Calcium Deficiency Diagnosis in Maize Leaves Using Imaging Methods Based on Texture Analysis

The artificial vision system (AVS) uses image analysis methods that can interpret images and identify nutritional deficiency symptoms in plant, even in the early stages of development. The objective of this study was to propose methods of image processing using analysis by texture to identify the deficiency of calcium (Ca) in maize (Zea mays L.) plants grown in nutrient solution. Plants were grown in nutrient solution in a greenhouse. Calcium doses were 0.0; 1.7; 3.3 and 5.0 mM of Ca, with four replications. Plant and leaf images were sampled at three main stages of maize development: V4 (plants with four leaves fully developed), V6 (plants with six leaves fully developed) and V8 (plants with eight leaves fully developed). Sampled material was split into (i) index leaf (IL) of the growing stage (V4 = leaf 4, V6 = leaf 6, and V8 = leaf 8), and (ii) new leaf (OL), both to image capture and chemical analysis. Such leaves were scanned, processed by the AVS and chemically analyzed. The texture methods used by the AVS to extract deficiency characteristics in the leaf images were: Volumetric Fractal Dimension (VFD), Gabor Wavelet Energy (GWE) and VFD with canonical analysis (VFDCA). The amount of Ca in the solution resulted in variation in the concentration of Ca in NL and IL, allowing the observation of typical symptoms of Ca deficiency. The AVS method was able to identify all Ca levels in leaves, being the GWE the best indicator using color images, scoring 80% of rights in images of the middle section of new leaves in V4.


Introduction
The world maize (Zea mays L.) production was 1162 million tons during the 2020/2021 crop season. The United States was responsible for 31% of that amount with average 10.8 ton ha -1 , China cropped 22.4% (6.3 ton ha -1 ) and Brazil 8.9% with average 5.7 ton ha -1 (FAO, 2022). To realize all its productive potential, the maize crops requires that nutrient supply (Amaral Filho et al., 2005) be adequate (Rambo et al., 2004). Symptoms of calcium (Ca) deficiency in maize results in internerval chlorosis and necrosis in younger leaves and tissues, reducing the cells stability and integrity, and growth is inhibited (Epstein & Bloom, 2006;Taiz & Zeiger, 2010;Marschner, 2011). The evaluation of nutritional state of the plants is usually done through chemical analysis or visual evaluation . Leaf chemical analyses of the nutrient status of the plant are time consuming and expensive Reis et al. (2006). In addition, the identification of the deficiency using leaf chemical analyses imply sampling at advanced phenological stage, which does not allow to take remediation actions for the crop (Wu et al., 2007). The visual diagnosis is a practical and quick method to investigate the nutrient deficiency in the plant, although its precision is limited and subjected to the experience of the observer (Baesso et al., 2007). The difficulties of evaluating the nutritional status of in maize plants on the same crop cycle are the motivation to propose additional approaches in nutrients . Since the chemical and visual diagnosis of nutrient deficiency have such disadvantages, the artificial vision system (AVS) may become an efficient method to early identification of plant nutrient deficiency. The AVS can apply various methods to extract information from scanned images. The AVS is a computing system that can compare the images with a data bank in an automatic or semi-automatic routine (Punam & Udupa, 2001). The use of image analysis in agriculture is not recent and several previous examples of success are available. Lukina et al. (2001) estimated vegetation coverage in wheat (Triticum aestivum L.) using digital images. Karcher and Richardson (2003) used digital image analysis to determine the lawn color. Baesso et al. (2007) and Baesso et al. (2012) used image analysis and remote sensing techniques to identify nitrogen (N) deficiency in bean (Phaseolus vulgaris L.) plants using neural networks and were able to identify the deficiency level. Florindo et al. (2014) studied brachiaria species identification using imaging techniques based on fractal descriptors, and maked possible the correct prediction of species in more than 93% of the samples. Silva et al. (2014) identified magnesium (Mg) deficiency in maize grown in a greenhouse and found a 75.5% of rights in the V4 stage, considered worthy trust through the Kappa index (Kappa = 0.9). Romualdo et al. (2014) used of artificial vision techniques for diagnostic of nitrogen nutritional status in maize plants, with percentage of right of 82.5 and 87.5% at V4 and V7, respectively, by Gabor Wavelet technique with color images. Luz et al. (2018) studied boron deficiency precisely identified on growth stage V4 of maize plant using texture image analysis, and achieved 88.75% of accuracy in differentiating between leaves using Fractal 3D, in V4 stage. Romualdo et al. (2018) used spectral indexes for identification of nitrogen deficiency in maize, and found accuracy rate for N patterns was 80% at V4 stage and 93% at V7 stage. Baesso et al. (2020) estudied artificial vision for nutritional diagnosis of corn grown with calcium silicate and magnesium and found a 66% of rights. Patrício and Riederb (2018) reviewed the computer vision and artificial intelligence in precision agriculture for the five most produced grains in the world: maize, rice, wheat, soybean, and barley and and concluded that Computer vision systems can be used in grading systems for maize and provides accurate descriptive data. It was identified that there are gaps to be filled with the development of artificial intelligence for automation of tasks in the field. The use of methods capable to precisely identify the nutrient status of plants is an excellent tool to manage maize nutrition, allowing to supply fertilizer in the same crop cycle, which is not possible using the present day human visual diagnosis and/or leaf chemical analysis.
The objective of this study was to propose methods of image processing using analysis by texture to identify the deficiency of calcium (Ca) in maize (Zea mays L.) plants grown in nutrient solution, using an AVS of different leaf sections.

