMSE of camera to object distance measurements.

^{2}of 0.87, for Golden Delicious, and up to 10% for the other cultivars, relative to actual mass of fruit at harvest. Khurshid and Braysher (2009) [11] predicted the final fruit size distribution of Washington Navel oranges from measurements made more than 150 days before harvest, using a non-linear model based on cubic smoothing splines developed on data of three seasons and tested on data of a fourth season. A prediction error of 10%, with R

^{2}of 0.82, was reported. However, such ‘long range’ predictions risk failure when growing conditions are not consistent.

## 2. Materials and Methods

#### 2.1. Plant Material

#### 2.2. Harvest Maturity Estimation

#### 2.3. Fruit Measurements

#### 2.4. Statistics

## 3. Results and Discussion

#### 3.1. Estimation of Fruit Mass from Linear Dimensions

^{2}> 0.997 and RMSE of 29.9 g, which was similar to that of cultivar specific models (Figure 2). Slopes (g/cm

^{3}) of 0.55, 0.55 and 0.54 (with SE of 0.005 or less in all cases) were recorded for the ‘Honey Gold’, ‘Keitt’ and ‘Calypso’ populations, while the slope for a combined cultivar model was 0.55 (SE of 0.004). Use of the combined model M (g) = 0.5472*LWT was considered acceptable for mass estimation of these three cultivars. The fit of a linear relationship between mass and volume infers that variation in fruit specific gravity with fruit maturation was negligible in context of the slope of mass to LWT.

^{2}0.95 to 0.98 and RMSE from 8 to 17 g for data of three seasons, and overall slope of 0.54 g/cm

^{3}. For the Australian cultivar ‘Calypso’, Anderson et al. [5] reported a R

^{2}of 0.97, RMSE of 28.7 g and slope of 0.49–0.51 g/cm

^{3}.

#### 3.2. Sampling

#### 3.3. Prediction of Fruit Mass at Harvest

^{2}of a linear regression fit to the time series data of fruit mass was above 0.89 for all populations assessed, on both a GDD (Figure 4) and calendar day (data not shown), reflecting relatively stable environmental conditions in these cases. However, growth rates varied between populations, i.e., cultivar and growing condition. Rates are reported in terms of g/GDD in Figure 4. For the same data sets, the rates estimated in units of g/week were: (i) between 16.9 and 34.2 g/week for the Calypso sets; (ii) between 17.0 and 32.5 g/week for the Honey Gold sets, and between 15.3 and 18.8 g/week for the ‘Keitt’ sets.

#### 3.4. Prediction of Tray Size Distribution at Harvest

#### 3.5. Recommendations for Future Work

^{2}, respectively, and the frequency distribution of fruit tray size distributions was not significantly affected. Use of fruit area as a machine vision input, as suggested by Utai et al. [6], is also warranted.

