Computers and Electronics in Agriculture 213 (2023) 108246 Contents lists available at ScienceDirect Computers and Electronics in Agriculture journal homepage: www.elsevier.com/locate/compag Differentiating nutritional and water statuses in Hass avocado plantations through a temporal analysis of vegetation indices computed from aerial RGB images Itamar Salazar-Reque a, Daniel Arteaga a, Fabiola Mendoza b, Maria Elena Rojas b, Jonell Soto b, Samuel Huaman a, Guillermo Kemper a,* a INICTEL-UNI, Universidad Nacional de Ingeniería, Lima, Peru b Instituto Nacional de Innovación Agraria, Lima, Peru A R T I C L E I N F O A B S T R A C T Keywords: Maximizing crop production efficiently and sustainably through plant health monitoring is key for global food Hass avocado security. Monitoring large areas with remote sensing technologies such as unmanned aerial vehicles (UAVs) with Aerial RGB images sensors deals with time and money issues; however, the usage of advanced sensors such as hyperspectral, Vegetation Indices multispectral and thermal cameras limit their usage among all the stakeholders. In this study we explore different Nutrient Status Monitoring Water Status Monitoring vegetation indices (VIs) extracted from aerial RGB images acquired in different flights to differentiate the nutritional and water statuses of Hass avocado plantations. We used an image processing workflow consisting of image selection through a convolutional neural network (CNN) model, tree crown segmentation, color correction and feature extraction to automate the computation of VIs from RGB images. To compare the performance of VIs in the differentiation of nutritional and water statuses, we proposed a comparison metric called Mean Distance between Vegetation Indices (MDVI), analyzed the evolution of the extracted features, and studied their re- lationships with gold standard Normalized Difference Vegetation Index (NDVI) measurements. Since the extracted features from each group vary from flight to flight due to multiple factors such as the light intensity of each season and the phenological stage of the plant, the proposed comparison metric leverages the differences between the features extracted from each group, thus reducing these temporal effects. We found that Modified Green Red Vegetation Index (MGRVI) allows a better differentiation of nutritional and water statuses. Furthermore, the correlation coefficients of this VI in the three statuses and NDVI for nitrogen group range between 0.63 and 0.85, indicating a positive strong relationship. The results of this work show that MGRVI has a potential to be used as a correlation variable in studies that only use RGB sensors in order to monitor the nutritional and water status of crops. 1. Introduction preventing diseases, and optimizing the use of agrichemicals, fertilizers, and water. By leveraging precision agriculture techniques, farmers can With the current socio-economic and climate change scenarios, maximize crop production while minimizing costs and environmental ensuring global food security has become a major concern. Projections impact, thereby ensuring long-term sustainability. to 2050 indicate a significant increase in global food demand by 35% to One crop that has garnered considerable attention due to the nutri- 56% between 2010 and 2050 (van Dijk et al., 2021), placing the onus on tional and commercial significance, not only of the pulp, but also of the the agriculture sector to enhance crop production in an efficient and seeds and peel, is the avocado (Persea Americana). For this reason, some sustainable manner. Monitoring plant health through nutrient and water studies propose the utilization of seeds and peels (Nyakang’i et al., 2023; status is a viable approach to optimize yields while mitigating envi- Bayomy et al., 2023) based on their abundance of bioactive compounds, ronmental impacts. This monitoring provides valuable insights that can including unsaturated fatty acids, vitamins C, B, and E, dietary fiber, be utilized for diagnosing existing nutrient deficiencies, preemptively lutein, phenolic compounds, as well as various pigments such as * Corresponding author. E-mail address: guillermo.kemper@gmail.com (G. Kemper). https://doi.org/10.1016/j.compag.2023.108246 Received 12 August 2022; Received in revised form 30 August 2023; Accepted 9 September 2023 Available online 22 September 2023 0168-1699/© 2023 Elsevier B.V. All rights reserved. I. Salazar-Reque et al. C o m p u t e r s a n d E l e c t r o n i c s i n A g r i c u l t u r e 213 (2023) 108246 chlorophylls, anthocyanins, and carotenoids (Kosińska et al., 2012; Lu intake for plants is closely