Greenhouse Experiment
The maize (Zea mays L.), hybrid DKB 499 was grown in a greenhouse using a hydroponic system with two plants per 3.6 L pot, in nutrient solution. Maize was sown in plastic trays filled with clean sand and kept there up to two weeks. Deionized water was supplied. Plants were then moved to the solution pots, supported by a foam layer in such a way that their roots were immersed in the nutrient solution. The nutrient solution was based on the Hoagland & Arnon (1950) formulation at 50% and with adaptation for the Ca levels. After five days, solution in the pots were brought 100% of the formulation. Solutions were replaced at each week. The pH was monitored and kept between 5 and 6 and temperature averaged at 28 °C. Each pot had their own bubbling system which worked for 10 seconds at each 30 seconds interval.
The levels of Ca were: 0.0; 1.7 (33% of full dose); 3.3 (66% of full dose) and 5.0 mM (of full dose-100%) of Ca. Plant and leaf images were sampled at three stages of maize development: V4 (plants with four leaves fully developed), V6 (plants with six leaves fully developed) and V8 (plants with eight leaves fully developed). According to Fancelli (1986), at stage V4 occurs the definition of the productive potential, at V6 the definition of the number of seeds in the ear, and at V8 he definition of the number and size of the ear.
Sampled material was split in shoot, roots, new leaf (NL) and index leaf (IL) of the growing stage (V4 = leaf four; V6 = leaf six, and V8 = leaf eight). NL and IL to image capture and chemical analysis. For chemical analysis, all material was washed, dried in an oven with air circulation at 65 °C, grind and saved in plastic bags for further nutrient analyses, according to methodology described in Bataglia et al. (1983). Samples were solubilized with nitric-perchloric acid for determination of Ca in IL and NL.

Experimental Design
Experimental design was fully random in a 4x3 factorial (four Ca levels and three sampling events) with four replications. In each collecting period established, 16 pots were sampled (samples destructive). positions of the leaf and allow discard windows that are completely different of homogeneous regions, that could contain out layers, such as leaf defects, insect bitten among others.
A texture descriptor is used to extract a numeric vector that represents the sub-image in the feature space. On the last step, a pattern classification scheme separates the feature space to classify the samples. Different texture methods were used separately to demonstrate our proposal. The methods used were Volumetric Fractal Dimension (VFD), Gabor Wavelet (GW) and Volumetric Fractal Dimension with canonical analysis (VFDCA). These methods were chosen based on the good results obtained in the leaf texture analysis. In Luz et al. (2018), Romualdo et al. (2018), Silva et al. (2014), Romualdo et al. (2014), Backes and Bruno (2013), Rossatto et al. (2011) and Backes et al. (2009), the authors compared state of art texture methods for leaf identification and the best results were achieved by them.
In all methods of extracting the AVS used the naive Bayes classification and the cross validation learning method were used. Each image processing, 80% of the images were used for training and 20% for testing "blind. The classification experiment was carried out considering the four levels of Ca deficiency. These levels were controlled and also validated with the chemistry analysis. The goal of the classification experiment is verifying the image analysis accuracy to detected the nutrient deficiency classifying the groups according both chemistry analysis and controlled level of Ca.
The VFD routines used works with binary images because it follows the proposal of Backes at al. (2009) in which the image signature is calculated for all reE values: Where, E is the set of Euclidean distances for a maximum radius r max . In this routine the radius varied from 1 μm to 20 μm.
The transformed of Gabor bi-dimensional is a Gaussian function modulated in a senoidal oriented with a frequency and a direction, and its bi-dimensional form in the space and frequency is given by the following equations. (4) Where, frequency W and a direction θ, and its bi-dimensional form in the space g(x,y) and frequency G(u,v).
The transformed of Gabor can be adapted as a wavelet and in such a case these equations are used as a mother wallet. In the next step, a filter dictionary can be obtained by dilation and rotation of gz(x,y) through the function generated as proposed by Manjunath and Ma (1996): Where, a > 1; m, n are the scale and orientation, respectively, with m = 0, 1, ... M -1 and n = 0, 1, … N -1; M is the total number of scales and N is the total number of orientations.

