WO2014122256A1

WO2014122256A1 - Method and electronic equipment for determining a leaf area index

Info

Publication number: WO2014122256A1
Application number: PCT/EP2014/052418
Authority: WO
Inventors: Roberto Confalonieri; Marco FOI; Marco ACUTIS; Raffaele CASA
Original assignee: Universita' Degli Studi Di Milano
Priority date: 2013-02-08
Filing date: 2014-02-07
Publication date: 2014-08-14
Also published as: ITMI20130185A1

Abstract

Method (200; 300) and portable electronic equipment (100) for determining leaf area index, or LAI, of a plant canopy sample. The equipment is movable with respect to an axis (X) perpendicular to the ground and to (Y) and (Z) axes parallel to the ground and orthogonal to said first axis and it has a digital image acquisition module (40, 102) and an accelerometer module (50). The method of invention comprises the steps of: - positioning (202; 202') said equipment at the plant canopy sample; - rotating (203) said equipment about axis (Y) from a first position, in which a camera lens (102) of said image acquisition module lies on a reference plane (XY), to a second position in which said camera lens (102) lies on a first plane (YZ); - during the rotation of the equipment, detecting, by the accelerometer module (50), the attainment of an intermediate position between the first and second position, in such intermediate position the equipment being inclined with respect to the reference plane (XY) by a reference inclination angle of about 57.5°; - acquiring (204) at least one digital image of said plant canopy sample at the intermediate position of the equipment; - sending (205) said at least one acquired digital image to a processing module (10) in the portable electronic equipment; - processing (206; 206') said at least one digital image to measure a parameter indicative of a light radiation transfer through the plant canopy sample at said reference inclination angle.

Description

DESCRIPTION

METHOD AND ELECTRONIC EQUIPMENT FOR DETERMINING A

LEAF AREA INDEX

TECHNOLOGICAL BACKGROUND OF THE INVENTION

Technical field

The present invention relates to a method and an electronic equipment for determining Leaf Area Index or LAI .

Description of the prior art

As it is known, the Leaf Area Index, or more simply LAI, is a crucial variable in studies relating to the atmosphere-vegetation interactions, for example, in agronomic-environmental and forest studies. In particular, the LAI, representing a ratio of leaf area and ground area, and which is expressed in square meters of leaves per square meter of ground, is particularly relevant for estimating the light radiation intercepted by a vegetal canopy and the assessment of the relative water requirements. Direct methods for the leaf area index estimation are known. Some of those are based on the collection of leaves from plants, and, consequently, on the use of special tools or the acquisition/processing of images of such leaves to measure the surface area thereof. Such direct methods are destructive, since they provide for the collection and destruction of the vegetal material, which are expensive and affected by errors in the LAI estimation, when improperly applied, especially in the case that the plants at issue belong to species with small leaves or hardly storable. In addition, direct methods are inapplicable to tree species, and generally to forest ecosystems.

Such drawbacks in the direct estimation methods lead to the development of indirect LAI estimation methods, based on the measurement of the light radiation transmission into the canopy by a gap fraction parameter (quantity) and the relative equipment allowing calculating such gap fraction. The gap fraction parameter, as it is known, represents the percentage of light rays reaching the ground, passing through the canopy. Generally, the indirect methods for LAI estimation provide, at a first time, measuring the gap fraction parameter, which is then processed by applying an operation of inversion of radiative transfer models to obtain the corresponding LAI.

In fact, some known apparatuses for measuring the gap fraction mainly provide for optical sensors suitable to detect the light radiation passing through the canopy. Among these apparatuses, for example, ceptometers are widespread. Other known devices are based on a computer-assisted processing of images of the canopy that are acquired, for example, by a device with an hemispherical camera.

The indirect methods for LAI estimation, based on the gap fraction measurement by the above- mentioned known apparatuses, are not free from drawbacks .

In fact, some of the known methods require to carry out measurements almost concomitantly both above and under the canopy, which is often troublesome in forest systems, or for some tree cultures .

Furthermore, some of the known apparatuses require an operator to set one or more parameters to describe the canopy structural characteristics.

In other cases, the apparatuses that are used have measurement times that are too long, or a reduced usability level by the operator, due to a complex or not very intuitive managing software.

Again, in other cases, the acquired images are processed based on selections carried out by the operator, particularly, defining analysis reference thresholds; such selections may adversely affect the accuracy of the measurement provided.

Furthermore, in order to carry out, each time, measurement with a proper arrangement of the instrument, the known apparatuses are provided with bubble levels. However, due to their reduced dimensions, such levels are not very accurate.

Finally, the known apparatuses comprise not very intuitive (not user-friendly) tool-operator interfaces, which have high purchase and managing costs .