related with the amount of water in the soil; et al., 2005; Saavedra et al., 2017; Wang et al., 2010; Corrales-García therefore, during drought, crops are negatively affected due to water et al., 2019; Ong et al., 2022). Consequently, the global production and and nitrogen constraints (Plett et al., 2020). In order to determine and consumption of avocados have witnessed a substantial surge in recent control the nutrients and water in plants, different monitoring proced- years. This surge has not only contributed to increased interest in avo- ures have been employed. cado as a functional ingredient in foods but has also led to diverse Silber et al. (2018) assessed the seasonal nutritional requirement of commercial applications, ranging from frozen products and ice cream to Hass avocado trees grown in lysimeters. Through this in-situ monitoring avocado oil, guacamole, and even cosmetic products (Colombo and of NPK macronutrients, they determined that continuous nutrient Papetti, 2019). application during the year, and the modification of fertilization rate Precision agriculture approaches that enable effective monitoring of together with the nutrient combination is required for guaranteeing nutrient and water status, especially in high-value crops like avocados, optimal yield. Moreover, they conclude that fruit analyses should be hold significant promise to cope with the escalating global food demand. used for scheduling fertilization instead of leaf analyses. Gaona et al. Although the advantages provided by precision agriculture, time and (2020) also employed an in-situ monitoring procedure to determine the money are limitations when monitoring large areas. Current plant effect of two doses of nitrogen and potassium in the initial growth phase analysis in laboratory is not suitable for this scenario because it involves of Hass avocado. They observed significant differences in the greenery sample collection, sample preparation, laboratory analysis and posterior index and nutrient concentration variables. interpretation. Emerging technologies have been applying to face these In-situ monitoring allows accurate evaluation of the nutritional and limitations. Roper et al. (Roper et al., 2021) discuss some approaches of water status of plants; nevertheless, it is time consuming and normally in vivo plant sensors for plant health monitoring. Remote sensing requires the completion of specific steps to interpret the data (Dezordi technologies are also used for the same purpose. UAVs and imaging et al., 2016). Remote sensing technologies cope with this drawback. sensors have been widely employed as a remote sensing system to Monitoring of the nutritional and water status with remote sensing compute different VIs, which are then used to diagnose nutrient prob- systems allows to cover medium and large areas in less time and data lems (Garza et al., 2020; Janoušek et al., 2021; Noguera et al., 2021) or processing is done autonomously through computer programs. predict nutrient status (Prado Osco et al., 2019; Zha et al., 2020; Osco Satellites are very popular remote sensing monitoring systems that et al., 2020). have been used for many precise agriculture applications such as In most of the studies, the calculation of VIs involves the usage of at pesticide usage monitoring (Adan et al., 2021), pest severity assessment least one spectral band other than those of the visible spectrum (the true (Salgadoe et al., 2018), yield mapping (Robson et al., 2017), and color bands red, green and blue), such as the near-infrared (NIR) or red nutritional plant status monitoring (Sharifi, 2020; Sims et al., 2013). edge (RE) bands. This imply the usage of multispectral cameras over Sims et al. (2013) presented a synopsis of studies using satellite hyper- UAVs for image acquisition, which can produce a limitation for stake- spectral imagery for foliar nutrition assessment which collectively holders that only possess RGB cameras. To make more extensible the demonstrate that several important nutrients can be accurately mapped monitoring of nutritional and water status through UAVs and imaging at critical ages for the management of plantation forests. However, some sensors, identifying some VIs extracted from aerial RGB images that are spatial and radiometric characteristics limit the practical usage. Sharifi useful for nutritional and water status assessment is required. (2020) used satellite imagery to evaluate the use of VIs for crop nutrition This work aims to explore different VIs extracted from aerial RGB mapping. They found that the two best VIs were TCARI (Transformed images that allow to differentiate trees with