Using the value of Lin’s concordance correlation coefficient as a criterion for efficient estimation of areas of leaves of eelgrass from noisy digital images

Seagrass meadows are highly productive plant communities that grant valuable ecological services in estuaries and near-shore environments worldwide. Seagrasses provide food and shelter for a myriad of economically and ecologically valued marine organisms [1]-[3], play an important role in nutrient cycling [4],[5], favor the stabilization of the shoreline as roots and rhizomes compact the substrate, preventing erosion [6],[7], participate in the foundation of the detrital food web [8], and play also, a fundamental role in carbon sequestration [9]. Eelgrass (Zostera marina L.) is particularly relevant not only because it is the dominant seagrass species along the coasts of both the North Pacific and North Atlantic [10], but also, because eelgrass communities have been traditionally recognized as among the richest and most varied in the abundance of sea life [11]. Indeed, this cosmopolitan macrophyte was found to produce up to 64% of the total primary production of an estuarine system [12].

The forcing of Zostera marina dynamics by environmental variables is well documented in the literature [13]-[18]. Light availability, temperature, and dissolved nutrients are the most important variables for explaining the observed variability [18],[19]. But even when light and nutrients are not limiting, temperatures ranging above the upper limit tolerated by eelgrass can provoke severe negative effects on its growth [20]. Indeed, the onset of warm ENSO events has been shown to dramatically diminish eelgrass growth [20]. Therefore, the productivity of Zostera marina populations could be diminished by global climate change, which is expected to result in warming and rising seas, thereby reducing the availability of both light and nutrients underwater [21]. Another concern for the health of eelgrass populations pertains to increasing deleterious anthropogenic influences. The loss of eelgrass habitat has been noted worldwide, with major losses in the past few decades [22]-[25]. Within restoration strategies, replanting plays an important role [26]-[28]. The monitoring of these efforts is fundamental for the evaluation of the effectiveness of restoration of functions and values of natural populations. Accurate measurements of the standing crop and productivity of transplanted populations at a given time constitute an important input for evaluating the restoration of the ecological functions and values of natural populations. Although traditional assessment methods do not cause damage to natural populations, their invasive nature could significantly alter the development of transplanted populations. Echavarria-Heras et al. [29] and Echavarria-Heras et al. [30] propose allometric methods that reduce eelgrass biomass and leaf growth rate estimations to measurements of leaf length or area. Besides, the use of digital imagery could provide leaf area estimations which avoid invasive effects. But in some cases noise effects could lead to misidentification of pixels placed on the peripheral contour of leaves images (see Figure 1). This could spread uncertainty on leaf area estimations that ultimately could render imprecise allometric projections of biomass and leaf growth rates. Therefore, for accurateness we must rely on an image selection method that produces an unambiguous identification of the sequence of pixels that form the peripheral contours of digitalized eelgrass leaves. In order to achieve this task, there are techniques developed on the basis of the concepts of adjacency, vicinity, connectivity and tolerance of similarity between pixels (see Appendix). Using this framework Leal-Ramirez and Echavarria-Heras [31] introduced a direct comparison method aimed to discriminate the interval of tolerance of similarity that produces the most accurate estimations of length, width or area of eelgrass leaves from digital images with noise induced by humidity contents. For a given interval of tolerance of similarity, the process initially identifies the peripheral contour of the images of leaves and then measures the concomitant lengths widths and areas. Next, individual deviations between leaf area measurements taken from images and those obtained directly from leaves are used to produce statistics aimed to obtain the proportions of leaves for which image assessments underestimate or overestimate observed values. The ratio of these proportions defines a selection index whose smallest value provides criterion for choosing the interval of tolerance of similarity that yields the most accurate image related measurements. The implementation of the direct comparison method uses lengthy computational stages that include various statistical inferences on deviations between observed an image obtained leaf areas. In this contribution, we present an alternative criterion for the selection of the named interval of tolerance of similarity. The present procedure called the concordance correlation method; is simpler to implement than the direct comparison method. It only requires calculating the values of the Concordance Correlation Coefficient (CCC) for the reproducibility of observed leaf areas through proxies obtained from corresponding images. The present criterion proposes the use of the interval of tolerance of similarity that yields the maximum value of the aforementioned CCC for consistent digital image estimations of eelgrass leaves areas. Our results show that on spite of its simplicity the present selection criterion yields highly reliable levels of accuracy.