SUMMARY OF THE INVENTION

The object of the present invention is to devise and provide a method for determining the Leaf Area

Index, or LAI, allowing at least partially obviating the drawbacks mentioned above in relation to the methods for determining the LAI of a known type mentioned above.

Such an object is achieved by a method for determining the Leaf Area Index, or LAI, in accordance with claim 1.

Preferred embodiments of such method are defined in the dependent claims 2-8.

It is the object of the present invention also a portable electronic equipment in accordance with claim 9, suitable to implement the method of the invention . BRIEF DESCRIPTION OF THE DRAWINGS

Further characteristics and advantages of the method according to the invention will be apparent from the description set forth below of preferred embodiments, given by way of illustrative, non- limiting examples, with reference to the appended figures, in which:

- Fig. 1 illustrates by a block diagram an internal structure of a portable electronic equipment implementing the method for determining the leaf area index of the present invention;

Figs. 2A and 2B illustrate front and rear perspective views, respectively, of an implementation example of the electronic equipment of Fig. 1 ;

- Fig. 3 illustrates a flow diagram of a first embodiment of the method for determining the leaf area index of the invention;

Fig. 4 illustrates a flow diagram of a second embodiment of the method for determining the leaf area index of the invention;

Fig. 5 illustrates in a diagram experimental results relating to a comparison of leaf area index values measured by a destructive method and those determined by indirect methods.

DETAILED DESCRIPTION

With reference to the Figs. 1, 2A, 2B, an example is now described, of an electronic equipment, generally indicated by the reference number 100, which is configured to carry out the method for determining the Leaf Area Index, or LAI, of the invention, which will be described herein below. The method that will be described is, in particular, an indirect-type method. Furthermore, in the following disclosure, the term determining will mean the same as estimating.

In particular, the electronic equipment 100 is of the portable type, and it is embodied, for example, by a smartphone, a tablet, or by a general portable device for processing multimedia files (music, movies, photos, games) , for example, an iPod.

Such portable electronic equipment 100 for determining leaf area index will be indicated herein below as portable equipment, or simply equipment.

With reference to the Fig. 1, the equipment 100 comprises a processing module or a central processing unit 10 comprising a CPU (Central Processing Unit) , for example, a microprocessor or a microcontroller, operatively connected to an operative memory 20 (MEM) of the volatile type. Such operative memory 20 may be external to the central processing unit 10, or be located inside the above-mentioned processing unit, as in the example of Fig. 1.

In addition to the operative memory 20, the equipment 100 comprises a respective mass memory or system memory 30 of a non-volatile type, controlled by the central processing unit 10 to permanently store a software for managing the method for determining the LAI of the invention. For example, such system memory 30 is implemented by a solid state drive memory (SSD) integrated to the equipment 100 or, alternatively, by a memory card of the flash type (Secure digital or SD) , which is external and insertable in a corresponding compartment pre^¬ arranged in the equipment 100.

Furthermore, the equipment 100 comprises a digital image acquisition module 40 operatively connected and controlled by the central processing unit 10 to acquire a flow of digital images or frames F to be sent to the processing unit. Such acquisition module 40 is implemented, for example, by a digital photocamera integrated in the equipment 100, the camera lens 102 of which is shown in Fig. 2B. In a preferred embodiment, such photocamera 40 also comprises a digital light meter.

Furthermore, the equipment 100 comprises a user interface module 60 that is implemented by an input/output interface module, connected and controlled by the central processing unit 10 to enable the insertion (input) and/or modification of parameters of the software for managing the method by an operator and to display (output) data indicative of the determined parameter LAI . Such interface module 60 is implemented, for example, by a keyboard and a display, or a touch-screen display 101, as in the example of Fig. 2A.

Furthermore, the equipment 100 is advantageously provided with a gravity acceleration measuring module, i.e. an accelerometer module or accelerometer 50 operatively connected and controlled by the central processing unit 10. As it is known, such accelerometer 50 is generally employed to detect the inertia of the mass of an object when the latter is subjected to an acceleration. In the particular case of the electronic equipment 100, such as a smartphone or a tablet, the accelerometer 50 is configured to act as an inclinometer to detect an orientation change of such equipment 100, for example, an orientation change from vertical to horizontal, and vice versa referred to ground. Such orientation change detected by the inclinometer is translated, for example, into an automatic rotation of a visualization on the display 101 of the equipment 100 itself.