adequate and inadequate Chlorophyll Absorption in Reflectance Index) (Haboudane et al., 2002) nutritional and water status. The study was developed with Hass avo- and MCARI (Modified Chlorophyll Absorption in Reflectance Index) cado trees. Because of the advantages of fertigation (Incrocci et al., (Daughtry et al., 2000). Moreover, they conclude that the use of NIR and 2017), it was used to induce deficiencies and excesses of nitrogen, RE multispectral bands in mid-season led to better results than VIs phosphorus and potassium (NPK) macronutrients, and water de- calculated at the end of the season or that do not include the RE band. ficiencies. During the study period, a UAV was employed to acquire With the development of UAVs and imagery sensors in the recent aerial RGB images of trees with adequate nutritional status (control years, there are more studies in the monitoring of nutritional and water groups) and trees with an induced inadequate nutritional and water status of plants. A review article by Jayme Arnal (Barbedo, 2019) pre- status. Different VIs were calculated for each group and flight, which sented 30 and 31 works dealing with the monitoring of nutrient and then were used to compute the comparison features. We proposed a water status in crops respectively. On one hand, multispectral cameras comparison metric called Mean Distance between Vegetation Indices were the sensors used in most of the studies for monitoring of nutritional (MDVI) that allows better differentiation among statuses for different status. On the other hand, most of the studies aiming to monitor water groups and VIs. In addition, a temporal analysis of these features and a status employed thermal cameras. correlation study with NDVI (Rouse et al., 1974) measurements were Regarding the studies with multispectral images, Lu et al. (2019) performed. Our results show that MGRVI (Bendig et al., 2015) per- acquire images at seven view zenith angles for three critical growth formed better in differentiating nutritional and water statuses. stages of winter wheat and computed four VIs as input variables: Visible Therefore, in this study, we propose a novel approach to differentiate Atmospherically Resistant Index (VARI) (Gitelson et al., 2002), Red edge the nutritional and water statuses in Hass avocado plantations through a Chlorophyll Index (CIred-edge) (Gitelson et al., 2003; Gitelson, 2005; temporal analysis of VIs computed from aerial RGB images. By Gitelson et al., 2006), Green band Chlorophyll Index (CIgreen) (Gitelson employing remote sensing techniques and advanced image analysis al- et al., 2003; Gitelson, 2005; Gitelson et al., 2006), and Modified gorithms, we aim to develop a non-invasive and cost-effective method Normalized Difference Vegetation Index with a blue band (mNDblue) for assessing the nutrient and water status of Hass avocado trees. Such (Jay et al., 2017). They used leaf nitrogen concentration (LNC), plant an approach has the potential to empower farmers with valuable in- nitrogen concentration (PNC), leaf nitrogen accumulation (LNA), and formation to make informed decisions regarding nutrient and water plant nitrogen accumulation (PNA) as target variables to be estimated by management, leading to improved yields and sustainable avocado a linear regression model. When using multiple view zenith angles, they production. used a two-variable regression model. The best result with single-angle images was obtained with CIgreen for LNC from a view zenith angle of 2. Related work − 60◦. Zhang et al. (2016) monitored heading rice growing based on UAV multispectral images by using linear regression model. They used One of the main limitations for the increase in crop productivity is GNDVI (Green Normalized Difference Vegetation Index) (Buschmann the availability of water and nutrients like nitrogen. Macronutrients and Nagel, 1993) as input variable, and SPAD values (chlorophyll) and 2 I. Salazar-Reque et al. C o m p u t e r s a n d E l e c t r o n i c s i n A g r i c u l t u r e 213 (2023) 108246 the nitrogen content as target variables, finding a higher correlation method the accuracies were 0.75, 0.8 and 0.94 respectively. between GNDVI and SPAD values. Another usage of multispectral im- RGB images acquired via UAVs have been also used in monitoring ages to compute VIs for estimating nutritional status was presented by plant health – nutrient and water – status. Garza et al. (2020) correlates Chungcharoen et al. (2022). In this study, they computed 34 VIs and 10 the triangular greenness index (TGI) (Hunt et al., 2011) with field features based on average and standard deviation values to be used as