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Edge Geometric Measurement Based Principal
Component Analysis in Strawberry Leaf Images

Jianlun Wang, Yu Han, Zetian Fu, Daoliang Li, Jianshu Chen, Shuting Wang

► To cite this version:

Jianlun Wang, Yu Han, Zetian Fu, Daoliang Li, Jianshu Chen, et al. Edge Geometric Measurement Based Principal Component Analysis in Strawberry Leaf Images. 6th Computer and Computing Technologies in Agriculture (CCTA), Oct 2012, Zhangjiajie, China. pp.58-68, 10.1007/978-3-642-36124-1_8. hal-01348081

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Distributed under a Creative Commons Attribution 4.0 International License
Edge Geometric Measurement Based Principal
Component Analysis in Strawberry Leaf Images

Jianlun Wang<fnref n="1" />*, Yu Han*, Zetian Fu, Daoliang Li, Jianshu Chen,
Shuting Wang

(College of Information and Electrical Engineering, China Agricultural
University, Beijing 100083, P.R.China)

**Abstract.** Edge geometric measurement analysis is an important method of image understanding and portraying the target feature. In this paper, we compress 17 interrelated shape descriptors which are based on edge geometric measure into 6 independent components, and discuss their meanings by using principal component analysis. The analyses in this article provide guidance for the shape feature optimization and accurate identification for greenhouse strawberry leaves images successfully.

**Key word:** Greenhouse strawberry leaves; Shape feature description; Principal Component Analysis; Edge geometric measure

# 1. Introductions

The performance comparison of several common description of shapes which are
used in identify the leaves of strawberry grown in the greenhouse. Strawberries have
a short growth cycle, less disease, easy to manage, high nutritional value, economic
value advantages, widely grown in the greenhouse [1]. With the popularity of
hardware and image processing technology matures, many field of agricultural
engineering applications[6] have used a variety of techniques based on computer
vision, such as automatic classification of the fruits and vegetables[2], quality
traceability[3], the robot picking[4], growth status monitoring, and the early warning
of pest and disease[5]. Among them, the target recognition are facing with many
problems of different varieties of agricultural crops, complexity of the imaging

<footnote>* These authors contributed equally to the article</footnote>

<footnote n="1">1 Corresponding author. Tel: +86 13691008152. E-mail address: wangjianlun@cau.edu.cn (J. Wang).</footnote>
background, range of issues such as characterization as a vital process in image
processing, so it is difficult to form a high recognition rate of the general algorithm.
Therefore, this paper according to greenhouse strawberry leaves, summarized 17
ways of shape description. On the high dimensional feature dimension reduction is
compressed into 6 comprehensive index by using the principal component analysis ,
and has carried on the detailed explanation to provide guidance in getting more
effective characteristics selection and comprehensive evaluation in practical
application.

## 2. The shape descriptors in target region

The main difficulties in shape quantitative description is the lack precise and uniform definition. ASM think that shape parameter which are used to describe the micro-structure have some common in no dimension, quantitative description and sensitive to shape change[7]. This paper will divide geometry characteristic which are commonly used into the following several forms: Geometric description of the target boundary (Including the ratio between perimeter and area, fineness ratio, eccentricity, etc)、Measure of the target area and its surround polygon (Including Surrounded by rectangular compact, surrounded by polygonal compact degree, etc)、Geometric description of the target area (Including Centroid offset rate, Area symmetry, Circumference symmetry, etc)、Invariant moments (Hu Invariant moments)。We will give explanation about it one by one below: (Among them, A represents the area, L represents the circumference, W represents the length of bounding rectangle, W represents the width of bounding rectangle, Aconvex is represents target convex hull area):

(1) Perimeter area ratio: $P/A$, Range in (0,1).

(2) Fineness ratio: $4*Pi*A/(P*P)$, Range in (0,1). Get the maximum value(1) while contiguous area is round.

(3) Exterior ratio: $W/L$, Used to describe the shape of the target after plastic deformation, Take the maximum value(1) of a square and circular target and it will be reduced with slender degree about slender target.

(4) Eccentricity: The eccentricity of target which is equivalent to an ellipse(E), and the equivalent ellipse is defined as a voal which has the same centroid and secondary center moment with target.
(5) Skeleton eccentricity: Eccentricity of skeleton equivalent ellipse (E), and skeleton equivalent ellipse is defined as a fitting ellipse which has the same skeleton with target. Generally, In order to avoid the influence of finely branch in skeleton, the first to do is deburring skeleton and then fitting ellipse.