To the purposes of the present invention, the accelerometer 50 of the equipment 100 acts as an inclinometer. Such inclinometer function is obtained since, in the absence of accelerations applied to the equipment 100, the only detected acceleration is the gravitational acceleration g. In particular, with reference to Fig. 2A, the accelerometer 50 is configured to decompose the gravitational acceleration g into three components parallel with three mutually orthogonal axes of a Cartesian orthogonal reference system X, Y, Z fixed or stationary with respect to the ground, respect to which the above-mentioned portable equipment 100 can be moved. In particular, such Cartesian reference system comprises a first axis or axis X substantially orthogonal to the ground, a second Y and a third Z axis, mutually orthogonal, which are both substantially parallel to the ground and orthogonal to the first axis X. Such gravitational acceleration g, decomposed into the above-mentioned components, is used to derive an inclination angle of the equipment 100 with respect to a reference plane XY by known trigonometric functions. Such reference plane XY is, in particular, the plane defined by the axes X and Y.

Starting from the coordinate system of Fig. 2A, possible non-linear position changes of the equipment 100 within the described system of axes Χ,Υ,Ζ are defined by roll φ, pitch Θ, and yaw ψ rotations with respect to the axes X, Y and Z, respectively. An exemplary three-axis accelerometer acting as an inclinometer is described in the published document "Tilt Sensing Using Linear Accelerometers" by Laura Salhuana - of Freescale Semiconductor, Inc., N. AN3461, rev. 4, 02/2012.

Starting from the above-mentioned document, in particular, the inclinometer of the equipment 100 derived from the accelerometer 50 is suitable to carry out measurements in the Earth gravitational field. Therefore, it is possible that an output of the accelerometer 50 takes the value +lg, indicative of an axis aligned with the gravitational field and facing downwards, being g the above-mentioned Earth gravitational acceleration.

Based on the latter, an output G_P of the three- axes accelerometer 50 of the equipment 100 oriented in the Earth gravitational field, and not subjected to other linear accelerations, can be expressed as:

wherein M represents a rotational matrix describing the orientation of the equipment 100 with respect to the coordinate system Χ,Υ,Ζ.

The components of the matrix M can be calculated based on: cp

tpj

sinijj

ζ(ψ)^: -sinijj (2)

0 0 1

From the previous equations (1) and

accelerometer 50 allows calculating the

related to the roll φ and pitch Bangles, i.

tancp_xvz _=^GPv

(4)

From these latter equations (3) and (4), and based on the information obtained from the accelerometer 50, the processing unit 10 is capable of deriving the values of the above-mentioned roll φ and pitch Θ angles .

From the above-mentioned structural and functional characteristics of the portable electronic equipment 100, with reference to the Figs. 3 and 4, two preferred embodiments of the method for determining the leaf area index, or LAI, of a plant canopy sample, and indicated with the references 200 and 300 will be described in detail. In the Figs. 3-4, similar or analogous elements are indicated with the same reference numerals. It shall be noted that, advantageously, the embodiments 200,300 of the method of the invention are set in coded algorithms of a computer program stored in the mass memory 30 of the equipment 100. Such program may be written, for example, by using the programming languages: C# or C Sharp, Java, or Obj ective-C .

For both embodiments 200 and 300, the method of the invention comprises a symbolic start step STR corresponding to a start step of the program. In such start step, the program algorithms are transferred to the operative memory 20 in order to be run. In an embodiment, the operator handling the portable electronic equipment 100 is informed of the completion of such program transfer step by a first alert signal, for example, of the acoustic or mechanic (vibration) type.

Both embodiments 200,300 of the method provide for an information acquisition step 201 on a sky portion that can be seen at a plant canopy sample from which a parameter indicative of the light radiation transfer through the canopy or gap fraction P₀ can be obtained.

As it is known, the gap fraction parameter Po is a function of the leaf area index, or LAI.

Furthermore, the document entitled "GAI estimates of row crops from downward looking digital photos taken perpendicular to rows at 57.5° zenith angle: theoretical considerations based on 3D architecture models and application to wheat crops" of Baret et al . , published in Agricultural and forest Meteorology, n. 150, 2010, pp. 1393-1401, illustrates that, by carrying out a gap fraction Po measurement in a neighborhood of the pitch Θ angle equal to about 57.5°, the measurement carried out does not require to have to know a priori an additional piece of information on the distribution of the insertion angles of the leaves of the studied canopies to reach a proper estimation of the LAI. In radiative transfer models independent from the measurement acquired at an inclination angle Θ of about 57.5°, a correct LAI estimation requires such additional piece of information, resulting in a corresponding parameter. On the contrary, performing measurements in a neighborhood of 57.5° allows disregarding the additional information on the distribution of the leaf insertion angles.

The above-mentioned document discloses that inclination errors of a few degrees to an angle Θ equal to about 57.5° may lead to a considerable uncertainty in the LAI estimation.

Furthermore, the measurements carried out with an inclination angle Θ of about 57.5° minimize the adverse effects deriving from the presence of unevenly distributed vegetation, or "clumping". This occurs - for example - when the cultures are seeded in rows .