measurements such as mineral nutrients and foot rot disease severity to input variables for analyses against 10 target nutritional status variables distinguish trees with disease. They found that TGI was different (encompassing NPK). They employed four machine learning techniques depending on disease or in combination of diseases and also explained (Random Forest, Support Vector Regression, Partial Least Square which factors were involved in these differences. Qiu et al. (Qiu et al., Regression, and Artificial Neural Network) finding that models for 2021) calculated different VIs from RGB images acquired through a UAV chlorophyll, nitrogen and calcium predictions were acceptable for and showed they are correlated with nitrogen nutrition index (NNI) for screening. The screening model based on Support Vector Regression for rice at different growth stages. Ballesteros et al. (2018) estimated crop nitrogen obtain a coefficient of determination ranging from 0.665 to biomass (which involves pest and weed status, soil quality, water stress, 0.718. Similarly, Guerra-Hernández et al. (2021) acquired multispectral yield prediction, among others) from high-resolution RGB images ob- images with a UAV to monitor health status in priority riparian forest. tained with a UAV. They extracted green canopy cover, crop height and They considered 34 remote sensing variables such as VIs, texture fea- canopy volume for predictor variables, finding strong correlation be- tures from NDVI and digital surface model, among others. The objective tween canopy volume and dry leaf biomass and dry bulb biomass. A was to classify trees in four categories: asymptomatic, dead, and defo- method for monitoring health status of Eucalyptus pellita in a large-scale liation above and below 50% threshold. The classification using Random area through the usage of RGB images acquired with a UAV was pro- Forest with four, three (asymptomatic, defoliated, dead) and two (alive, posed by Megat Mohamed Nazir et al., (2021). They generated an ortho- dead) classes yielded overall accuracies of 0.67, 0.72 and 0.91 respec- image and computed VARI-green (Gitelson et al., 2002) to classify four tively. By using three logistic models with leave-out cross validation levels of pest and disease: dead, severely infected, mildly infected and Fig. 1. Geographic location from the study area. a) Lima location (brown colored) related to Peru. b) La Molina location (brown colored) related to Lima. c) National Institute of Agrarian Innovation (INIA) and study area (pink box). d) Mosaicked image from study area in false color. Fill-colored rectangles group trees with some common features. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.) 3 I. Salazar-Reque et al. C o m p u t e r s a n d E l e c t r o n i c s i n A g r i c u l t u r e 213 (2023) 108246 healthy trees. The VARI-green indices were verified by manual ground- N-7 has excess of nitrogen; P-19 has deficiency of phosphorus and K-12 true values and by comparison with NDVI, showing a correlation of 0.73. is control of potassium (i.e., potassium in optimal conditions). To induce Ge et al. (2021) estimated PNC of rice using a fusion of VIs and color these statuses, macronutrients were provided in the amounts shown in moments from UAV-based RGB images. They used Partial Least Square Table 1 in three different dates: May 10th, September 6th and November Regression and Random Forest models and demonstrated that the fusion 15th. of VIs and color moments as input variables improve the accuracy of PNC estimation compared to VIs or color moments only. 3.2.2. Water variation experiment The last three rows in the study area were used to study the effect of 3. Methodology different levels of water in the trees. We varied the level of water while keeping macronutrients in optimal conditions. Each row had a different 3.1. Area of study level of water: 50% (black), 75% (gray) and control (sky blue) (see Fig. 1d and Table 1). Water pressure through the pipes was controlled to This study was conducted over a hectare of Hass Avocado at the induce the three different water statuses. National Institute of Agrarian Innovation located (INIA) in La Molina, Lima, Peru (see Fig. 1a-c). We analyzed 123 trees that were distributed 3.3. NDVI measurements in seven rows and twenty-one columns (pink box in Fig. 1d). The sep- aration between trees was five meters approximately as show in Fig. 2. Normalized Difference Vegetation Index (NDVI) has been used Latitude and longitude coordinates from study area vertices are: widely in the literature to analyze crops. We captured in-field NDVI (− 12.074588, − 76.947483), (− 12.074266, − 