In section two, we present a brief review of the direct comparison method. Section three formally explains the present concordance correlation method. Section four describes the results of this study and discusses the advantages and possible drawbacks of the present approach.

For the purposes of the present study, we used a data set obtained by randomly sampling 5 shoots biweekly from January through December 2009 in a Zostera marina field at Punta Banda estuary, a shallow coastal lagoon located near Ensenada, Baja California, Mexico (31° 43–46 N and 116° 37–40 W). For each sampled leaf, a millimeter ruler was used to obtain leaf length measurements l _o to the nearest 1/10 mm taken as the distance from the top of the sheath to the leaf tip. Meanwhile, observed leaf width h _o was measured at a point halfway between the top of the sheath and the tip [32]. Observed leaf area estimations a _o were calculated by means of length times width proxy a _o  = l _o  ⋅ h _o .

We obtained l _max  = 460 mm. For the data grouping required by the DCM we choose n = 46 so we acquired q = 10 mm, and for the interval [0, l _max ] we formed a partition $P_0^{460}$ of disjoint intervals I _k of the form I _k  = {l | q(k − 1) ≤ l < qk}, with 1 ≤ k ≤ 46. Hence, for each value of the index k, we formed a group G _k (l) containing leaves with sizes varying in the interval I _k . Longer and older leaves displayed darker tonalities than younger and shorter ones, but leaves with lengths varying on a given partition interval I _k displayed a similar color distribution. For some of the partition intervals there was at most one leaf with length placed in the linked variation range. Therefore, these groups are not taken into account because they do not provide information for the statistical analysis.

According to the DCM, for each leaf belonging to the group G _k (l) we obtained its digital image. For dealing out with all these individual images we selected an RGB color format with a number C _max of 256 colors. For processing each one of the available leaves images, we choose different tolerance of similarity levels ST(r) = [0, r] with the upper bound r satisfying 0 ≤ r ≤ C _max  − 1. Then for a given ST(r) range, we selected a starting point inside the considered leaf image, and identified using equations (A1), (A2) and (A3) all adjacent pixels falling within the named similarity range ST(r). This recognizes the outer contour of the digital blade, and produce concomitant leaf width, length and area estimations. The next step in the DCM concerns the calculation of the selection index IS(r) which depends on the value of the λ _a (r) statistics. But according to equation (6) obtaining the value of λ _a (r) requires counting the number of leaves in each group G _k (l), that comply with conditions (1) through (5) and these numbers depend on the chosen value of r. Moreover, for small values of r the number of different tonalities included in ST(r) is limited so identification of pixels within an image can be expected to be imprecise. This is handily clarified by Figure 2, produced using r = 10 and that shows a systematic tendency for average length deviations ${\overline{\delta }}_l^k\left(r\right)$ depending on group index k. As a result we can observe a large number of ${\overline{\delta }}_l^k\left(r\right)$ values lying above the ${\overline{\delta }}_l\left(r\right)+{\sigma }_{\delta l}\left(r\right)$ and beyond the ${\overline{\delta }}_l\left(r\right)-{\sigma }_{\delta l}\left(r\right)$ thresholds in inequality (3). The bigger the value of r, the greater the number of color tonalities included in the interval ST(r) and precision in image contour identification improves. This is observed in Figure 3, produced using r = 128 and which does not display the above quoted systematic tendency, but a reduced number of groups of leaves with average length deviations ${\overline{\delta }}_l^k\left(r\right)$ lying outside the interval bounded by ${\overline{\delta }}_l\left(r\right)+{\sigma }_{\delta l}\left(r\right)$ and ${\overline{\delta }}_l\left(r\right)-{\sigma }_{\delta l}\left(r\right)$. Consequently, for small values of r we can expect reduced values of λ _a (r) and as a result according to equation (7) large values of IS(r). Additionally, when the interval of tolerance of similarity becomes wider, smaller values of IS(r) can be expected. In fact, as shown in Figure 4, the DCM captures this effect in a consistent way, with small values of r leading to large values for the selection index IS(r). Moreover, through the interval 1 ≤ r < 128, IS(r), decreases reaching a minimum value of 0.91, attained at r = 128. Meanwhile, for r ≥ 128, the values of the selection index IS(r) steadily increased towards a value of 1.84, attained at r = 255. Therefore, according to the DCM selection criterion ST(128) must be chosen for efficient estimation of areas of eelgrass leaves using images with noise induced by humidity contents.