(6) Compactness of bounding rectangle: $A/(L*W)$, Reflects the bump on the bounding rectangle of the target area.

(7) Compactness of bounding polygon: $A/A_{convex}$, Reflects the bump on the minimum convex hull of the target area.

(8) Centroid offset rate: The ratio of the distance between centroid to boundary in the upper-left corner and lower right corner to the upper left corner, it reflects the relationship of the centroid position in the target area.

(9) Area symmetrical degrees: $min(A_{left}, A_{right})/max(A_{left}, A_{right})$, A_{left} and A_{right} are represents the area size of left and right side of symmetry axis, regional symmetry in the area. It's the performance of regional symmetry in the area. If the region is completely symmetrical, the maximum value will be 1.

(10) Perimeter symmetric degrees: $min(P_{left}, P_{right})/max(P_{left}, P_{right})$, P_{left} and P_{right} represents the perimeter size of left and right side of symmetry axis, regional symmetry in the area. It's the performance of regional symmetry in the perimeter. If the region is completely symmetrical, the maximum value will be 1.

(11) Hu Invariant moments: Ming-Kuei Hu apply algebraic invariant moment to pattern recognition and regard seven moment features about rotation and scaling translation invariant in the target area as the target shape characteristics.

### 3. Statistical analysis about the descriptor of shape

Statistical frequency of the above shape descriptor as follows to show:

<table><caption>**Table 1.** Statistical description of shape feature</caption><thead><tr><td>Shape descriptors</td><td>Mean</td><td>Standard Error</td><td>Standard deviation</td><td>Coefficient of variation</td></tr></thead><tbody><tr><td>Perimeter area ratio</td><td>0.009293</td><td>0.000254</td><td>0.002365</td><td>0.25451</td></tr><tr><td>Fineness ratio</td><td>0.654973</td><td>0.005491</td><td>0.051218</td><td>0.078199</td></tr><tr><td>Appearance ratio</td><td>0.755404</td><td>0.010079</td><td>0.094009</td><td>0.124449</td></tr><tr><td>Eccentricity</td><td>0.637541</td><td>0.012837</td><td>0.119733</td><td>0.187805</td></tr></tbody></table>
<table><tr><td>Skeleton eccentricity</td><td>0.664242</td><td>0.01463</td><td>0.136462</td><td>0.20544</td></tr><tr><td>Bounding rectangle compactness</td><td>0.774389</td><td>0.000705</td><td>0.006572</td><td>0.008487</td></tr><tr><td>Bounding polygon compactness</td><td>0.957814</td><td>0.001167</td><td>0.010888</td><td>0.011367</td></tr><tr><td>Centroid offset rate</td><td>0.521226</td><td>0.006561</td><td>0.061194</td><td>0.117403</td></tr><tr><td>Area symmetric rate</td><td>0.963479</td><td>0.011393</td><td>0.106268</td><td>0.110296</td></tr><tr><td>Perimeter symmetric rate</td><td>0.961412</td><td>0.002981</td><td>0.027803</td><td>0.028919</td></tr><tr><td>Hu1 Moment</td><td>0.206821</td><td>0.001691</td><td>0.015774</td><td>0.076269</td></tr><tr><td>Hu2 Moment</td><td>0.003439</td><td>0.000557</td><td>0.005196</td><td>1.511056</td></tr><tr><td>Hu3 Moment</td><td>9.22E-06</td><td>3.03E-06</td><td>2.83E-05</td><td>3.069955</td></tr><tr><td>Hu4 Moment</td><td>8.95E-06</td><td>3.02E-06</td><td>2.82E-05</td><td>3.147928</td></tr><tr><td>Hu5 Moment</td><td>8.67E-10</td><td>5.99E-10</td><td>5.59E-09</td><td>6.445866</td></tr><tr><td>Hu6 Moment</td><td>5.25E-07</td><td>2.61E-07</td><td>2.43E-06</td><td>4.631451</td></tr><tr><td>Hu7 Moment</td><td>6.24E-09</td><td>3.06E-09</td><td>2.86E-08</td><td>4.579208</td></tr></table>

## 4. Principal component analysis of the shape factor

Principal component analysis is a statistical method which is first proposed by Pearson in 1901, and then developed by Hotelling (1933). Its main purpose is that to reduce the number of variables, and make change for the formation of a linear combination of a few independent variables (principal components), but by the difference of the linear combination of ingredients into the largest, making the original multi-dimensional characteristics of these principal components show the greatest individual differences. In short, Principal component analysis is a number of variables into a few principal components (i.e. integrated variable) dimension reduction statistical method.