76.946131), measurements using the GreenSeeker Handheld Crop Sensor. Measure- (− 12.074826, − 76.946021) and (− 12.075139, − 76.947359). Trees ments were taken approximately 60 cm above the top of the tree with were six meter tall and three years old on average. The soil was loan with the help of a step ladder. an average pH of 7.55 and an electrical conductivity of 2.06 mS cm− 1 (measured according to UNE 77308:2001 using a mixture of soil and water in the ratio 2 to 1). The organic matter value was 0.55. Soil phosphorus (P) and potassium (K) values were 18.7 ppm and 355 ppm Table 1 respectively. These values were obtained from a laboratory analysis of Amount of macronutrients and water provided to trees per group and statuses. soil samples at different layers made in January 2020. Group (G) Status (s) N P K Water N Excess 120 kg ha− 1 60 kg ha− 1 80 kg ha− 1 100% 3.2. Experimental design Control 80 kg ha− 1 60 kg ha− 1 80 kg ha− 1 100% Deficiency 0 kg ha− 1 60 kg ha− 1 60 kg ha− 1 100% 3.2.1. Macronutrient variation experiment P Excess 80 kg ha− 1 100 kg ha− 1 80 kg ha− 1 100% The first three rows in the study area were used to study the effect of Control 80 kg ha− 1 60 kg ha− 1 80 kg ha− 1 100% different levels of macronutrients, either nitrogen (N), phosphorus (P) or Deficiency 80 kg ha− 1 0 kg ha− 1 60 kg ha− 1 100% − 1 − 1 − 1 potassium (K) in the trees. We provided nutrients using fertigation as it K Excess 80 kg ha 60 kg ha 120 kg ha 100% Control 80 kg ha− 1 60 kg ha− 1 80 kg ha− 1 100% allowed us to vary the amount of macronutrients in a practical way. We Deficiency 80 kg ha− 1 60 kg ha− 1 0 kg ha− 1 100% varied the level of one macronutrient while keeping the others and Water Control 80 kg ha− 1 60 kg ha− 1 80 kg ha− 1 100% water in optimal conditions. Trees in each row were subdivided in three 75 80 kg ha− 1 60 kg ha− 1 80 kg ha− 1 75% statuses according to the level of the nutrient: excess (red), control (blue 50 80 kg ha− 1 60 kg ha− 1 80 kg ha− 1 50% sky) and deficiency (yellow) (see Fig. 1d). For example, a tree located in Fig. 2. Sequential images acquired from a single tree using UAV. Note that before any image processing we need to select the best acquired image (number 3 in this case). 4 I. Salazar-Reque et al. C o m p u t e r s a n d E l e c t r o n i c s i n A g r i c u l t u r e 213 (2023) 108246 3.4. Image acquisition First, we have to clean our image set per flight and tag them according to the group and status they belong to by performing image selection Images from the top of the trees were acquired using a Phantom Pro through a CNN. Next, we need to perform a proper crown segmentation V2 UAV from DJI (https://www.dji.com/phantom-4-pro-v2) equipped of the trees. Finally, leveraging these segmentations several features per with a SENTERA Double 4 K multispectral camera. This camera has two group, status and flight are extracted for comparison. These steps were lenses: one of them acquires RGB images and the other, NIR and RE performed through Python scripts. A summary of this procedure is bands together. In this study we are interested in the use of RGB images. shown in Fig. 3. The UAV flights followed a single grid path starting in tree N-1 and finishing in tree C-21 as shown in Fig. 1d. To do so, coordinates of each 3.5.1. Image selection based on CNN row extreme were set in the flight planning software considering a As mentioned before, our flight configuration allowed us to complete height of 7 m above the ground. UAV was configured to have an average the acquisition in a few minutes but with the compromise of having speed of 2 m/s and images were acquired every 1 s. Although, this unnecessary images (see Fig. 2). Thus, we need to clean our image set configuration implies to have more images than trees, we guarantee to and tag each image according to the group and status the tree belongs to. complete the desired path rapidly and to have at least one image of a To do so, we perform the following steps which are based on our pre- complete tree with the least number of images per flight. A sample of vious work on tree image selection (Salazar-Reque et al., 2021): continuous images acquired under this configuration is shown in Fig. 2, note that as there are many images per tree we will need to select the A manual selection of “best images” per tree was made for one flight. best. The procedure to deal with image selection is described in section This is done only once and will be used as a reference in future 3.5. flights. Manual selection means human selection and “best images” We conducted 21 flights over a period of seven months. Each flight stand for those images in