The LAI may be calculated by assuming that the leaves of the canopy sample are randomly distributed, according to a Poisson' s distribution, that may be expressed by the equation:

In other terms, once the value taken by the gap fraction parameter PQ at a neighborhood of the pitch angle Θ of about 57.5° has been measured, the leaf area index, or LAI, is derivable by inverting the equation (5) .

The above-indicated acquisition step 201 comprises a positioning step 202,202' of the portable electronic equipment 100 at the plant canopy sample. With reference to the second embodiment of the method 300, the positioning step 202' is implemented by positioning the electronic equipment 100 only below the plant canopy sample to be studied. On the contrary, with reference to the first embodiment of the method 200, the positioning step 202 provides for positioning the electronic equipment 100 both under and above the plant canopy sample to carry out two successive measurements, as it will be described herein below.

Next, such acquisition step 201 provides for a rotation step 203 of the portable electronic equipment 100 about the second axis Y. Such rotation, performed by the operator handling the equipment, brings the equipment 100 from a first position, in which the camera lens 102 of the photocamera 40 lies substantially on the reference plane XY defined by the first axis X and by the second Y axis, to a second position, in which such camera lens 102 lies on a first plane YZ defined by the above-mentioned second Y and third Z axes. In other terms, the first plane YZ is orthogonal to the reference plane XY and the equipment 100 is rotated of about 90°.

Again in the acquisition step 201, the method

200,300 provides for, during the rotation of the portable electronic equipment 100, a step of detecting, by the accelerometer module 50, the attainment of a position intermediate between said first and second positions. In addition, the method comprises an acquisition step 204 of at least one digital image of the plant canopy sample corresponding to the above-mentioned intermediate position of the equipment 100 between the first and the second positions. In particular, in such intermediate position, the electronic equipment 100 is inclined with respect to the reference plane XY by a reference inclination or pitch Θ angle equal to about 57.5°. During the rotation, the operator is informed of when such reference inclination angle is reached by a second alert signal, for example, of the acoustic or mechanic (vibration) type.

In accordance with a first embodiment, this step of acquiring 204 at least a digital image is implemented by the acquisition 204' of a single image by the photocamera 40 at the occurrence of a "click event" following the attainment of the reference inclination Θ angle equal to about 57.5°. The image acquisition time is about one frame per second.

In a second embodiment of the method 200,300, such acquisition step 204 of at least one digital image comprises the step 204' of taking a sequence of images or frames F by the photocamera 40 in "live- preview" mode, i.e., without performing a real snapshot event, as it is known to those skilled in the art. This allows acquiring and storing temporarily a plurality of acquired digital images in succession during the rotation of the equipment 100, for example, at a rate of twenty-five frames per second, in a preset neighborhood of the pitch angle Θ equal to about 57.5°. The method 200,300 then proceeds, always in the acquisition phase 204, to the further step of storing 204'' in the operative memory 20 a single image of the plurality of captured images, typically the image acquired after the achievement of the reference inclination Θ angle of about 57.5°.

In particular, whatever the mode of image acquisition is, the method of the invention provides that a space of the operative memory 20 of the equipment 100 is available to store digital data representing the images captured by the photocamera 40. In addition, with reference to memory occupation of such operative memory 20, from an implementation point of view, a single allocation space of this memory is provided whatever the shooting mode adopted. This means that every time a new image is captured by the photocamera 40, it is stored in the same memory location, possibly overwriting the image data acquired previously. As a result, all the images captured by the photocamera 40 (both in "live preview" and in "click event") that are not processed for the calculation of LAI are systematically eliminated. In this way, the method of the invention avoids the storage of a plurality of images inside the portable equipment 100 in correspondence with each measurement. This is advantageous in the case the method is implemented in portable equipment 100 provided with memories having a reduced storage capacity .

In one embodiment, the method includes a step of storing the captured image also on the system memory 30 of non-volatile type. This phase of storage into the system memory 30 is a user-selectable option for purposes of traceability and reproducibility of measurements .

Again in the acquisition step 201, the method then provides for a sending step 205 of such at least one acquired digital image to the central processing unit 10 of the portable electronic equipment 100.

Such processing unit 10 is, in turn, configured to carry out a processing step 206, 206' of such at least one digital image to measure the gap fraction parameter Po . In particular, such processing is performed for each of the two embodiments of the method 200, 300 based on different algorithms.

With reference to Fig. 3, in the first embodiment 200 of the method, the step 206 of determining the gap fraction parameter P₀ comprises a step of calculating 207 a first luminance value L_b below the plant canopy sample starting from the image or first image acquired during the above-mentioned steps 202-205 and the step of detecting the reaching of the intermediate position between the first and the second position.