## 4. Conclusions

## Supplementary Materials

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

- Anderson, N.; Walsh, K.; Wulfsohn, D. Technologies for forecasting tree fruit load and harvest timing from ground, sky and time. Agronomy
**2021**, 11, 1409. [Google Scholar] [CrossRef] - Anderson, N.; Walsh, K.; Koirala, A.; Wang, Z.; Amaral, M.H.; Dickinson, G. Estimation of fruit load in Australian mango orchards using machine vision. Agronomy
**2021**, 11, 1711. [Google Scholar] [CrossRef] - Spreer, W.; Müller, J. Estimating the mass of mango fruit (Mangifera indica, cv. Chok Anan) from its geometric dimensions by optical measurement. Comput. Electron. Agric.
**2011**, 75, 125–131. [Google Scholar] [CrossRef] - Wang, Z.; Walsh, K.B.; Verma, B. On-tree mango fruit size estimation using RGB-D images. Sensors
**2017**, 17, 2738. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Anderson, N.; Subedi, P.; Walsh, K. Manipulation of mango fruit dry matter content to improve eating quality. Sci. Hortic.
**2017**, 226, 316–321. [Google Scholar] [CrossRef] - Utai, K.; Nagle, M.; Hämmerle, S.; Spreer, W.; Mahayothee, B.; Müller, J. Mass estimation of mango fruits (Mangifera indica L.; cv. ‘Nam Dokmai’) by linking image processing and artificial neural network. Eng. Agric. Environ. Food
**2019**, 12, 103–110. [Google Scholar] [CrossRef] - Wang, Z.; Koirala, A.; Walsh, K.; Anderson, N.; Verma, B. In field fruit sizing using a smart phone application. Sensors
**2018**, 18, 3331. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Neupane, C.; Koirala, A.; Wang, Z.; Walsh, K. Evaluation of depth cameras for use in fruit localization and sizing: Finding a successor to Kinect v2. Agronomy
**2021**, 11, 1780. [Google Scholar] [CrossRef] - Carella, A.; Gianguzzi, G.; Scalisi, A.; Farina, V.; Inglese, P.; Bianco, R. Fruit growth stage transitions in two mango cultivars grown in a Mediterranean environment. Plants
**2021**, 10, 1332. [Google Scholar] [CrossRef] [PubMed] - Costa, G.; Noferini, M.; Bucchi, F.; Corelli-Grappadelli, L. Methods for early forecasting apple size at harvest. Acta Hortic.
**2004**, 636, 651–659. [Google Scholar] [CrossRef] - Khurshid, T.; Braysher, B. Early fruit size prediction model using cubic smoothing splines for ‘Washington Navel’ (Citrus sinensis L. Osbeck) oranges in Australia. Int. J. Fruit Sci.
**2009**, 9, 394–408. [Google Scholar] [CrossRef] - Da Silva, D.F.; Salomão, L.C.; Pereira, L.D.; Valle, K.D.; Assunção, H.F.; Cruz, S.C. Development and maturation of mango fruits CV. ‘ubá’ in Visconde do rio branco, Minas Gerais State, Brazil. Rev. Ceres
**2018**, 65, 507–516. [Google Scholar] [CrossRef] - Souza, J.; Leonel, S.; Modesto, J.; Ferraz, R.; Gonçalves, B. Phenological cycles, thermal time and growth curves of mango fruit cultivars in subtropical conditions. Br. J. Appl. Sci. Technol.
**2015**, 9, 100–107. [Google Scholar] [CrossRef] [Green Version] - Anila, R.; Radha, T. Studies on fruit drop in mango varieties. Coll. Hortic. J. Trop. Agric.
**2003**, 41, 30–32. [Google Scholar] - Ometto, J. Bioclimatologia vegetal [Plant Bioclimatology]. Agron. Ceres
**1981**, 1, 129–155. [Google Scholar] - Moore, C. Developing a Crop Forecasting System for the Australian Mango Industry. Available online: https://www.horticulture.com.au/globalassets/hort-innovation/historic-reports/developing-a-crop-forecasting-system-for-the-australian-mango-industry-mg05004.pdf (accessed on 3 March 2022).
- Amaral, M.H.P. Benchmarking New Methods for Estimation of Quantity and Harvest Timing of the Mango Crop. Master’s Thesis, Central Queensland University, Rockhampton, Australia, 2022. [Google Scholar]
- Walsh, K.B. In-field estimation of fruit quality and quantity. Agronomy
**2022**, 12, 1074. [Google Scholar] [CrossRef] - Scalisi, A.; O’Connell, G.M.; Stefanelli, D.; Lo Biancco, R. Fruit and leaf sensing for continuous detection of Nectarine Water Status. Front. Plant Sci.
**2019**, 10, 805. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Walsh, K.B.; Long, R.L.; Middleton, S.G. Use of near infra-red spectroscopy in evaluation of source-sink manipulation to increase the soluble sugar content of stonefruit. J. Hortic. Sci. Biotechnol.
**2007**, 82, 316–322. [Google Scholar] [CrossRef] - Kernot, I.; Meurant, N. Mango Information Kit; Agrilink, Dept. of Primary Industries: Nambour, Queensland, 1999. Available online: http://era.daf.qld.gov.au/id/eprint/1647/1/0tit-mango.pdf (accessed on 12 November 2021).
- Neupane, C.; Koirala, A.; Walsh, K.B. In-orchard sizing of Mango Fruit: 1. comparison of machine vision-based methods for on-the-go estimation. Horticulturae
**2022**, 8, 1223. [Google Scholar] [CrossRef]