which all or the most of the tree crown acquired an average of 700 georeferenced images (some of them will be appears, and in which it is as centered as possible. discarded). Dates, number of images as well as some flight conditions are An automatic pre-selection of images per tree was made based on reported in Table 2. proximity using geolocation information from images from step 1. We generate binary masks per each image from step 2 using a UNET (Ronneberger et al., 2015) like architecture trained for coarse crown 3.5. Image processing segmentation of trees. Binary images from step 3 were used to discard images that do not For each flight we have to follow a procedure composed of three meet the criteria of a good acquisition (e.g., tree centered in the steps in order to generate a proper feature to compare between statuses. image). We select the best image available per tree by comparing binary Table 2 masks from images from step 4 with binary masks from the images of UAV flights information. reference from step 1. As each tree is associated with a group, the Date DOY # of Flight conditions (t) images March 29 88 835 RH: 56, T: 24, WS: 2 April 14 104 820 RH: 67, T: 22, WS: 3, LCC: 6, MCC: 0, HCC: 82 April 28 118 760 T: 27, WS: 2.5, LCC: 1, MCC: 1, HCC: 41 May 7 127 702 T: 25.5, WS: 3, LCC: 3, MCC: 13, HCC: 0 May 12 132 805 T: 24, WS: 2, LCC: 13, MCC: 5, HCC: 20 May 19 139 730 RH: 81, T: 23.5, WS: 3, LCC: 0, MCC: 0, HCC: 0 May 26 146 750 RH: 78.5, T: 24, WS: 1, LCC: 13, MCC: 8, HCC: 0 Jun 02 153 835 WS: 2, LCC: 59, MCC: 0, HCC: 7 Jun 11 162 820 RH: 62, T: 19, WS: 3, LCC: 17, MCC: 3, HCC: 0 Jun 16 167 795 RH: 73, T: 27, WS: 3, LCC: 2, MCC: 0, HCC: 2 Jun 23 174 889 T: 18, WS: 3, LCC: 12, MCC: 0, HCC: 19 July 02 183 803 RH: 54, T: 19.5, WS: 2, LCC: 43, MCC: 0, HCC: 1 July 09 190 786 RH: 53, T: 22, WS: 2, LCC: 4, MCC: 0, HCC: 0 July 14 195 708 – July 23 204 750 RH: 62, T: 20, WS: 3, LCC: 21, MCC: 0, HCC: 0 August 05 217 770 RH: 76, T: 20.5, WS: 3, LCC: 55, MCC: 0, HCC: 0 August 13 225 802 RH: 60, T: 20.5, WS: 3, LCC: 5, MCC: 1, HCC: 10 August 19 231 815 – September 258 752 RH: 60, T: 19, WS: 3, LCC: 5, MCC: 1, 15 HCC: 2 September 267 798 RH: 62, T: 21, WS: 2, LCC: 10, MCC: 0, 24 HCC: 6 October 15 288 770 – October 24 302 821 RH: 62, T: 23, WS: 2, LCC: 62, MCC: 4, HCC: 4 Note: RH: relative humidity, T: ambient temperature in Celsius degrees, WS: wind speed, LCC: percentage of low cloud cover, MCC: percentage of medium cloud cover, HCC: percentage of high cloud cover. Fig. 3. Image processing flowchart. 5 I. Salazar-Reque et al. C o m p u t e r s a n d E l e c t r o n i c s i n A g r i c u l t u r e 213 (2023) 108246 final outcome is one image per tree labeled according to their cor- 3.6. Comparison metric responding group. To compare the differentiation between nutritional and water sta- If we repeat this process in every flight, we ended up with a set of tuses that each VI indicates, we proposed the Mean Distance between images ordered by tree and date. Vegetation Indices (MDVI) as a metric (see Equation 3). 1∑ 3.5.2. Crown segmentation MDVIVI(s1, s2) = |zs1 (t) − zs2 (t)| (3) Previous binary masks were coarse crown segmentations that were T t useful for tree image comparison with reference images from another In Equation 3, z(t) is the value of VI at time t. The value of VI at time t flight. However, when viewed in detail, these binary masks also include for a certain status s is denoted as zs(t), so the distance between VIs for shadows or poorly lit areas of the trees that can generate artifacts in the statuses s1 and s2 at time t is the absolute value of the difference between features we are intended to generate. To reduce these artifacts, we zs1 (t) and zs2 (t). Finally, to compute the mean value of this distance, the eliminate these dark areas by means of the Otsu’s method (Otsu, 1979) absolute value of the difference (|zs1 (t) − zs2 (t)|) for each time t is sum- on each of the color components of the RGB images clipped to the med together and divided by the total number of time instants T. This rectangle with the maximum area that is inside the segmented tree. allows comparisons between studies with different temporal resolutions. Otsu’s method maximizes the means and minimizes the variance of the MDVI basically computes the area of the difference between the tem- distribution of pixel values by assuming that there are two groups poral evolution (signals) of VIs for the compared statuses per time (leaves and dark areas in our case). Thus, we reduce the influence of instant, and therefore this is a measurement of how similar or different dark areas in the final features. the temporal