Next, the method 200 provides for a calculating step 208 of a second luminance value L_a above the canopy. In particular, such step 208 is implemented by positioning the equipment 100 above the plant canopy sample to be studied to carry out again the above-mentioned steps, i.e.: rotating the portable electronic equipment in the manner indicated in step 203; detecting the reaching of the intermediate position; acquiring a second digital image above the canopy in accordance with what has been described in steps 204, 204', 204''; sending 205 such second image to the central processing unit 10. Based on the information acquired under and above the canopy, the steps 207, 208 are completed by implementing the following formula:

, N² - k

L =

t - S (6) where

L indicates the luminance (measured in candles/m²) ,

N is a first coefficient indicative of a focal ratio number,

- t is a second coefficient relating to an exposure time (measured in seconds) ,

S is a third coefficient indicative of a ISO , i.e., the sensitivity of the sensor of the photocamera 40,

- k is a fourth coefficient indicative of a calibration constant of light meter on the reflected light. Such constant is equal to about 12.5.

The values of the coefficients N, t, and S, in particular, are provided by the digital light meter, with which the photocamera 40 of the equipment 100 is equipped .

Based on the latter, in the first embodiment of the method 200, the gap fraction parameter P₀ is calculated in the step 209 by carrying out the ratio of the above-mentioned first L_b and second L_a luminance values in accordance with the equation:

which β represents a multiplication factor depending on the ratio of direct radiation (above the canopy) and radiation diffused under the canopy. In particular, this multiplicative factor β depends on the structure of the plant cover examined, namely by the physical characteristics of the plant cover, such as the distribution of the angles of insertion of the leaves and the size of the same. Advantageously, having this multiplicative factor β in equation (7) allows to estimate the parameter gap fraction Po in a simpler way than the direct methods that use specific sensors for the assessment of luminance values.

From the thus-calculated gap fraction Po value, the leaf area index, or LAI, is determined, in the step 210, by inverting the equation (5), i.e., based on the equation:

LAI = -^{COS (57}'^5O)logP₀(57,5°) (8)

0,5

With reference to Fig. 4, in the second embodiment 300 of the method of the invention, the processing step 206' of the at least one digital image to determine the gap fraction parameter P₀ provides for an estimation of the percentage of "sky" pixels present in an image acquired only below the plant canopy sample.

In such step 206', the method 300 provides for processing routines based on the subdivision or segmentation of the image into "subareas", each of which comprises a given number of image units, for example, the image pixels. Such routines provide for the steps of selecting the image pixels based on the chromatic values they contain. Specifically, the embodiment 300 of the method provides for, in the processing step of the image 206', the implementation of two mutually alternative image segmentation algorithms: a first algorithm 207' based on the image colors, and a second algorithm 208' based on the light intensity thereof.

The first algorithm 207' can be advantageously used on clear sky days, or, generally, in the cases when the image is acquired in the presence of a substantially direct sunlight radiation. Such algorithm 207' is configured to perform a distinction between the sky and clouds from those parts of the vegetation that, when directly hit by sunrays, are often lighter and brighter than the same sky.

In a preferred embodiment, such first algorithm is based on an image processing based on the color space model HSI (an acronym of hue, saturation, intensity) of a known type, and indicative of a model whereby the chrominance components are explicitly correlated to the properties of the colors to which the human visual system is sensitive.

In other terms, the method 300 provides for a converting step 207' of the stored single image based on the color space model HSI. In particular, with the model HSI, hue and saturation are the parameters used to segment the image, while intensity is not used, since it does not contain information relating to the colors .

The method 300 proceeds through a selecting step 207'' of pixels of the image obtained following such conversion. Such selection step 207'' is implemented by the accumulation of multiple segmentation events of the original image by individuating the image pixels falling within a preset number of color ranges. Such color ranges comprise, at the corresponding end boundaries, pairs of scalars (in particular, terns of numbers) of the tridimensional space HSI. The above-mentioned color ranges are, for example :

HSI (125, 7, 123) to HS I ( 189 , 128 , 255 ) ;

HSI (123, 12, 249) to HS I ( 134 , 26 , 255 ) ;

HSI (133, 15, 115) to HS I ( 166 , 51 , 153 ) .

The sum of such thus-selected pixels is equal to a first number ni . For example, such pixel selection step comprises the selection of white and sky blue pixels corresponding to the sky portions of the image .

Next, the method provides for a calculating step 207a of the ratio of the first number of selected pixels ni and a second number ni+n2 representative of the total pixels of the converted image to estimate the gap fraction parameter Po.