Classification/Identification
Finally, the last part is the classification/identification, where the pattern recognition algorithms performance the classification of the leaves based on the feature vector extracted in the previous step.
For all methods the Naive Bayes classification and the cross validation learning method were used. For the evaluation, the samples were separated randomly into n groups of roughly equal size and was made "to let an outside group" the cross-validation which can also be called a "n-fold cross-validation" test scheme. Samples were independent for each class, and these samples did not appear in the same training and testing. In each processing, 80% of the images were used for training and 20% for testing "blind".
For the best recognition result of Ca deficiency by the methods of AVS, the confusion matrices were generated to assess the amount of right classifications made by AVS. And it is important to know classes that were difficult to classify. In addition, were assessed the percentage of images correctly classified or Global Percentage of Right (GPR) and Kappa index (K). x y x y x y g x y jWx

Calciu
In all three Ca concen 2b). The s present stu stages (

Visual
In plants w apex of lea solution c deficiency < 0.01) as    Another interesting aspect of the confusion matrix is the percentage of rights for the 0.0 mM and 3.3 mM. The results point to the 0.0 mM as being the easiest to classify, and that the greatest percentage of errors occurs in the 3.3 mM (Table 3). This probably happens because the images obtained from the leaves grown into the 3.3 mM solution are very close to those of leaves grown into the 1.7 mM. Even though, the AVS still can correctly classify a large amount of images. This happens because the Ca concentration in the NL of V4 plants grown into the 3.3 mM is 0.94 g kg -1 (Figure 2b) and are very close to the Ca concentration in the NL of V4 plants grown into the 1.7 mM of Ca solution, which is 0.85 g kg -1 of Ca (Figure 2b). Such closeness may have caused the difficulty of the AVS to identify the nutritional status of plants. However, the discrimination among the Ca levels is still reasonable, since it would be nearly impossible to distinguish visual symptoms in plants with Ca levels this close to each other. The AVS was able to identify Ca severe (0.0 mM) and moderate (1.7 mM) deficiencies, when the deficiency is to small (3.3 mM), the percentage of rights is 80%. Therefore, it would be possible to correct deficiency even at very small levels, but still causes decrease in the crop production.

Discussion
The results of Ca concentration in NL and IL are in accord with those reported by Silveira and Monteiro (2010) in their study of N and Ca nutrition of Tanzania grass, where the isolated effect of Ca concentration in recently expanded leaves fit a quadratic model. The concentration of Ca in the IL was greater as compared to the NL because Ca is usually immobile, therefore the Ca deficiency symptoms appears firstly in the newer leaves (Malavolta, 2006). Grangeiro et al. (2006) also stated that Ca inside the plant moves together with water and once deposited, do not show relocation towards other plant tissues, being accumulated mainly in tissues with intense transpiration. According to Malavolta (2006), the amount of Ca transfer through phloem is very small, resulting in Ca deficiency symptoms to appear first in new leaves.
The visual symptoms of Ca deficiency in NL agrees with Ramos et al. (2009). According to Epstein & Bloom (2006), Ca demand seems to be intense in such tissues and Ca in older tissues is not relocates to younger tissues. The small mobility of Ca is mainly due to the low solubility forms it assumes inside plants, such as the pectate of the medium lamellae of cell wall, which makes plant requirement of Ca be constant along its growth (Malavolta, 2006). The visual symptoms are in accordance with previous reports (Taiz & Zeiger, 2010;Epstein & Bloom, 2006;Epstein, 1975). Malavolta (2006) reported such symptoms, and according to Mengel and Kirkby (1987), the requirement of Ca by maize can be easily demonstrated by interrupting the supply to the plant roots and observing the immediate decrease in growth. According to Marschner (2011), Ca deficiency usually retards the plant growth. Mengel and Kirkby (1987) states the need of Ca for plant growth is easily demonstrated by the interruption of Ca supply to roots.
According to Patrício and Riederb (2018) computer vision systems are already widely employed in different segments of agricultural production and they can be used in grading systems for maize. The use of such systems provides a simple, producing accurate descriptive data. Studying the identification of Mg concentrations in maize by AVS, Silva et al. (2014) also found that the analysis of color images scored higher than gray images in all stages of development of the plant and then the AVS identified the images of the leaves of corn with levels of Mg with 75.5% rights using the middle section of the IL by the VFDCA technique, based on color images in V4 stage. Romualdo et al. (2014) studying nitrogen nutritional status in maize plants, found percentage of right of 82.5% using Gabor Wavelet technique, as in this study in which the percentage of rights is 80% in V4 stage.  found accuracy rate for nitrogen patterns was 80% at V4 stage using spectral indexes for identification of nitrogen deficiency in maize.
In study de boron deficiency identification on maize, the best method texture image analysis was Fractal and achieved 88.75% of accuracy in V4 stage; Gabor has already reached 81.75% of accuracy in differentiating . Baesso et al. (2020) found a 66% of rights for nutritional diagnosis of maize with calcium silicate and magnesium.
Through these systems it is possible to automate laborious tasks, in a non-destructive way, producing adequate data, bringing gains of production, quality, and food security (Patrício & Riederb, 2018).

Conclusion
Maize plants grown into greenhouse show visual symptoms related to Ca deficiency, which significantly interfere in shoot and root dry mass production. The NL of maize is the leaf that has the greatest amount of information for the AVS classification using color images. IN color images, the best routine to identify Ca deficiency was the GWE. The AVS had 80% of rights in identifying Ca deficiency in color images, with a Kappa of 0.941 "very reliable". This was superior to all gray scale images in all growth stages studied.