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This paper aims to provide a method to represent the virtual

As an important model plant,

The phenotypes of

However, the number of contour points is quite large because of the high resolution of image. It will require much storage to directly store the contour pixels. Besides, the plant varies at different growth stages, resulting in different numbers of contour pixels. And it will also add difficulties to store the data for their different lengths.

So how to represent the shapes of different

In this paper, EFDs will be used to analyse the contour, and each

At each pot of

Image preprocessing. (a) Original image of an

It is inevitable that the image is distorted. It needs to be corrected for further geometrical measurement. The distortion can be expressed as

In this paper, the corners of the checkerboard were detected to compute the transform function. The checkerboard region was first automatically detected by using (

The region of green plant in an image was segmented by using Excess Green (ExG) minus Excess Red (ExR) index [

The binary images were obtained with fixing threshold 0. Figure

Image segmentation. (a) Binary image of segmentation result. (b) Image after filling the holes. (c) Outer contour of the image.

The holes inside the region were filled, as shown in Figure

After obtaining the plant region, the boundary pixels need to be stored clockwise or counter clockwise. This could be done by using boundary point tracking algorithm [

Select the pixel of the minimum row coordinate from the pixels of the minimum column value of the region. Let this pixel

Search the

Repeat Step

With these steps, the boundary point series is obtained.

In the boundary series, each pixel has two values. The image can be viewed as a complex space and the two coordinates can be regarded as the real part and imaginary part. Therefore, the boundary series can be expressed as a discrete function shown in

Figure

Contour reconstruction. (a)–(f) Contour reconstruction with 10, 20, 30, 40, 50, and 60 harmonics numbers, respectively.

From the overall contour, it can be seen that the distance between the apex of each leaf and the region centroid is a local maximum. In this case, we firstly calculated the distance between each boundary point and the centroid. Thus we obtain a 1D signal. The next step is to identify the local maximum points of the signal.

The distance between the contour point and the centroid is calculated as

The original distance curve signal contains much noise. It is impossible to locate the local maximum only by comparing each contour point with the points at its two sides. In this paper, we used wavelet transform to detect the local maximum point.

Wavelet transform is often used to detect the singularity of the signal. When the signal contains much change, the wavelet coefficients will be quite large. While on the contrary, the wavelet coefficients will be zero if the point is a local minimum or maximum. Another merit of wavelet analysis is that it provides a decomposition of the original signal into different scales. So it is very convenient to choose the scale according to different demands to analyse the signal.

In the experiment, we first expand the signal into

Local maximum recognition. (a) Wavelet coefficients in the fifth level. The zero coefficients are marked with red dots. (b) Distance curve between the contour point and the centroid. The local maximum points are labelled with red dots. (c) The apex of each leaf.

The images of

Growth simulation. (a)–(e) Contour reconstruction during 5 days. The leaves apexes are marked with red dots. (f) Increase of the total area of the plant.

This paper provides a method to represent the virtual

The authors declare that there is no conflict of interests regarding the publication of this paper.

This paper is supported by the Fundamental Research Funds for the Central Universities (Grant no. YX2013-24) and the Scientific Research Foundation for the Returned Overseas Chinese Scholars, State Education Ministry (2010), which are greatly acknowledged by the authors.