**Figure 2.**Scatter plots of fruit mass (g) against LWT (cm

^{3}) for (

**a**) ‘Honey Gold’ (populations 1a, 1b, 2a, 2b and 8 n = 110) (top panel), (

**b**) ‘Keitt’ (populations 3, 4 and 9, n = 75); (

**c**) ‘Calypso’ (population 5, 6 and 7, n = 100), and (

**d**) all populations, i.e., combined cultivars (n = 285). Pearson’s linear regression fit, equation with SE of slope, R

^{2}and RMSE are shown. Mean and SD of fruit mass of ‘Calypso’, ‘Honey Gold’ and ‘Keitt’ populations were 369 ± 74, 553 ± 118, and 524 ± 149 g, respectively.

**Figure 3.**Scatter plot of fruit mass (g) against L ($\frac{(W+T)}{2}$)

^{2}(cm

^{3}) for all populations, i.e., combined cultivar data. Pearson’s linear regression fit, equation and R

^{2}shown on graph. Samples are common to those presented in Figure 2.

**Figure 4.**Plot of fruit mass estimated from lineal measurements of L, W and T using a combined cultivar model against Growing Degree Days (GDD) from ‘asparagus’ stage. Measurements were made at intervals of 7 days. Top panel: ‘Calypso’ fruit from two blocks that flowered two weeks apart (pop. 5 and 6) in the same farm in NT, and from a FNQLD orchard (pop. 7). Middle panel: populations of Honey Gold fruit from two flowering events in each of two blocks in CQLD (pop. 1 and 2) and a block from FNQLD region (pop. 8). Bottom panel: ‘Keitt’ fruit from two blocks that flowered two weeks apart (pop. 3 and 4) and a block from Northeast, Brazil (pop. 9); Data is presented as mean with associated SE, for n = 17 to 44 (see Table 1). Harvest maturity date (by GDD) for each fruit cultivar is indicated by a vertical red line.

**Figure 5.**Frequency distributions of fruit mass (kLWT) (using 30 g categories) of population 9 for each of four weeks (panels

**A**–

**D**) and of actual mass at harvest (panel

**E**). Mean fruit mass at each date is shown as a red arrow. Mean and SD of mass (kLWT) was 424 ± 79, 448 ± 86 and 469 ± 88, 479 ± 85 and 485 ± 88 g for panels A to E, respectively.

**Figure 6.**kLWT estimate. Frequency (% of total fruit number) for fruit mass ranges equivalent to tray sizes for Populations 1 (top), 5 (middle) and 9 (bottom), i.e., example ‘Calypso’, ‘Honey Gold’ and ‘Keitt’ populations, respectively. Each panel displays a distribution for four and three weeks before harvest (bars), and for the forecast and actual fruit size at harvest (lines). Forecast size was based on a growth rate of 23.2, 32.7 and 25.1 g/week (as estimated from the mass change between weeks 4 and 3) for populations 1, 5 and 9, respectively. Fruit mass was calculated using fruit L, W and T (Equation (1)).

**Table 1.**Fruit populations derived from separate orchards, cultivars, and flowering events, as used in sizing exercises. Farm A was in central Queensland, B in Northern Territory, C in Far North Queensland (Australia) and D in northern Brazil. In orchards 1 and 2, fruit from which of two flowering events (a,b) were monitored. The monitored period refers to the period (weeks before harvest) over which measurements were made. Dates of fruit size assessment refer to day-month and GDD units from asparagus stage of panicle development.