The gap fraction parameter P₀ can be expressed as:

(9) n_i+n₂

It should be noted that between the models of color space known, the Applicant has selected the color space model HSI because such color space HSI is the most suitable to calculate the leaf area index or LAI starting from the information obtainable from the portion of sky represented in the processed image. In fact, since the HSI space makes available the H parameter, this parameter is suitable to translate the two main colors in the images, that is, the sky blue of the sky and the green of the leaves, in precise intervals along this dimension of the space. Contrary to other color spaces known in the art, such as the RGB color space, the method of the invention has the advantage of avoiding to locate the shades as complex compositions and less controllable of different sizes.

The above-mentioned second algorithm 208', based on the image brightness parameter, can be advantageously used on days in which the sky is substantially covered, when the even brightness of the cloud covering allows efficiently distinguishing the sky from the leaves of the plant canopy sample. Such algorithm is configured to perform a distinction between clouds and vegetation parts that, under a diffused light condition, are usually darker than the sky above.

In a preferred embodiment, such second algorithm comprises a step of converting 208' the stored single image to a color space of grey tones. In particular, the hue and saturation parameters of the image are removed from the image itself, while the parameter intensity is used to obtain a representation of the image pixels in the grey scale (values from 0=black pixel and 255=white pixel) .

The method proceeds with a setting step of a reference threshold value in said space of grey tones, for example, of 105, to select 208'' pixels of the single image obtained following said conversion having a grey tone value greater than the preset reference threshold. In particular, the selected pixels are equal to a further first number ni' . In particular, the central processing unit 10 discriminates the number ni' of representative pixels in the image of the sky portions, from the pixel ¾' relating to image portions of plants. Next, the method provides for a calculating step 208a of the ratio of said further first number ni' of selected pixels and a further second number ni'+n2' representative of the total pixels of the converted image to estimate the gap fraction parameter Po, based on the equation:

Based on the gap fraction Po value calculated by the equations (9) or (10), the leaf area index, or LAI, can be calculated, in the step 210, based on the equation (8) set forth above.

The algorithms relating to both embodiments of the method 200,300 are symbolically completed by an end step ED.

In a preferred embodiment, the method for determining the LAI advantageously provides for an analysis step, which may be carried out before the above-mentioned algorithms, to determine an optimal number of measurements to be carried out by the equipment 100, which takes into account the variability of the vegetation studied. In particular, such preliminary analysis step is implemented by a corresponding algorithm of a known type, also advantageously stored in the equipment 100, based on resampling methods, such as described, for example, in the document "A Jackknife-derived visual approach for sample size determination" of R. Confalonieri - Rivista Italiana di Agrometeorologia, pp. 9-13(1) 2004. Such algorithm has the advantage to be extensively applicable, since it does not require that the assumptions of the classical (or parametric) statistics are met. Furthermore, the use of such algorithm in an integrated manner to the method for determining the LAI of the invention allows eliminating one of the main uncertainty factors deriving from the known commercially available apparatuses for the LAI determination, i.e., the uncertainty due to measurements that are not always representative of the plant populations analyzed.

In another embodiment, the electronic equipment 100 comprises a geo-localization module, for example, a GPS (Global Positioning System) receiver, so as to be able to associate to the LAI value determined also additional information on the latitude and longitude of the plant canopy sample examined. In such a manner, it is possible to create distribution maps of the leaf area index LAI on the monitored area.

The method for determining a leaf area index, or LAI, of the invention has a number of advantages compared to the methods implementable with the known apparatuses .

First of all, the method for the estimation of the LAI index of the invention is completely automatic, not requiring an operator to set parameters suitable to describe the structure of the canopy to be studied. In particular, by choosing to perform the measurement at the reference inclination angle of 57.5°, the method of the invention is independent from the characteristics of the vegetation, for example, the operator is not obliged to know a priori the extinction coefficient of radiation in the plant cover (determined by the insertion angle formed by the leaves) . Furthermore, the method does not require to the operator to perform manual attempts to perform the LAI measurement by changing the thresholds or interpreting the acquired image as occurs in many devices of known type.

Furthermore, the portable electronic equipment 100 implementing the method has reduced overall dimensions and weight (a weight of about 110-150 grams in the case of a smartphone) , while the instrument currently commercially available are heavy (4Kg to 12Kg, including their cases) and not easily handled.

Furthermore, the method of the invention allows a continuous interaction with the operator through a touch-screen interface 60 present on the smartphone or tablet 100, also by virtue of a much more intuitive interface than those already present in the known devices.

The proposed method is based on the inclination information of the equipment 100 acquired by the digital inclinometer obtained by the accelerometer 50 of the equipment 100. This avoids the use of inaccurate bubble levels as those in the commercial apparatuses. As already pointed out, the use of such levels having reduced dimensions may adversely affect the measurement accuracy, due to the operator subjectivity in assessing the operative condition thereof .

