leafprocessor: a new leaf phenotyping tool using contour bending energy and shape cluster analysis

Authors

  • Andreas Backhaus,

    1. Department of Animal and Plant Sciences, University of Sheffield, Western Bank, Sheffield S10 2TN, UK
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    • These authors contributed equally to this work.

  • Asuka Kuwabara,

    1. Department of Animal and Plant Sciences, University of Sheffield, Western Bank, Sheffield S10 2TN, UK
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    • These authors contributed equally to this work.

  • Marion Bauch,

    1. Department of Animal and Plant Sciences, University of Sheffield, Western Bank, Sheffield S10 2TN, UK
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  • Nick Monk,

    1. School of Mathematical Sciences, University of Nottingham, University Park, Nottingham NG7 2RD, UK
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  • Guido Sanguinetti,

    1. Department of Computer Science, University of Sheffield, Regent Court, 211 Portobello, Sheffield S1 4DP, UK
    2. Department of Chemical and Process Engineering, University of Sheffield, Mappin Street, Sheffield S1 3JD, UK
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  • Andrew Fleming

    1. Department of Animal and Plant Sciences, University of Sheffield, Western Bank, Sheffield S10 2TN, UK
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Author for correspondence:
Andrew Fleming
Tel: +44 (0)114 2224830
Email: a.fleming@sheffield.ac.uk

Summary

  • Significant progress has been made in the identification of the genetic factors controlling leaf shape. However, no integrated solution for the quantification and categorization of leaf form has been developed. In particular, the analysis of local changes in margin growth, which define many of the differences in shape, remains problematical.
  • Here, we report on a software package (leafprocessor) which provides a semi-automatic and landmark-free method for the analysis of a range of leaf-shape parameters, combining both single metrics and principal component analysis. In particular, we explore the use of bending energy as a tool for the analysis of global and local leaf perimeter deformation.
  • As a test case for the implementation of the leafprocessor program, we show that this integrated analysis leads to deeper insights into the morphogenic changes underpinning a series of previously identified Arabidopsis leaf-shape mutants. Our analysis reveals that many of these mutants which, at first sight, show similar leaf morphology, can be distinguished via our shape analysis.
  • The leafprocessor program provides a novel integrated tool for the analysis of leaf shape.

Introduction

Leaves act as the main site of light interception for photosynthesis in most plants. Despite this common function, leaves exist in many different forms, reflecting the variety of evolutionary strategies to cope with different environments. Almost by definition, when considering leaf shape the leaf edge is very important. Indeed, a significant amount of the classical botanical description of leaf form depends on global and local variations of the leaf edge shape. For example, although some leaves have a smooth perimeter, many leaves are distinguished by regions of nonsmoothness. Depending on the degree and frequency of this area of nonsmoothness, the leaf perimeter can be described as, for example, lobed or serrated (or, indeed, a combination of the two) and recent work has identified transcription factor modules and patterning processes that underpin this key aspect of leaf development (Hay & Tsiantis, 2006; Anastasiou et al., 2007; Blein et al., 2008). In terms of physiology, it has been suggested that differences in margin form influence the ability of a leaf to withstand environmental stress (Royer et al., 2008) and, indeed, leaf edge shape has been used as a proxy for temperature estimations in palaeobotany (Huff et al., 2003). The evaluation of leaf margin form is thus important in a number of areas of plant science.

Traditionally, visual-inspection-based botanical terms have been used for the description of leaf shape. However, this method involves the use of a range of specific terms and tends to be subjective in its application because these terms are not based on precise quantification. To combat this problem, many single-metric shape parameters have been proposed to quantify the complexity of the leaf margin. These include perimeter : area ratio, shape factor (4π× area/perimeter2), angle-based margin roughness and fractal dimension (McLellan & Endler, 1998). These parameters have been reported to effectively quantify the complexity of the leaf margin at a whole-leaf level, but information on the local distribution of leaf margin complexity has not been provided. In addition, although single-metric parameters are powerful tools for the statistical comparison (McLellan & Endler, 1998), they are limited in that they are generally not unique for specific leaf shapes. Thus, a combination of several parameters is considered to be required for effective shape description.