Farm | Population | Cultivar | Season | Fruit Sample Size (n) | Monitored Period (weeks) | Day-Month of Initial Assessment (GDD) | Day-Month of Final Assessment (GDD) |
---|---|---|---|---|---|---|---|

A | 1a | Honey Gold | 2020/21 | 25 | 7 | 19-11 (1250) | 14-01 (1886) |

A | 1b | Honey Gold | 2020/21 | 25 | 7 | 19-11 (1328) | 14-01 (1965) |

A | 2a | Honey Gold | 2020/21 | 25 | 9 | 19-11 (1250) | 14-01 (1886) |

A | 2b | Honey Gold | 2020/21 | 15 | 9 | 19-11 (1318) | 14-01 (2141) |

A | 3 | Keitt | 2020/21 | 26 | 7 | 22-12 (1796) | 02-02 (2456) |

A | 4 | Keitt | 2020/21 | 17 | 9 | 14-01 (2053) | 11-03 (2922) |

B | 5 | Calypso | 2021/22 | 44 | 5 | 02-09 (1243) | 30-09 (1669) |

B | 6 | Calypso | 2021/22 | 27 | 4 | 02-09 (1410) | 23-09 (1739) |

C | 7 | Calypso | 2021/22 | 29 | 4 | 03-11 (1369) | 29-11 (1739) |

C | 8 | Honey Gold | 2021/22 | 20 | 4 | 03-11 (1369) | 29-11(1739) |

D | 9 | Keitt | 2021/22 | 32 | 5 | 14-10 (1755) | 8-11 (2188) |

**Table 2.**Prediction of harvest fruit mass from pre-harvest measurements of fruit L, W and T dimensions at between 5 and 4, or 4 and 3, weeks before harvest. The GDD values for the start date of size measurements (nominally 4 and 5 weeks from target harvest date) are given. Percentage error is calculated as (predicted mass—actual mass) divided by actual mass × 100. Bottom rows (*) present mean and SD of absolute errors. Sample size per population varied between 17 and 44 (see Table 1).

Population | GDD at Measurement Start (Weeks before Harvest) | Period (Weeks before Harvest) | Slope (g/week) | Predicted Mass at Harvest Maturity | Actual Mass (LWT) at Harvest Maturity | Percentage Error (%) |
---|---|---|---|---|---|---|