In addition, the portable electronic equipment 100 provided with the software implementing the method 200, 300 has, on the whole, a cost that is lesser than that of the commercially available instruments, and it does not require expensive maintenance or repair interventions.

In addition, the second embodiment of the method based on the recognition of the "sky" pixels does not require the acquisition of information above the vegetation. This is particularly advantageous in the case of the analysis of tree species. In fact, in the case of surveys in a forest, the known apparatuses require that the measurements are performed in clearings located very far from the points of interest. Therefore, the measurements performed under the canopy and in a clearing may be temporarily far from one another; therefore they cannot be compared.

EXAMPLE

The Applicant performed experimental tests to compare the accuracy of the method of the invention, in the two embodiments 200 and 300, to that of the known methods implemented with the currently commercially available instruments. In particular, such accuracy (comprising the parameters of "trueness" and precision, the latter in turn comprising the parameters repeatability and reproducibility) was determined by adapting the regulation ISO 5725, devised for analytic methods, to full-field methods.

It shall be noted that direct (destructive) measurements of the LAI index were used as reference values. Analyses were carried out on broadcast seeded rice as the plant canopy sample by carrying out measurements in three moments of the cultural cycle, in particular on plots having the same dimension, but including a different number of plants.

As regards the "trueness" parameter of the methods used, i.e., their ability to be true by averaging a high number of measurements, the first embodiment 200 of the method of the invention based on the luminance turned out to be the most performing among the compared methods, obtaining the best values for all the error metrics.

As regards the precision parameter (i.e., repeatability and reproducibility) , the second embodiment 300 of the method described above generally showed the best performance among all the considered methods.

In more detail, Fig. 5 shows in a Cartesian diagram a comparison of the leaf area index LAI values measured by a disruptive (planimetric) method, and values estimated by indirect methods, among which the two embodiments 200,300 of the invention and the methods implemented by two widespread and commercially available instruments, specifically, the AccuPAR ceptometer and LAI-2000 (in the two configurations having five rings (5R) and four rings (4R) ) .

From Fig. 5, it follows that the first embodiment 200 of the method has a higher linearity (compared to the reference straight line 1:1 ratio REF) , i.e., a lesser tendency to "saturate" compared to the other methods, thus a lesser tendency to underestimate high LAI values. Therefore, the method 200 is particularly advantageous compared to those tested in the case where the estimations are carried out by averaging a very high number of measurements, especially if the time within which the measurements have to be completed is not a stringent requirement.

The second embodiment 300 is the best in precision, thus allowing the user obtaining LAI estimations while performing a lesser number of measurements compared to the other methods. As regards the "trueness" parameter, the second embodiment is approximately intermediate between the AccuPAR ceptometer and the LAI-2000, having a lesser tendency to saturate compared to the latter.

To the above-described embodiments of the method, those of ordinary skill in the art, in order to meet contingent needs, will be able to make modifications, adaptations, and replacements of elements with functionally equivalent other ones, without departing from the scope of the following claims. Each of the characteristics described as belonging to possible embodiment may be implemented independently from the other embodiments described.

Claims

1. A method (200; 300) for determining Leaf Area Index, or LAI, of a plant canopy sample by a portable electronic equipment (100) movable with respect to a Cartesian orthogonal reference system (X, Y, Z) fixed with respect to the ground, said reference system having a first axis (X) perpendicular to the ground and a second (Y) and third (Z) axes parallel to the ground and orthogonal to said first axis, said equipment being provided with a digital image acquisition module (40, 102) and with an accelerometer module (50) operable to detect an inclination relative to the ground of the electronic portable equipment (100), comprising the steps of: - positioning (202; 202') said portable electronic equipment (100) at the plant canopy sample to be studied;

- rotating (203) said portable electronic equipment (100) about said second axis (Y) from a first position, in which a camera lens (102) of said image acquisition module lies on a reference plane (XY) orthogonal to the ground identified by said first (X) and second (Y) axes, to a second position in which said camera lens (102) lies on a first plane (YZ) parallel to the ground identified by said second (Y) and third (Z) axes and orthogonal to the reference plane (XY) ;

during the rotation of the portable electronic equipment (100), detecting, by the accelerometer module (50), the attainment of an intermediate position between said first and second position, in said intermediate position the equipment (100) being inclined with respect to the reference plane (XY) by a reference inclination angle (Θ) of about 57.5°;

- acquiring (204) at least one digital image of said plant canopy sample at said intermediate position of the equipment (100);

- sending (205) said at least one acquired digital image to a processing module (10) provided for in the portable electronic equipment (100);

- processing (206; 206') said at least one digital image to measure a parameter (Po) indicative of a light radiation transfer through the plant canopy sample at said reference inclination angle (θ) , said parameter (Po) being a function of the leaf area index, or LAI .