Another option for the comparison of complex leaf shapes is landmark-based methods. Tips of teeth and bases of sinuses can be manually marked and the distances between landmarks subjected to statistical analyses (such as principal component analysis (PCA) and Burnaby’s transformation) in order to extract the major variances from various leaf shapes, such as shown in Young et al. (1995) and McLellan & Endler (1998). These methods allow categorization of the differences in leaf shapes, although relating the features of the major factors that are responsible for the shape differences (principal components) to the biological events that generate can be problematic. Moreover, these methods also often incorporate an element of subjectivity as the landmarks used for the measurement are chosen manually. In addition, the detected variations identified by the principal components are dependent on the statistical distribution of the available leaf samples (Sanguinetti, 2008). To summarize, although a number of methods have been developed for the analysis of leaf shape, each method has advantages and disadvantages and no single method is ideal for all situations or experimental approaches.

Our previous work led us to focus on the margin as a key region of the leaf (Reinhardt et al., 2007) and a number of lines of evidence suggest that important events related to patterning, signalling and morphogenesis occur in the leaf perimeter (Scarpella et al., 2006). To allow a more in-depth analysis of the leaf margin, we set out to develop a method that would allow a better quantitative comparison of the shape defined by the leaf edge. As there is clearly a non-uniform distribution of deformation around many leaves, we implemented a solution that allowed analysis of both local regions of a leaf perimeter, as well as a global perimeter analysis. This solution involved the analysis of a scale-independent metric termed ‘bending energy’, which is described in this paper. In addition, because (as described earlier) no single parameter is optimal for the description and comparison of leaf shape in all circumstances, we incorporated this new solution into a software package (leafprocessor), which allows the analysis of a number of other standard parameters. The program provides 10 types of single-metric-leaf-shape parameters as well as a scale-independent PCA that utilises k-means clustering to identify shape groups within a population. The program thus allows an integrated analysis and comparison of leaf shape using both single metric parameters (for direct statistical analysis of predefined characteristics of leaf shape), and PCA (for the detection of un-predefined characteristics). leafprocessor performs all processing (from extraction of the outline of leaves to measurement of parameters as well as statistical analysis) in a semi-automatic manner. In addition, the analysis works in a landmark-free manner, so is ideal for the analysis of leaves with a relatively variable pattern of serrations/lobes, such as adult leaves of Arabidopsis.

To demonstrate the leafprocessor package we have implemented the analysis of nine genotypes of Arabidopsis which display a variety of leaf forms. The mutations responsible for these shape changes have been previously analysed and the relevant gene products identified (Kim et al., 1998; Prigge & Wagner, 2001; Ullah et al., 2001; Ohno et al., 2004; Nelissen et al., 2005). This has revealed that altering the expression of a highly disparate group of gene products can lead to apparently similar phenotypic outcomes. We reasoned that a more precise, quantitative analysis of the shape changes might reveal more subtle phenotypes which could inform future investigation aimed at unravelling the riddle of how such a variety of genetic pathways affect morphogenesis. The analysis reported here provides a deeper insight into the nature of the changes that underpin these leaf-shape mutants.

Materials and Methods

Plant materials

In addition to Col-0 and Ws-2, the following mutant lines of Arabidopsis thaliana (L.) Heynh. were used (see Table 1): an (Kim et al., 2002), elo1-1 (Nelissen et al., 2005), gpa1-1 and gpa1-2 (Ullah et al., 2001), jag1 (Ohno et al., 2004), rot-3 (Kim et al., 1998) and se (Prigge & Wagner, 2001). Seeds of gpa1-1, gpa1-2, rot3-1 and se were purchased from NASC (NASC, Nottingham, UK) (gpa1-1, N3910; gpa1-2, N3911; rot3-1, N3727; se, N3257). Seeds were surface sterilized with 20% (v : v) aqueous bleach solution and 0.1% (v : v) Tween 20 (Sigma), rinsed with sterilized water three times and placed in the dark at 4°C for 7 d before sowing. Three seeds were sown per Petri dish (5 cm in diameter, 2 cm in depth) containing half strength Murashige and Skoog salt mix and 1% (w : v) sucrose solidified with 0.8% (w : v) agar. Growth conditions were 100 μmol m−2 s−1 light, with a 16 : 8 h photoperiod and a temperature regime of 22°C : 18°C (light : dark).