Now for the CCM, since a small value of r fails to recognize some pixels in the digital image, we might expect a low reproducibility of directly obtained measurements (a₀₁, a₀₂, ⋯, a_0m) by means of digitally obtained proxies (a_{d 0}(r), a_{d 1}(r), ⋯, a _dm (r)). This is indeed shown in Figure 5. Moreover , the larger the value of r, the greater the number of color tonalities included in the interval ST(r), as a result exactness in image contour identification increases, and reproducibility improves, this explaining why Figure 5 shows increasing values of $\widehat{\rho }\left(r\right)$ through the interval 1 ≤ r < 128. Moreover, through the domain 128 ≤ r < 178 the values of $\widehat{\rho }\left(r\right)$ are maintained within a plateau of slight variation around $\widehat{\rho }\left(128\right)=0.90$, but for 178 ≤ r ≤ 255, $\widehat{\rho }\left(r\right)$ decreases dropping to a value of 0.8464, attained at r = 255. Thenceforth, intervals of tolerance of similarity, wider than ST(128) do not improve reproducibility of observed values of leaves areas by means of their image obtained surrogates. Thus, for the sake of accuracy and simplicity, ST(128) should be used for image selection when noise due to environmental factors is present and efficient estimations of eelgrass leaf area taken from these images are required.

In order to assess robustness of the CCM, we performed a resampling experiment. We chose a sample size index p = 1, 2, …, 8 then for each value of p a set s(p) of samples of size 100p each were uniformly drawn from the (a₀₁, a₀₂, ⋯, a_0m) population. Next, we selected one of the s(p) samples, for each value of r through the interval 1 ≤ r ≤ 255, we designated the matching areas obtained from digital images and calculated the concomitant Concordance Correlation Coefficient values $\widehat{\rho }\left(r\right)$. We recorded the value of r at which the maximum for $\widehat{\rho }\left(r\right)$ was attained for the selected sample. We repeated this procedure for all the samples in the set s(p) and then averaged the obtained r values for maximum $\widehat{\rho }\left(r\right)$. Figure 6 displays the obtained averages for the different values of the sample size index p. The maximum values of $\widehat{\rho }\left(r\right)$ per sample were also averaged over the s(p) sets. These last average values are shown in Figure 6. The results of this study show that the optimal interval of tolerance of similarity, as well as, the reproducibility of observed leaf areas by means of their digital image surrogates can be considered independent of sample size. Therefore, the CCM can be regarded as a robust procedure.

According to our results, both methods sustain the same conclusion regarding the choosing of ST(128) on behalf of accuracy. However, in comparison to the complicated multi-stage procedures of the DCM, using $\widehat{\rho }\left(r\right)$ values provide a direct and simpler criterion for choosing an interval of tolerance of similarity ST(r) for reliable digital image related assessments of eelgrass leaf area under the specified noise effects. But the main advantage of the CCM resides on the fact that it allows a straightforward interpretation of the addressed digital image selection procedures in terms of a measure of reproducibility. Indeed the plateau in $\widehat{\rho }\left(r\right)$ values linked to the domain 128 ≤ r ≤ 178, and the subsequent decreasing mode associated to r ≥ 178 shown in Figure 5 indicate that intervals of tolerance of similarity wider than ST( 128) will fail to improve reproducibility of observed values of leaf area by means of their image produced proxies. In other words for r ≥ 128, ST(r) includes more tonalities than those contained within the real image, thereby favoring the incorporation of spurious entries appearing beyond its peripheral contour and within the framing of the image. Thus including more color tonalities than necessary in the image processing task could not grant a gain in accuracy, but instead, depending on the severity of the noise effects (Figure 1), and on the size of the framing enclosing the peripheral contour of the image (Figure 1), more spurious pixels could be taken in to account by the image processing devise, which could lead to increased miscalculation of leaf area obtained from images. Meanwhile, our analysis confirms that when noise induced into images by the humidity contents of the leaves reduces the accuracy of estimations of the associated areas we could use a RGB color format, an ST( 128) interval of tolerance of similarity and equations (A1), (A2) and (A3) to identify the peripheral contour of leaves images for optimal reproducibility.