The general steps are as follows:
(1) The standardization of original data

First of all to the standardization of original data, each index data of the sample is mean 0, variance 1.

$$ \chi_{ij} = (\chi_{ij} - \bar{\chi}_{j}) / \sqrt{\sigma_{j}} \quad (i = 1, 2, \dots, n, j = 1, 2, \dots, 17) $$

$\chi_{ij}$ as the i sample of the j shape descriptor value, $\bar{\chi}_{j}$ as mean value of the j shape descriptor value, $\sigma_{j}$ as variance of the j shape descriptor value. In the principal component analysis of SPSS statistical software, standardization is automatically executed.

(2) Calculate the indicators of the correlation matrix R

$$ r_{ij} = \frac{\sum_{k=1}^{n} (x_{ki} - \bar{x}_{i})(x_{kj} - \bar{x}_{j})}{\sqrt{\sum_{k=1}^{n} (x_{ki} - \bar{x}_{i})^2 \sum_{k=1}^{n} (x_{kj} - \bar{x}_{j})^2}} \quad (i = 1, 2, \dots, n, j = 1, 2, \dots, 17) $$

$\hat{r}_{ij}$ as matrix of I rows and j columns representing related elements, namely the index I and index J correlation coefficient.

(3) Seek the correlation matrix R eigenvalue and characteristic vector

The characteristic equation is expressed as $|\lambda I - R| = 0$, Commonly used Jacobi method to calculate the eigenvalues and the corresponding eigenvectors, and the size of the eigenvalues in descending order. The correlation matrix are given below:
<table><caption>**Table 2.** The correlation matrix of shape characteristics about SPSS</caption><thead><tr><th></th><th>PjArea</th><th>Fineness ratio</th><th>Appearance ratio</th><th>Eccentricity</th><th>Skeleton eccentricity</th><th>Bounding rectangle compactness</th><th>Bounding polygon compactness</th><th>Centroid offset</th><th>Area symmetric rate</th><th>Perimeter symmetric rate</th><th>Hu1 invariant moment</th><th>Hu2 invariant moment</th><th>Hu3 invariant moment</th><th>Hu4 invariant moment</th><th>Hu5 invariant moment</th><th>Hu6 invariant moment</th><th>Hu7 invariant moment</th></tr></thead><tbody><tr><td>PjArea</td><td>1.000</td><td>-0.390</td><td>-0.493</td><td>0.484</td><td>0.394</td><td>-0.457</td><td>-0.603</td><td>0.047</td><td>-0.246</td><td>-0.087</td><td>0.453</td><td>0.297</td><td>0.191</td><td>0.197</td><td>0.121</td><td>0.156</td><td>0.162</td></tr><tr><td>Fineness ratio</td><td>-0.390</td><td>1.000</td><td>0.586</td><td>-0.558</td><td>-0.339</td><td>0.377</td><td>0.685</td><td>0.084</td><td>0.095</td><td>0.347</td><td>-0.357</td><td>-0.212</td><td>-0.296</td><td>-0.294</td><td>-0.188</td><td>-0.255</td><td>-0.243</td></tr><tr><td>Appearance ratio</td><td>-0.493</td><td>0.586</td><td>1.000</td><td>-0.983</td><td>-0.643</td><td>0.315</td><td>0.404</td><td>0.109</td><td>0.114</td><td>0.041</td><td>-0.540</td><td>-0.394</td><td>-0.306</td><td>-0.310</td><td>-0.238</td><td>-0.291</td><td>-0.280</td></tr><tr><td>Eccentricity</td><td>0.484</td><td>-0.558</td><td>-0.983</td><td>1.000</td><td>0.591</td><td>-0.309</td><td>-0.400</td><td>-0.130</td><td>-0.113</td><td>-0.045</td><td>0.524</td><td>0.326</td><td>0.261</td><td>0.264</td><td>0.197</td><td>0.245</td><td>0.235</td></tr><tr><td>Skeleton eccentricity</td><td>0.394</td><td>-0.339</td><td>-0.643</td><td>1.000</td><td>0.591</td><td>-0.240</td><td>-0.388</td><td>-0.012</td><td>-0.154</td><td>-0.104</td><td>0.479</td><td>0.424</td><td>0.247</td><td>0.253</td><td>0.211</td><td>0.261</td><td>0.237</td></tr><tr><td>Bounding rectangle