Table 1.   Wild-type and mutant lines of Arabidopsis used in this study
MutantProtein (putative function)Text descriptionQuantitative measurementReference
  1. L : W, length : width.

anCarboxyl-terminal binding protein (vesicle trafficking/microtubule/dynamics)Elongated leaf shape with decreased widthYesTsuge et al. (1996)
Higher L : W ratio
elo1-1Histone acetyl transferase complex (RNA polymerase recruitment)Decreased width, increased lengthNoNelissen et al. (2005)
gpa1-1 and gpa1-2GTP-binding protein (signal transduction)Increased areaYesUllah et al. (2001)
Rot-like shape
jag1Zinc finger proteins (transcription)Serrated ‘shredded’ leafNoOhno et al. (2004)
Jagged serration at tip of the leaf
Narrow, elongated leaves
rot3-1Cytochrome P450 (brassinosteroid synthesis)Rounded leafYesTsuge et al. (1996)
Decreased length, unchanged width
Lower L : W ratio
seZinc finger proteins (transcription)Serrated leavesNoPrigge & Wagner (2001)

Image data acquisition

Between 14 and 24 leaves per line (one leaf per plant, leaf number 6 at 28 d after sowing) were fixed in a mixture of ethanol and acetic acid (7 : 1, v : v). Fixed leaves were transferred into 50% (v : v) aqueous ethanol solution, carefully flattened, then images were taken using a charge coupled device camera (Diagnostic Instruments Inc., MI, USA, Sterling Heights, MI, USA) mounted on a stereomicroscope (MZFLIII; Leica Microsystems, Wetzlar, Germany) at 13919 DPI as 8-bit grey value tiff files.

leafprocessor implementation

We implemented a software system (leafprocessor) which provides various single-metric leaf-shape parameters (Table 2) in addition to PCA with k-means clustering and discrimination index. Fig. 1 shows the work-flow of shape processing and analysis within the leafprocessor software. The leafprocessor system was realized using C/C++ and Matlab R2007a (Mathworks, Natik, MA, USA) under Linux Ubuntu. leafprocessor will be available in 2010 as a stand-alone program. The Matlab code and leafprocessor contour digitization program are available online at (http://gips.group.shef.ac.uk/resources.html).

Table 2.   Single-metric parameters provided by leafprocessor
ParameterDescription
  1. *Parameters are scale independent.

AreaArea of leaf lamina
LengthMaximum length of leaf lamina
WidthMaximum width of leaf lamina
PerimeterPerimeter length along the leaf lamina
P : A ratioPerimeter : area
L : W ratio*Length : width
Compactness*Perimeter2: area
Eccentricity*L : W ratio of an ellipse which shares the centre of gravity, principal axes of inertia and central moment with the leaf lamina shape
Whole-leaf bending energy*Integration of the square of contour’s curvature along the perimeter times with perimeter length
Sectored bending energy*Integration of the square of contour’s curvature along the sectored perimeter times with sectored perimeter length
Figure 1.

 The work-flow of leafprocessor from digitization of leaf contour to statistical analyses. From a grey value image (a) a binary image was obtained by thresholding (b); edge detection creates a boundary trace (c); a contour is initialized by hand with c. 10 points (d); 50-60 points are automatically added and fitted to the boundary (e). A total of 500 points are evenly spread on the leaf contour by means of interpolation and sampling (arc length parameterization) (f). Subsequently, single-metric shape parameters and principal component analysis (PCA) are obtained.

