- Methodology
- Open Access
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
- Héctor Echavarría-Heras1Email author,
- Cecilia Leal-Ramírez1,
- Enrique Villa-Diharce2 and
- Oscar Castillo3
https://doi.org/10.1186/s13029-014-0029-8
© Echavarría-Heras et al.; licensee BioMed Central. 2014
- Received: 8 August 2014
- Accepted: 30 November 2014
- Published: 20 December 2014
Abstract
Background
Eelgrass is a cosmopolitan seagrass species that provides important ecological services in coastal and near-shore environments. Despite its relevance, loss of eelgrass habitats is noted worldwide. Restoration by replanting plays an important role, and accurate measurements of the standing crop and productivity of transplants are important for evaluating restoration of the ecological functions of natural populations. Traditional assessments are destructive, and although they do not harm natural populations, in transplants the destruction of shoots might cause undesirable alterations. Non-destructive assessments of the aforementioned variables are obtained through allometric proxies expressed in terms of measurements of the lengths or areas of leaves. Digital imagery could produce measurements of leaf attributes without the removal of shoots, but sediment attachments, damage infringed by drag forces or humidity contents induce noise-effects, reducing precision. Available techniques for dealing with noise caused by humidity contents on leaves use the concepts of adjacency, vicinity, connectivity and tolerance of similarity between pixels. Selection of an interval of tolerance of similarity for efficient measurements requires extended computational routines with tied statistical inferences making concomitant tasks complicated and time consuming. The present approach proposes a simplified and cost-effective alternative, and also a general tool aimed to deal with any sort of noise modifying eelgrass leaves images. Moreover, this selection criterion relies only on a single statistics; the calculation of the maximum value of the Concordance Correlation Coefficient for reproducibility of observed areas of leaves through proxies obtained from digital images.
Results
Available data reveals that the present method delivers simplified, consistent estimations of areas of eelgrass leaves taken from noisy digital images. Moreover, the proposed procedure is robust because both the optimal interval of tolerance of similarity and the reproducibility of observed leaf areas through digital image surrogates were independent of sample size.
Conclusion
The present method provides simplified, unbiased and non-destructive measurements of eelgrass leaf area. These measurements, in conjunction with allometric methods, can predict the dynamics of eelgrass biomass and leaf growth through indirect techniques, reducing the destructive effect of sampling, fundamental to the evaluation of eelgrass restoration projects thereby contributing to the conservation of this important seagrass species.
Keywords
- Eelgrass leaf
- Area estimations
- Noisy digital images selection criterion
- Concordance correlation coefficient
Background
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].
A digital image of a Zostera marina leaf. a) An image of a Zostera marina leaf exhibiting the typical belted shape. Related area is commonly approximated by the product of length and average width. b) The display of the image of the leaf using a darker tonality reveals pixels placed beyond the peripheral contours, which do not belong to the image and whose presence is explained by humidity- noise-related effects. Improper identification of the peripheral contour of the leaf image due to spurious entries can lead to miscalculation of related area.
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.
The Direct Comparison Method (DCM)
Finally, the DCM proposes the use of the ST(r) interval producing the smallest value of IS(r) for reliable estimation of the areas of leaves of eelgrass using images whose peripheral contour is distorted by noise induced by humidity contents.