1a | 505.1 (5) | 5 and 4 | 42.6 | 599 | 506 | 18 |

1a | 421.2 (4) | 4 and 3 | 12.5 | 479 | 506 | −5 |

1b | 523.6 (5) | 5 and 4 | 41.5 | 560 | 487 | 15 |

1b | 418.5 (4) | 4 and 3 | 23.2 | 487 | 487 | 0 |

2a | 505.1 (5) | 5 and 4 | 52.2 | 686 | 590 | 16 |

2a | 421.2 (4) | 4 and 3 | 24.3 | 574 | 590 | −3 |

2b | 523.6 (5) | 5 and 4 | 1.2 | 444 | 526 | −15 |

2b | 431.0 (4) | 4 and 3 | 30.2 | 560 | 526 | 6 |

8 | 371.3 (4) | 4 and 3 | 20.1 | 465 | 453 | 3 |

5 | 443.1 (4) | 4 and 3 | 32.7 | 402 | 408 | −2 |

6 | 434.0 (4) | 4 and 3 * | 16.0 | 339 | 353 | −4 |

7 | 371.3 (4) | 4 and 3 | 22.6 | 393 | 367 | 7 |

3 | 469.5 (4) | 4 and 3 | 8.1 | 449 | 479 | −6 |

4 | 427.8 (4) | 4 and 3 | 26.9 | 594 | 572 | 4 |

9 | 433.9 (4) | 4 and 3 | 25.1 | 523 | 485 | 8 |

Mean ± SD | 514.3 ± 9.2 | 5 and 4 | 34.4 ± 22.0 | 16.3 ± 1.3 * | ||

Mean ± SD | 422.1 ± 27.4 | 4 and 3 | 19.6 ± 7.1 | 4.5 ± 2.4 * |

**Table 3.**k L* ($\frac{(W+T)}{2}$)

^{2}estimate. Frequency (% of total fruit number) fruit mass ranges equivalent to tray sizes at (i) four and (ii) three weeks before harvest, (iii) the forecast fruit size and (iv) for the actual harvest mass of fruit, for populations 1, 5 and 9, being example ‘Calypso’, ‘Honey Gold’ and ‘Keitt’ populations. Forecast fruit size was based on a growth rate of 17.9, 30.3 and 25.1 g/week, as estimated from the mass change between weeks 4 and 3, for the three populations, respectively. Fruit mass was calculated using fruit L and the average of W and T (Equation (4)). Each estimated distribution (i.e., each table column) was compared to that generated using kLWT (Equation (1)) to estimate mass, as displayed in Figure 6, using a chi-squared test.

Population | 1 | 1 | 1 | 1 | 5 | 5 | 5 | 5 | 9 | 9 | 9 | 9 |
---|---|---|---|---|---|---|---|---|---|---|---|---|

Fruit mass | (i) week 4 | (ii) week 3 | (iii) harvest prediction | (iv) harvest actual | (i) week 4 | (ii) week 3 | (iii) harvest prediction | (iv) harvest actual | (i) week 4 | (ii) week 3 | (iii) harvest prediction | (iv) harvest actual |

(g) | (%) | (%) | (%) | (%) | (%) | (%) | (%) | (%) | (%) | (%) | (%) | (%) |

<290 | 10 | 4 | 4 | 4 | 59 | 39 | 5 | 11 | 6 | 0 | ||

290–325 | 16 | 12 | 18 | 23 | 9 | 9 | 3 | 9 | ||||

325–360 | 10 | 10 | 4 | 4 | 20 | 18 | 11 | 5 | 16 | 6 | 6 | |

361–405 | 18 | 24 | 18 | 4 | 2 | 18 | 34 | 20 | 16 | 16 | 9 | 19 |

405–463 | 40 | 24 | 24 | 22 | 32 | 27 | 25 | 28 | 16 | 16 | ||

464–514 | 6 | 26 | 28 | 24 | 9 | 23 | 16 | 13 | 22 | 19 | ||

515–600 | 22 | 32 | 5 | 16 | 25 | 31 | 31 | |||||

601–720 | 10 | 3 | 3 | 19 | 9 | |||||||

>720 | ||||||||||||

Comparison to distribution based on kLWT estimated mass (as presented in Figure 6), by column. | ||||||||||||

X^{2} * | 2.8 | 1.4 | 11.3 | 0.0 | 0.6 | 5.5 | 2.8 | 0.3 | 1.9 | |||

p value * | 0.723 | 0.910 | 0.080 | 1.000 | 0.880 | 0.360 | 0.900 | 1.000 | 0.749 | |||

^{2}) and p-value compared to data of Figure 6 (Equation (1)).

Disclaimer/Publisher’s Note: The statements, opinions and data contained in all publications are solely those of the individual author(s) and contributor(s) and not of MDPI and/or the editor(s). MDPI and/or the editor(s) disclaim responsibility for any injury to people or property resulting from any ideas, methods, instructions or products referred to in the content. |

© 2023 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Amaral, M.H.; Walsh, K.B.
In-Orchard Sizing of Mango Fruit: 2. Forward Estimation of Size at Harvest. *Horticulturae* **2023**, *9*, 54.
https://doi.org/10.3390/horticulturae9010054

**AMA Style**

Amaral MH, Walsh KB.
In-Orchard Sizing of Mango Fruit: 2. Forward Estimation of Size at Harvest. *Horticulturae*. 2023; 9(1):54.
https://doi.org/10.3390/horticulturae9010054

**Chicago/Turabian Style**

Amaral, Marcelo H., and Kerry B. Walsh.
2023. "In-Orchard Sizing of Mango Fruit: 2. Forward Estimation of Size at Harvest" *Horticulturae* 9, no. 1: 54.
https://doi.org/10.3390/horticulturae9010054