compactness</td><td>-0.457</td><td>0.377</td><td>0.315</td><td>-0.309</td><td>-0.240</td><td>1.000</td><td>0.536</td><td>-0.282</td><td>0.540</td><td>0.157</td><td>-0.547</td><td>-0.368</td><td>-0.604</td><td>-0.606</td><td>-0.461</td><td>-0.532</td><td>-0.540</td></tr><tr><td>Bounding polygon compactness</td><td>-0.603</td><td>0.685</td><td>0.404</td><td>-0.400</td><td>-0.388</td><td>0.536</td><td>1.000</td><td>-0.022</td><td>0.320</td><td>0.338</td><td>-0.438</td><td>-0.216</td><td>-0.226</td><td>-0.222</td><td>-0.106</td><td>-0.161</td><td>-0.168</td></tr><tr><td>Centroid offset rate</td><td>0.047</td><td>0.084</td><td>0.109</td><td>-0.130</td><td>-0.012</td><td>-0.282</td><td>-0.022</td><td>1.000</td><td>0.057</td><td>-0.011</td><td>0.084</td><td>-0.023</td><td>0.294</td><td>0.295</td><td>0.275</td><td>0.283</td><td>0.289</td></tr><tr><td>Area symmetric rate</td><td>-0.246</td><td>0.095</td><td>0.114</td><td>-0.113</td><td>-0.154</td><td>0.540</td><td>0.320</td><td>0.057</td><td>1.000</td><td>-0.016</td><td>-0.222</td><td>-0.282</td><td>-0.096</td><td>-0.097</td><td>-0.071</td><td>-0.096</td><td>-0.084</td></tr><tr><td>Perimeter symmetric rate</td><td>-0.087</td><td>0.347</td><td>0.041</td><td>-0.045</td><td>-0.104</td><td>0.157</td><td>0.338</td><td>-0.011</td><td>-0.016</td><td>-0.040</td><td>-0.040</td><td>0.085</td><td>-0.291</td><td>-0.289</td><td>-0.267</td><td>-0.272</td><td>-0.282</td></tr><tr><td>Hu1 Invariant moment</td><td>0.453</td><td>-0.357</td><td>-0.540</td><td>0.524</td><td>0.479</td><td>-0.547</td><td>-0.438</td><td>0.084</td><td>0.222</td><td>-0.040</td><td>1.000</td><td>0.779</td><td>0.331</td><td>0.337</td><td>0.274</td><td>0.329</td><td>0.317</td></tr><tr><td>Hu2 Invariant moment</td><td>0.297</td><td>-0.212</td><td>-0.349</td><td>0.326</td><td>0.424</td><td>-0.368</td><td>-0.216</td><td>-0.023</td><td>-0.282</td><td>0.085</td><td>0.779</td><td>1.000</td><td>0.074</td><td>0.078</td><td>0.110</td><td>0.160</td><td>0.100</td></tr><tr><td>Hu3 Invariant moment</td><td>0.191</td><td>-0.296</td><td>-0.306</td><td>0.261</td><td>0.247</td><td>-0.604</td><td>-0.226</td><td>0.294</td><td>-0.096</td><td>-0.291</td><td>0.331</td><td>0.074</td><td>1.000</td><td>0.999</td><td>0.926</td><td>0.960</td><td>0.979</td></tr><tr><td>Hu4 Invariant moment</td><td>0.197</td><td>-0.294</td><td>-0.310</td><td>0.264</td><td>0.253</td><td>-0.606</td><td>-0.222</td><td>0.295</td><td>-0.097</td><td>-0.289</td><td>0.337</td><td>0.078</td><td>0.999</td><td>1.000</td><td>0.927</td><td>0.961</td><td>0.980</td></tr><tr><td>Hu5 Invariant moment</td><td>0.123</td><td>-0.188</td><td>-0.238</td><td>0.197</td><td>0.211</td><td>-0.461</td><td>-0.106</td><td>0.275</td><td>-0.071</td><td>-0.267</td><td>0.274</td><td>0.110</td><td>0.926</td><td>0.927</td><td>1.000</td><td>0.985</td><td>0.981</td></tr><tr><td>Hu6 Invariant moment</td><td>0.156</td><td>-0.255</td><td>-0.291</td><td>0.245</td><td>0.261</td><td>-0.532</td><td>-0.161</td><td>0.283</td><td>-0.096</td><td>-0.272</td><td>0.329</td><td>0.160</td><td>0.960</td><td>0.961</td><td>0.985</td><td>1.000</td><td>0.989</td></tr><tr><td>Hu7 Invariant moment</td><td>0.162</td><td>-0.243</td><td>-0.280</td><td>0.235</td><td>0.237</td><td>-0.540</td><td>-0.168</td><td>0.289</td><td>-0.084</td><td>-0.282</td><td>0.317</td><td>0.100</td><td>0.979</td><td>0.980</td><td>0.981</td><td>0.989</td><td>1.000</td></tr></tbody></table>