The Concordance Correlation Method (CCM)
In the present work the value of will provide a criterion for the incumbent digital image selection process. The linked CCM does not require the sorting of observed leaf lengths into the G k (l) groups of the DCM. As it is done in the DCM, in the present CCM, the digital images of sampled leaves are primarily processed by a specified color format with a number C max of colors and using intervals of tolerance of similarity ST (r) = [0, r] with 0 ≤ r ≤ C max − 1. Again by keeping ST(r) fixed and within the jth leaf image, a routine selects a starting point, and using Eqs. (A1), (A2) and (A3) detects all adjacent pixels connected within the realm of the designated interval of tolerance of similarity ST(r). This device identifies the peripheral contour of the leaf image allowing associated measurements of length l dj (r) and width h dj (r) whose product for 1 ≤ j ≤ m, yields image estimated leaf areas a dj (r). Instead of performing the statistical steps required to calculate IS(r), simply for r fixed in equations (9), (10) and (11) we make x j stand for observed leaf area measurements (a01, a02, ⋯, a0m) and let y match digital image produced estimations (ad 0(r), ad 1(r), ⋯, a dm (r)). Then equation (8) yields the resulting value of the Concordance Correlation Coefficient. In the present settings this will be denoted through by means of the symbol to emphasize its dependence on r, that is, changing ST(r) produces different pairs of observed and image calculated leaf areas (a0j , a dj (r)), 1 ≤ j ≤ m, as well as different values of the associated . After all values of r in the chosen color format are exhausted, we select the tolerance of similarity interval ST(r) that produces the highest value for for efficient estimation of eelgrass leaves area from digital images with noise related to environmental factors.
Results and discussion
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 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.
The effect of similarity index r = 10 on average deviations. For r = 10 a regular tendency of depending on group index k is shown. This yields a large proportion of groups with lying outside the interval bounded by and (cf. inequality 3).
The effect of similarity index r = 128 on average deviations. For r = 128 the regular tendency of increasing values shown figure 2 is no longer observed and a reduced number of values lying outside the interval bounded by and is observed.
The behavior of the IS (r) selection index through the interval 1 ≤ r < 255. For small values of r the interval of tolerance of similarity ST(r) does not include the necessary tonalities that the image identification procedure requires. Therefore identification of pixels within an image can be expected to be imprecise. Consequently reduced values of λ a (r), will be expected, which lead to large values of the IS(r) selection index. For r ≥ 25, values of IS(r) decrease until its minimum value is attained at r = 128. According to the DCM selection criterion for the present data, both an RGB color format and ST(128) interval of tolerance of similarity can be used for efficient estimation of areas of eelgrass leaves using images with noise induced by humidity contents.
The behavior of the concordance correlation coefficient, through the interval 1 ≤ r < 255. Increasing values of through the interval 1 ≤ r < 128 are displayed. This means that the wider the interval of similarity ST(r) the greater the reproducibility of observed leaf areas by image proxies becomes. Interestingly through the domain 128 ≤ r < 178 values of are maintained within a plateau of slight variation around . Afterwards, for 178 ≤ r ≤ 255 values of decrease slightly until drops to a value of 0.8464 attained at r = 255. Then for values of r larger than r = 128 reproducibility is not improved and coinciding with the criterion in the DCM for the present data, both an RGB color format and the ST(128) interval of tolerance of similarity could be used for image selection when noise due to humidity contents is present and efficient estimations of eelgrass leaf area taken from these images is required.
Dependence of both the value of r for maximumand the maximum value ofitself on sample size. For each value of the sample size index p = 1, 2, … 8 a fixed number s(p) of samples of size 100p each were uniformly drawn from the population of observed leaf areas. For each one of the samples in a set s(p), we iterated values of r through the interval 1 ≤ r ≤ 255, and for each one of these r values we obtained the concomitant concordance correlation coefficient values . We repeated this procedure for all the samples in the set s(p) and averaged the r values at which attained its maximum value, the obtained averages for the different values of the sample size index p are shown in a). The maximum values that obtained in a sample were also averaged over the s(p) sets. These average values depending on sample size are correspondingly shown in b). The results of this study shows that neither the optimal interval of tolerance of similarity ST(r) or the reproducibility of observed leaf areas by means of their digital image surrogates depend on sample size, therefore the CCM can be considered 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 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 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.
Conclusions
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 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 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 , 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.
Appendix
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.
Declarations
Acknowledgements
We are grateful to Jose Maria Dominguez and Francisco Ponce for the art work.
Authors’ Affiliations
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