evolution of VIs for each status are. 3.5.3. Feature extraction 4. Results Using our previous crown segmentations, we can create a set of Np square patches per group G in a given time t. Then, for each of these 4.1. Comparison of VIs patches we compute its density function h(i)G (x; t) for a random variable X where i = 1, ...,Np. Our objective here is to generate a signal zG(t) that Taking into consideration the groups, denoted by G, Equation 3 can represents the temporal evolution of group G. We compute this signal as be formulated as follow: the expected value over X as follows: G 1∑MDVI (s , s G GVI 1 2) = |z (t) − z (t)| (3) zG(t) = E[fG(x; t)] (1) T s1 s2 t G where fG(x; t) represents the probability density function of a group G in For each VI in Table 3, we computed a value of MDVIVI(s1, s2) where a given time t. This is computed as the average of the previous density G represented the group and was either {N, P, K or W} and s1 and s2 functions h(i) x t . represented the statuses and were chosen from {Excess, Control or G ( ; ) Deficiency} for macronutrients or from {50, 75 or Control} for water 1 ∑Np (W). This computation also involves to calculate zG(i) s (t) for each DOY (see fG(x; t) = hG (x; t) (2) N Table 2). It is important to mention that MDVI computation for a group p i=1 involves multiple trees, so zGs (t) is the average value of VI for all the trees The random variable X is defined by the pixel-wise combination belonging to group G at time t for a certain status s. between red, green and blue channels according to the VI of interest. The The MDVI values for each combination of groups, statuses and VIs VIs explored in this work are the same used in (Qiu et al., 2021) which are summarized in the plots shown in Figs. 4 and 5. Better differentiation we summarized in Table 3. between statuses is achieved for nitrogen because most MDVI values are higher for this group (MDVINVI > MDVI P N K VI and MDVIVI > MDVIVI) as shown by red lines being in the outermost part of the radar plot Table 3 compared to blue and green lines. Similar MDVI values (but usually Vegetation indexes explored. lower than nitrogen) were obtained in the phosphorus group. For po- tassium, the MDVI values for any VIs were always lower than for ni- Vegetation Index X References trogen and phosphorus. In general, this shows that it is harder to Red Green Ratio Index (RGRI) r/g (Gamon and Surfus, distinguish between groups for this macronutrient, especially when a 1999) Blue Green Ratio Index (BGRI) b g (Yue et al., 2018) deficiency status is involved. / Green Leaf Algorithm (GLA) (2g − r − b)/(2g + r + (Louhaichi et al., When analyzing only the results for nitrogen and phosphorus groups, b) 2001) we note that higher values of MDVI were always given by MGRVI. This Green Leaf Index (GLI) (2g − r + b)/(2g + r + (Qiu et al., 2021) indicates that this VI better differentiates between statuses for these b) macronutrients. Not surprisingly, the Excess vs Deficiency statuses Green Red Vegetation Index (g − r)/(g + r) (Tucker, 1979) (GRVI) comparison was easy to differentiate than the others as can be noted by Modified Green Red Vegetation (g2 − r2)/(g2 + r2) (Bendig et al., the higher MDVI values reported. On the other hand, the Deficiency and Index (MGRVI) 2015) Control statuses comparison had the smallest values indicating that lack Excess Green minus Excess Red (2g − r − b) − (1.4r − g) (Meyer and Neto, of nitrogen or phosphorus macronutrients are difficult to distinguish (ExGR) 2008) Excess Red Vegetation Index (ExR) 1.4r − g (Meyer et al., 1998) from controls. Excess Blue Vegetation Index 1.4b − g (Mao et al., 2003) A similar analysis can be done for the water experiment results. (ExB) Again, MGRVI has the higher values of MDVI (see Figs. 4 and 5) but only Excess Green Vegetation Index 2g − r − b (Woebbecke et al., for 50% vs CONTROL and 50% vs 75% comparisons. In the case of of (ExG) 1995) 75% vs CONTROL comparison we can expect that these statuses to Visible Atmospherically Resistant (g − r)/(g + r + b) (Gitelson et al., Index (VARI) [] 2002) behave very similar as MDVI values for this comparison are very low for Red Green Blue Vegetation Index (g2 − br2)/(g2 + br2) (Bendig et al., all the VIs. (RGBVI) 2015) Note: All operations are pixel-wise operations. 6 I. Salazar-Reque et al. C o m p u t e r s a n d E l e c t r o n i c s i n A g r i c u l t u r e 213 (2023) 108246 Fig. 4. MDVI values for each combination of groups, statuses and VIs. First row: Comparison between excess and control statuses (left), comparison between deficiency and control statuses (middle) and comparison between excess and deficiency statuses (right). Second row: Comparison between water50 and control statuses (left), comparison between water75 and control statuses (middle) and comparison between water50 and water75 statuses (right). Fig. 5. Bar plots with MDVI values for multiple VIs. Each row represents a group, and each column represents a pair of statuses being compared. 