Image processing and leaf contour digitization

leafprocessor detects a leaf contour and assigns 500 points on the contour evenly in a landmark-free manner. First, as implemented in Weight et al. (2008) and Bylesjöet al. (2008), a threshold is applied to the image’s grey value to obtain a binary image (Fig. 1a,b). Simple thresholding techniques, however, often detect a pseudo-contour of leaves owing to trichomes on the margin of young leaves, nonuniform illumination or leaf surface shading. Therefore, in a second stage three techniques were applied to obtain a fine leaf contour (Fig. 1c–e). A Canny edge detector (Canny, 1986) is used to create an activation trace along the shape’s contour (Fig. 1c) and a mechanism called Snakes or Active Contours (Kass et al., 1987; Blake & Isard, 1998) is used to fit a sequence of 50–60 contour points around the initial leaf-shape representation. These algorithms were taken from Intel OpenCV image processing library (http://sourceforge.net/projects/opencvlibrary/). Fig. 1(d,e) shows the initialized and fitted contour. It should be noted that the initial points can be distributed freely and no specific landmarks (except for the start and end of the contour) have to be set manually. This is in contrast to some previously published approaches to leaf-shape analysis (Langlade et al., 2005) and builds on previous morphometric analyses (reviewed in Slice, 2007). In addition, the user can apply small corrections to the point distribution in the cases where the automatic contour detection is obviously incorrect.

In a final stage, a plane curve is created through spline interpolation. The spline fitting for acquiring a plane curve of the shape contour was performed using Matlab Spline toolbox. From this curve representation, 500 points are sampled with equal curve length between each point per leaf contour (arc length parameterization). The shape is then automatically rotated so that the axis of longest leaf extension is aligned to the y-axis. The user can define the leaf base. However, we have also implemented a mathematical description of the leaf blade and petiole junction in this study by defining the leaf base as a point where the petiole has increased by 40% from its average width. This value can be altered by the user. The middle of the shape base is then translated to the coordinate origin. Fig. 2 shows the shapes obtained for two examples of each of the lines of plant analysed in this study. To facilitate further analysis of potential differences in leaf shape, the final shape is then further divided into four sectors. The y-axis forms the vertical division and the horizontal division is performed at 50% of the leaf length (Fig. 1f). These sectors are labelled: PL, left proximal; PR, right proximal; DL, distal left and DR, distal right.

Figure 2.

 Sample leaf images used in this study. Depicted are two sample silhouette images of Arabidopsis thaliana leaves (leaf number 6) for each of the lines analysed by leafprocessor. Images have been rescaled to allow visual comparison of shape.

Leaf-shape parameter analysis

leafprocessor evaluates 10 leaf-shape parameters (Table 2) and performs PCA based on the 500 points evenly spread on each leaf contour. Six conventional leaf-shape parameters are determined: length (L), width (W), length : width ratio (L : W ratio), leaf area (A), leaf perimeter length (P) and leaf perimeter : area ratio (P : A). To allow a more detailed quantification of leaf perimeter deformation, we also introduce four additional scale-independent parameters: bending energy (whole leaf and per sector), shape eccentricity and compactness. These enable comparison of leaf shapes and are described below. The shape analysis was implemented using Matlab R2007a (Mathworks). The leaf-shape parameters of area, perimeter length, compactness, eccentricity and P : A ratio were calculated according to methods found in Jähne (2002). As individual lines failed the test for a normal distribution (Shapiro–Wilk test) for each parameter, a Kruskal–Wallis test was carried out followed by a post hoc test which calculated whether two lines were significantly different from each other (as indicated in the individual bar charts).

Bending energy

Bending energy (BE) (Young et al., 1974; Bowie & Young, 1977; Castleman, 1996; Cesar & Fontoura Costa, 1997) provides a global measure of the curvature of the leaf perimeter and is obtained by integrating the square of the contour’s curvature along the perimeter. In order to compare contour deformation between leaves with different sizes, we implemented scale-independent bending energy by multiplying the curvature with the leaf perimeter length.