2. The method (200) according to claim 1, wherein said positioning step (202) comprises the steps of:

- positioning the portable electronic equipment (100) under the plant canopy sample to acquire a first digital image by carrying out the steps of rotating (203) the portable electronic equipment (100), detecting the attainment of the intermediate position, acquiring (204) at least one digital image and sending (205) said at least one digital image acquired at the processing module (10);

- positioning the portable electronic equipment (100) above the plant canopy sample to acquire a second digital image by carrying out the steps of rotating (203) the portable electronic equipment (100), detecting the attainment of the intermediate position, acquiring (204) at least one digital image and sending (205) said at least one digital image acquired at the processing module (10); said processing step (206) comprising the further steps of:

calculating (207) a first (L_b) luminance value starting from said first image; calculating (208) a second (L_a) luminance value starting from said second image; said parameter (P₀) measured at the reference inclination angle (Θ) being proportional to a ratio of the first (L_b) and the second (L_a) luminance values.

3. The method (200) according to claim 2, wherein said parameter (Po) is calculated based on the e uation :

wherein :

L_b and L_a are the first and the second luminance values, respectively;

β represents a multiplication factor depending on the ratio of a radiation directed above the plant canopy sample and a radiation diffused below said sample .

4. The method (200) according to claim 2, wherein said first (L_b) and second (L_a) luminance values are calculated by the formula:

, N² - k

L =

t - S

where

L indicates the luminance;

N is a first coefficient indicative of a focal ratio number; t is a second coefficient relating to an exposure time;

S is a third coefficient of ISO sensitivity;

k is a fourth coefficient;

wherein the values of said coefficients N, t, S are provided by a digital light meter included in the digital image acquisition module (40) of the portable electronic equipment (100), and said fourth coefficient k is indicative of a calibration constant of light meter on reflected light.

5. The method (200; 300) according to claim 1, wherein said acquisition step (204) of at least one digital image comprises the further steps of:

taking (204') a plurality of digital images (F) during said rotation step (203) in a preset neighborhood of the reference inclination angle (Θ) ; storing (204'') a single image of the plurality of images (F) corresponding to the acquired image after reaching the reference inclination angle (Θ) equal to about 57.5°, during the equipment (100) rotation .

6. The method (300) according to claim 1, wherein said positioning step (202') comprises the step of positioning the portable electronic equipment (100) only below the plant canopy sample and wherein said processing step (206') comprises the steps of:

converting (207') said at least one digital image acquired based on the tridimensional color space model HSI (Hue, Saturation, Intensity) ;

- selecting (207'') pixels of the respective image obtained following said conversion, said selection step (207'') comprising a step of cumulating multiple segmentation events of the original image by identifying those image pixels falling within a preset number of color ranges, said selected pixels being equal to a first number (ηχ) ;

calculating (207a) the ratio of said first number of selected pixels (ni) and a second number (ni+^) representative of the total pixels of the converted image to estimate said parameter (Po) .

7. The method (300) according to claim 6, wherein said color intervals include, to their respective extreme limits, pairs of scalars of three-dimensional space HSI, said intervals being, for example:

from HSI (125,7,123) to HSI (189, 128, 255);

from HSI (123,12,249) to HSI (134,26,255);

from HSI (133, 15, 115) to HSI (166,51,153).

8. The method (300) according to claim 1, wherein said positioning step (202') comprises the step of positioning the portable electronic equipment (100) only below the plant canopy sample and wherein said processing step (206') comprises the steps of:

converting (208') the at least one digital image acquired to a color space of grey tones;

setting a reference threshold value in said color space of grey tones;

selecting (208'') pixels of the single image obtained following said conversion, having a grey tone value greater than the preset reference threshold, said selected pixels being equal to a further first number (ni' ) ;

calculating (208a) the ratio of said further first number (ni' ) of selected pixels and a further second number (ηι'+^') representative of the total pixels of the converted image to estimate said parameter (P₀) .

9. A portable electronic equipment (100), comprising: a processing module (10);

- a memory module operatively connected to said processing module (10);

a digital image acquisition module (40) operatively connected to and controlled by the processing module (10) to acquire a flow (F) of digital images to be sent to the processing module; an accelerometer module (50) operatively connected to and controlled by the processing module (10) ,

said portable electronic equipment being configured to carry out the method in accordance with any of the claims 1-8.

10. The portable electronic equipment (100) according to claim 9, wherein said equipment is selected from the group consisting of:

- a smartphone,

a tablet,

a general portable multimedia file processing device .

11. A computer program comprising a program code loadable in a memory of a computer to carry out the steps of the method (200; 300) for determining a leaf area index, or LAI, in accordance with one of the preceding claims 1 to 8.