The results of the present digital image selection procedure provide simple, unbiased and non-destructive measurements of eelgrass leaf area. These measurements in conjunction with allometric methods [35] can predict the dynamics of biomass and leaf growth through indirect techniques, reducing the destructive effect of sampling and simplifying time consuming methods in the laboratory [36]. Nevertheless, it is worth to emphasize, that leaves removed from a shoot readily begin to lose water and degrade, so changes in shape may occur [37]. Therefore, even though humidity contents could certainly induce noise effects, an efficient digitalizing of a Zostera marina blade requires the maintenance of an optimal humidity for increased image fidelity. By taking this into account we can assert that the apparent similarity of values of $\widehat{\rho }\left(r\right)$ linked to the interval 128 ≤ r ≤ 178 could not be exhibited as a weakness of the CCM, that is, the plateau shown in Figure 5 does not associate to vagueness in the imbedded selection criteria. Indeed in this study both the preparation of lives before digitalization procedures and the framing used to bound the area surrounding the peripheral contour of the digital leaves was effective (1) for reducing inconsistencies attributable to a biased mapping of leaf shape into images, (2) by lessening bias due to the inclusion of spurious entries linked to noise into images and (3) because the framing size used in the present identification procedure further limited the participation of spurious entries in image processing tasks. Therefore, r = 128 (that is, the entrance threshold for the plateau of maximum $\widehat{\rho }\left(r\right)$ values in Figure 5) includes the required number of different tonalities for the processing of the present set of images and we choose it for a consistent estimation of the pertinent leaf area. Although, in the present settings the aforementioned bias reduction practices explain why values of r beyond r = 128 sustain the same selection criterion, using r ≥ 128 could lead to extended time consuming computational procedures, because more than necessary tonalities will be included in the identification undertaking. It is also worth to highlight that in further applications, before the CCM could provide consistent results, care should be taken in order to ensure that the handling of samples be performed in an efficient way for reducing bias in the overall image selection procedures. Indeed we could anticipate that in settings where points (1) through (3) above are disregarded, the inherent bias could seriously reduce reproducibility. Nevertheless, this could not be exhibited as a weakness of the present CCM, since the DCM itself as well as any other image selection procedure is subject to the same bias effects. In summary, the CCM, not only provides a simplified and robust image processing device, besides, (a) this criterion offers a conceptual substantiation for the DCM itself by linking the minimum values of the selection index IS(x), to the maximum values of the Concordance Correlation Coefficient $\widehat{\rho }\left(r\right)$, and (b) even though here we applied the CCM to account solely for the effects of noise linked to humidity contents, it is worth to mention that since the core of the CCM criterion is the evaluation of reproducibility, its scope directly embraces the treatment of any kind of noise effects that can reduce the accurateness of digital image proxies of areas of eelgrass leaves.

Studies of seagrass communities such as those composed of Zostera marina show that these systems are among the most productive marine systems [38]. The characterization of the dynamics of such ecosystems is important from both a scientific and conservation perspective. Moreover, the methods sustained by the present research may be fundamental to the evaluation of eelgrass restoration projects and could thereby contribute to the conservation of this important seagrass species.

is satisfied. The range ST(r) is called “interval of tolerance of similarity” and the upper bound r can be interpreted as the maximum distance that two points located within the extent of an object can attain in a RGB color space in order to be considered similar. Connectivity between pixels is used to identify the limits in objects and regions in an image. We will say that two pixels P and Q are connected with tolerance of similarity ST(r) if they fulfill the definition of adjacency and also if inequality (A3) holds.