For a plane curve c(t) = (x(t), y(t)), the signed curvature κ is computed via

image(Eqn 1)

where t can be any kind of curve parameterization. The bending energy is defined as the integral of the squared curvature along the shapes perimeter,

image(Eqn 2)

with P being the shape perimeter length and κ(s) the curvature in arc length parameterization. The division by perimeter normalizes all shapes to a perimeter of P = 1. The curvature values are not invariant to the shape scaling. A method to reach scale invariance uses the relationship that the curvature is inversely proportional to P (Cesar & Fontoura Costa, 1997). We therefore multiply the curvature values by P to obtain a scale-invariant bending energy:

image(Eqn 3)

The bending energy values used in this paper are calculated as scale invariant.

An advantage of bending energy as a quantifier of perimeter deformation is that it can be calculated for the entire perimeter of an object or for parts of a contour as a regional/local measure of contour deformation (van Vliet & Verbeek, 1993). leafprocessor measures the bending energy for the complete shape (whole-leaf bending energy) as well as for the four leaf sectors (sectored bending energy) in order to measure the distribution of shape deformation across the longitudinal and transverse axes of the leaf. In the global (whole-leaf) case, a circle would be the lowest energy configuration, while in the local (sectored) case a straight line is the lowest energy configuration. Any deformation of these – be it elongation, lobe formation or serration – increases the bending energy.

Eccentricity

Although L : W ratio (Tsuge et al., 1996; Tsukaya, 2006; Sato et al., 2008) is a convenient indicator of leaf elongation in leaves with an entire (smooth) leaf edge, this parameter is of more limited use when comparing leaves with different degrees of serrations/lobes. Shape eccentricity (E) is commonly used in computational shape analysis and can be understood as the axis ratio of a fitted ellipse that has the same moment of inertia as the leaf image and which shares the centre of gravity and principal axes of inertia (Jähne, 2002). This parameter value is zero for a straight line and one for a circle, so that narrower leaves have higher values of E.

Compactness

Perimeter to area (P : A) ratio is a simple way to assess leaf margin complexity. However, this is a scale-dependent parameter and is of limited value for comparison of leaves of different shape and size. In leafprocessor we used compactness (squared perimeter to area ratio) as an alternative to the P : A ratio. Compactness is a commonly used scale-independent parameter in the analysis of shape complexity in digital image processing (Cesar & Fontoura Costa, 1997; Jähne, 2002). This parameter has a value of 4π for a circle (which is the most compact shape representation) and increases in value without upper bound for any other type of shape. A high compactness value indicates that a given area is less efficiently contained within a given perimeter.

Discrimination analysis

To identify which leaf-shape parameter was highly discriminative for the mutant lines analysed, a discrimination index was calculated for the 10 single-metric shape parameters introduced above. This value is basically calculated from the ratio of between class variance of the means and the sum of within-class variance (Bartlett, 2001). Discrimination ratio σi for the ith single metric parameter is calculated as:

image(Eqn 4)

The term inline image is the mean of all leaf parameter values of the ith shape single metric while inline imageis the mean per leaf population and n and inline image are the individual parameter values for population n out of c populations in total. For high discrimination, the mean values of each class within an analysis should be as far apart as possible and the samples in each class should have a small within-class variance.

Principal component analysis

As it has been reported that (unsurprisingly) size is often the biggest factor contributing to the variance of leaf shapes (Young et al., 1995; McLellan & Endler, 1998; Langlade et al., 2005; Weigh et al., 2008), we implemented both size-dependent and size-independent PCA. For size-independent PCA, all leaf images are normalized with respect to their perimeter length by dividing the (x,y) coordinates by the total perimeter length. The x and y data are then combined to form a one-dimensional sample vector and the principal components (the eigenvectors of the covariance matrix of the data) are calculated. The Eigen values order these components according to their covered variance in the data.