7 I. Salazar-Reque et al. C o m p u t e r s a n d E l e c t r o n i c s i n A g r i c u l t u r e 213 (2023) 108246 4.2. Temporal analysis of VIs for nitrogen group Table 4 Correlation between NDVI and RGB-based vegetation indices for different ni- As the MDVI values were higher for nitrogen group, we decided to trogen statuses. analyze the temporal evolution of NDVI compared with three VIs that VI Deficiency Control Excess allow good (MGRVI), normal (GLA) and poor (ExB) differentiation GLA 0.6585 0.7921 0.4775 (according to MDVI) for this group (see Fig. 6). This selection is due to MGRVI 0.8086 0.8488 0.6289 we wanted to perform a posterior correlation study with NDVI, so the ExB − 0.2863 − 0.4269 − 0.2909 possibility of unexpected correlations had to be considered. For the computation of the distributions, we have used 50 bins in the range of [-0.2, 0.8]. We used this range because VIs varied between those values. VIs align with previous studies in the field. Nitrogen has demonstrated NDVI values were computed from multispectral images acquired in the the highest differentiating power among the macronutrients analyzed, same flight conditions with a Sentera Double 4 K Sensor Multispectral which is consistent with the strongest influence this macronutrient has camera (https://sentera.com/products/fieldcapture/sensors/double-4 on tree growth and development as reported by Jiaying et al. (2022) and k/). Silber et al. (2022). In Figs. 4 and 5, we presented radar and bar plots that demonstrate the differentiation between macronutrient statuses based on MDVI 4.3. Correlation with NDVI measurements values for each VI. Notably, MGRVI, BGRI, RGRI, and VARI consistently outperformed other indices in differentiating between the nitrogen and The results of correlation study (see Table 4) demonstrate a positive phosphorus groups, particularly for nitrogen. These findings are relationship between MGRVI for nitrogen group and NDVI due to the consistent with the results reported in previous studies (Qiu et al., 2021; correlation coefficients in the three statuses range from 0.63 to 0.85. Megat Mohamed Nazir et al., 2021). These values were computed considering the fruit and harvesting period Interestingly, the worst-performing indices (ExB, ExR, and ExG) were (approximately from DOY 163 to DOY 259). those computed using linear operations of color components, while best VIs always involved a non-linear operation (a division). This might be 5. Discussion due to the fact that images acquired by UAV are prone to light variations and division between color components are more robust to this kind of The purpose of this study was to investigate the relationship between artifacts than linear combination, as discussed by (Barbedo, 2017) in the NPK macronutrients status and VIs as well as water status and VIs. In this context of disease segmentation over leaves. discussion, we will compare our results with findings from other au- As anticipated, the MDVI values were highest when comparing the thors, providing a more comprehensive analysis of the obtained results excess and deficiency groups, demonstrating their strong discriminatory and their implications. Our findings regarding macronutrient status and Fig. 6. Comparison of temporal evolution of NDVI, MDVIN , MDVINMGRVI GLA, and MDVI N ExB for trees under different nitrogen statuses. 8 I. Salazar-Reque et al. C o m p u t e r s a n d E l e c t r o n i c s i n A g r i c u l t u r e 213 (2023) 108246 capability in identifying extreme nutrient statuses. In contrast, the Acknowledgement comparison between the deficiency and control groups resulted in lower values, indicating the difficulty in distinguishing nutrient deficiencies To the World Bank and “PROCIENCIA” (formerly FONDECYT), an from the normal range. This finding poses a challenge in practical ap- initiative of CONCYTEC, for the funds allocated to the project under the plications where the detection of deficiencies is of significant interest. contract N◦ 097-2018-FONDECYT-BM-IADT-AV. Notably, during the fruit production and harvest period (DOY 163 to DOY 259), the density distributions for the deficiency status in nitrogen References and phosphorus groups shifted to higher values compared to the control and excess statuses. 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