In order to provide an objective categorization, leafprocessor provides a k-means clustering technique to find separable groups of shape categories in the data. A k-means clustering is an unsupervised method of cluster analysis that partitions observations into k clusters in which each observation belongs to the cluster with the nearest mean prototype. The results are k-prototypes which can be displayed as shapes. The leafprocessor cluster algorithm validates cluster results generated with different k-values and chooses the best clustering according to the Davies–Bouldin (DB) index (Davies & Bouldin, 1979). This index is a function of the ratio of the sum of within-cluster scatter to between-cluster separation. The automatic k-means cluster algorithm was taken from the SOM Toolbox (http://www.cis.hut.fi/somtoolbox/). The discrimination index σi of the ith principal component is calculated as the ratio between the between-population variance and the sum of the within-population variance according to Eqn 4.

Results and Discussion

A key aim of this study was to explore the use of bending energy as a parameter to describe and compare leaf perimeters, both globally and locally. In addition, because single metrics generally do not capture complex shapes, we wanted to incorporate bending energy analysis with a compendium of other shape parameters, thus allowing the user to quantify leaf shape in an integrated fashion. The resulting software package, leafprocessor, allows the user to perform such an integrated analysis in a semi-automated fashion and without over-reliance on landmark distribution. The utility of this approach is described in the subsequent section using the analysis of previously described leaf-shape mutants of Arabidopsis. This analysis reveals previously unreported elements of shape change present in a number of these mutants. The identification of novel elements of shape change will aid in future investigations aimed at understanding the precise mechanism by which such diverse gene products influence morphogenesis.

Fig. 3 shows the output files for the analysis of the parameters measured in leafprocessor for each of the lines of Arabidopsis analysed. Clearly each of the parameters measured distinguishes at least some of the lines analysed.

Figure 3.

 Single-metric shape parameters obtained from the analysis of nine Arabidopsis lines. (a) Length (L), (b) width (W), (c) L : W ratio, (d) eccentricity, (e) bending energy, (f) sectored bending energy. Inset shows a leaf with proximal sectors PL and PR and distal sectors DL and DR. (g) Leaf area, (h) perimeter, (i) perimeter : area ratio, (j) compactness and (k) discrimination index for each of the parameters shown in (a) to (j). Bars with the same letters were not statistically not different. Bars represent mean ± SE from 15 to 24 leaves per line (leaf number 6 at 28 d after sowing).

Whole-leaf bending energy

Focusing on the analysis of whole-leaf bending energy (Fig. 3e), this parameter provided insights into shape differences that were not apparent from other parameter analyses. For example, the leaves of the an and elo1-1 mutants had lower bending energy values than the col-0 control. These mutants have previously been described as being relatively elongated (as confirmed by the L : W ratio and eccentricity values, Fig. 3c,d); however, there is clearly an added shape change component of a smoother perimeter, suggesting less severe or fewer serrations. Similarly, while rot3 has been characterized as having rounder leaves (lower L : W ratio, lower eccentricity, Fig. 3c,d), the rot3 leaves also have an increased bending energy (suggesting increased degree or more serration). As ROT3 encodes an enzyme involved in brassinosteroid biosynthesis (Kim et al., 1998) and recent data suggest a specific role for brassinosteroids in the leaf epidermis and margin (Reinhardt et al., 2007; Savaldi-Goldstein et al., 2007), further investigation of the potential role of ROT3 in leaf perimeter growth is suggested by this type of analysis.

The mutants gpa1-1 and gpa1-2 have been described as having a similar leaf phenotype to rot3, that is, rounder leaves. Again, leafprocessor analysis confirms this (the L : W ratio and eccentricity values are similar and low in value), but the bending energy values (Fig. 3e) distinguish the gpa and rot3 leaf shapes, with the gpa mutant leaves being smoother. These types of data can be incorporated into hypotheses on the different molecular mechanisms of the relevant gene products on leaf morphogenesis (i.e. they help to distinguish mutant phenotypes which at first sight appear very similar).

Sectored bending energy

The utility of bending energy analysis becomes even more apparent when a sectored bending energy analysis is per-formed (Fig. 3f). This allows a comparison of the distribution of shape change around the leaf perimeter, and in this study we have focused on the comparison of the proximal base and distal tip. For example, an mutant leaves show almost uniform bending energy over the four sectors analysed, while all other lines (with the exception of elo1-1 and possibly se) show higher values of bending energy in the proximal region (Fig. 3f). Indeed, the sectored bending energy analysis indicates that elo1-1 leaves have a higher bending energy in the distal region of the leaf relative to the proximal base. This difference in distribution of bending energy allows an to be distinguished from elo1-1, which otherwise has very similar values of leaf area, L : W ratio, eccentricity and total bending energy.

As mentioned earlier, consideration of total bending energy revealed a previously unreported difference in leaf shape between gpa and rot3 mutants. When this difference is analysed at a higher spatial resolution (Fig. 3f), it becomes apparent that the gpa leaves show a steeper gradient of bending energy around the perimeter along the distal–proximal axis, suggesting that the normal GPA product may be acting in the distal perimeter region to promote shape change (differential growth).

The differences in curvature distribution around the leaf perimeter already described provide important clues for future experimentation, suggesting where specific gene products may be acting to elicit the final resultant changes in leaf form observed when the gene is mutated. Bearing in mind the recent advances in our understanding of the spatial control of signalling and transcription factor networks that influence leaf form (Hay & Tsiantis, 2006; Blein et al., 2008), such data will be vital if we are to gain an integrated understanding of leaf morphogenesis. By allowing a focused spatial analysis of perimeter deformation, bending energy provides a useful tool to phenotype leaves and to guide investigations on gene function.

Eccentricity and compactness

At first sight, L : W ratio seems sufficient to compare the relative narrowness of leaves (Fig. 3c). For example, leaves of an and elo1-1 show higher values of L : W ratio than the rounder leaves characteristic of rot3, gpa1-1 and gpa1-2. However, analysis of eccentricity reveals differences that are not highlighted by L : W ratio. For example, se leaves have a higher eccentricity than jag1 leaves, which is consistent with a visual impression (Figs 2, 3d) but is not indicated by L : W ratio. As the maximum leaf width is often measured at the tip-point of the serration, deeper serration tends to lead to the calculation of higher L : W ratio values (i.e. the L : W ratio measured is dependent on the form of the serration). Eccentricity is calculated based on an ellipse which has the same moment of inertia, centre of gravity and principal axis of inertia as the leaf image (i.e. the parameter essentially integrates over differences in perimeter shape).

leafprocessor provides analysis of both P : A ratio and compactness (Fig. 3i,j). Both methods distinguish the an, elo1-1and se leaves as having distinct values. However, P : A ratio is a size-dependent parameter, and so the relatively high values calculated for an and elo1-1 could be a reflection simply of their relatively small area (Fig. 3g). Compactness is scale independent, and confirms the initial interpretation provided by the P : A ratio that the an leaves enclose a given area in a relatively inefficient manner. The compactness calculation also distinguishes jag-1 from the other lines, which was not apparent from the P : A or L : W ratios. The compactness measurement indicates that jag-1 and se leaves are the most inefficient in terms of area contained within a given perimeter. The surface area for a given mass has important outcomes for physiological processes such as temperature control and transpiration (Osborne et al., 2004), thus quantitative data on leaf compactness coupled with mass measurements could be used to inform future experimentation on the expected physiological outcome of altered leaf shape.

Discrimination analysis

To identify which leaf-shape parameter was the best discriminator for the mutant leaf shapes, a discrimination index was calculated for the nine whole-leaf shape parameters used here. As shown in Fig. 3(k), absolute parameters such as length, width, area and perimeter generally scored worse than relative parameters such as L : W ratio, eccentricity and compactness, with the exception of the P : A ratio. Somewhat surprisingly, compactness showed the highest discrimination index (0.53), while bending energy scored the second highest discrimination index for the dataset (0.4). The high discrimination index score of leaf compactness results mainly from the extremely small variance within populations. Our data suggest that compactness is a very stable parameter within a particular leaf mutant population, yet one that is distinct for different mutant backgrounds. As the compactness is calculated based on the square of the perimeter relative to the area, our analysis is consistent with the view that the leaf margin might be the source of signals that determine leaf shape. An essentially linearly-sourced signal acting on a two-dimensional surface could act as a robust system for size control (Anastasiou et al., 2007).

Principal component analysis

As outlined in the Introduction, PCA has previously been implemented to uncover variation in leaf shape (Langlade et al., 2005; Bensmihen et al., 2008; Weight et al., 2008). However, in these previous analyses there has been a variable treatment of the issue of scaling (i.e. whether the shape data have been normalized to allow for different leaf size before analysis). We subjected the data obtained in this study to a PCA, which allowed us to test the difference of normalizing for size before analysis. In particular, we incorporated a k-clustering technique (MacQueen, 1967). This is an unsupervised method for categorization which identifies clusters of genotypes that make a similar contribution to a particular PC.

Fig. 4 shows the initial PCA of the shape data analysed either without (Fig. 4a) or with (Fig. 4b) a prior normalization for size. These data can be portrayed in conventional images which identify mean shapes (with standard errors) that define the PCs that make a contribution to the shape differences (see the Supporting Information Fig. S1). However, an alternative method of analysing these data is to subject them to a k-clustering analysis. Using this approach a number of different groupings were identified. These are shown in Fig. 4(c,d), with five clusters forming in the size-dependent analysis (Fig. 4c) and four clusters in the size-independent analysis (Fig. 4d). Fig. 4(e,f) shows the composition of each of these clusters. Each cluster derived from the size-independent PCA (Fig. 4f) consisted of fewer mutant lines than those from size-dependent PCA (Fig. 4c). This indicates that the categorization derived from the size-independent PCA more effectively reflects the unique leaf shape of each Arabidopsis line. Indeed, in cluster 4 (Fig. 4f), k-means clustering was sufficient to identify the se mutant leaf shape as a unique grouping. Thus, as well as showing that scale-independent analysis is a better approach for discrimination of leaf shape, our analysis indicates that k-clustering linked to scale-independent PCA can be used to identify individual genotypes which have distinct leaf forms from a mixture of leaf shapes obtained from a mixture of genotypes. In practise, we envision that the k-means, scale-independent PCA incorporated into leafprocessor will be used as a first method to analyse populations of leaf shape to identify categories showing a distinctive contribution to particular PCs. This initial screen could then be followed up by the single-metric analyses provided in leafprocessor to more precisely identify the morphological changes underpinning those differences. In particular, the use of bending energy provides a means of pinpointing – at both, global and local scales – alterations of perimeter deformation that play a significant role in defining leaf shape. Identifying where and when shape changes occur during leaf development places important constraints on where and when the genetic factors controlling those changes are likely to act.

Figure 4.

 Size-dependent and size-independent principal component analysis (PCA) with k-means clustering. The two-dimensional principal components (PCs) maps generated by standard deviations from the mean leaf along PC1 and PC2 were compared between size-dependent (a) and size-independent (b) PCA. The k-means clustering for size-dependent PCA resulted in five clusters of similar shapes (c), while that for size-independent PCA provided four groups (d). Composition of each cluster was compared between clustering from size-dependent (e) and size-independent (f) PCA. Note that each cluster derived from size-independent PCA (f) consisted of fewer mutant lines than those from size-dependent PCA (e). Mutant lines contributing to each cluster are indicated.

Conclusion

We have generated, leafprocessor, a novel tool for leaf-shape analysis. By implementing bending energy analysis, the program provides a precise quantification of the changes in leaf perimeter deformation that underpin many differences in leaf form. By providing this tool in a compendium, the program can be used to provide an integrated analysis of leaf shape. The combination of quantitative leaf-shape phenotyping with genetic tools will lead to a better understanding of the genes and signal pathways determining leaf shape.

Acknowledgements

This work was supported by funding from the European Union- Transfer of Knowledge scheme – Generating an Integrative Plant Science (GIPS) to A.F., N.M. and G.S. and a JSPS Fellowship to A.K. We thank Prof. Jose Luise Micol, Universidad Miguel Hermandez, Spain, for supplying the seeds of elo1-1 and colleagues in the Fleming lab for their constructive comments and trialling of the program.

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