(4) Calculate the variance contribution rate and cumulative variance contribution rate

Contribution rate:

$$ \frac{\lambda_i}{\sum_{k=1}^{p} \lambda_k} (i = 1, 2, \dots, p) $$

The cumulative variance contribution rate:

$$ \frac{\sum_{k=1}^{p} \lambda_k}{\sum_{k=1}^{p} \lambda_k} (i = 1, 2, \dots, p) $$

Generally it takes the cumulative contribution rate of 85% ~ 95% m eigenvalues corresponding to the former m variables as main components, number of principal components for M.

Variance and the cumulative variance contribution rate as shown in the following table:

<table><caption>**Table 3.** Variance contribution rate and cumulative variance contribution rate of shape features about SPSS.</caption><thead><tr><th colspan="3">Total Variance Explained</th></tr><tr><th>Component</th><th>Initial Eigenvalues</th><th>Extraction Sums of Squared<br>Loadings</th></tr></thead></table>
<table><thead><tr><th></th><th>Total</th><th>%of Variance</th><th>Cumulative %</th><th>Total</th><th>%of Variance</th><th>Cumulative %</th></tr></thead><tbody><tr><td>1</td><td>6.783</td><td>39.901</td><td>39.901</td><td>6.783</td><td>39.901</td><td>39.901</td></tr><tr><td>2</td><td>3.334</td><td>19.614</td><td>59.515</td><td>3.334</td><td>19.614</td><td>59.515</td></tr><tr><td>3</td><td>1.504</td><td>8.847</td><td>68.362</td><td>1.504</td><td>8.847</td><td>68.362</td></tr><tr><td>4</td><td>1.405</td><td>8.264</td><td>76.626</td><td>1.405</td><td>8.264</td><td>76.626</td></tr><tr><td>5</td><td>0.933</td><td>5.489</td><td>82.115</td><td>0.933</td><td>5.489</td><td>82.115</td></tr><tr><td>6</td><td>0.848</td><td>4.985</td><td>87.100</td><td>0.848</td><td>4.985</td><td>87.100</td></tr><tr><td>7</td><td>0.608</td><td>3.578</td><td>90.679</td><td>0.608</td><td>3.578</td><td>90.679</td></tr><tr><td>8</td><td>0.535</td><td>3.145</td><td>93.824</td><td>0.535</td><td>3.145</td><td>93.824</td></tr><tr><td>9</td><td>0.409</td><td>2.408</td><td>96.232</td><td>0.409</td><td>2.408</td><td>96.232</td></tr><tr><td>10</td><td>0.263</td><td>1.545</td><td>97.777</td><td>0.263</td><td>1.545</td><td>97.777</td></tr><tr><td>11</td><td>0.191</td><td>1.123</td><td>98.901</td><td>0.191</td><td>1.123</td><td>98.901</td></tr><tr><td>12</td><td>0.114</td><td>0.674</td><td>99.574</td><td>0.114</td><td>0.674</td><td>99.574</td></tr><tr><td>13</td><td>0.052</td><td>0.308</td><td>99.882</td><td>0.052</td><td>0.308</td><td>99.882</td></tr><tr><td>14</td><td>0.011</td><td>0.065</td><td>99.947</td><td>0.011</td><td>0.065</td><td>99.947</td></tr><tr><td>15</td><td>0.007</td><td>0.042</td><td>99.989</td><td>0.007</td><td>0.042</td><td>99.989</td></tr><tr><td>16</td><td>0.001</td><td>0.007</td><td>99.996</td><td>0.001</td><td>0.007</td><td>99.996</td></tr><tr><td>17</td><td>0.001</td><td>0.004</td><td>100.00</td><td></td><td></td><td></td></tr></tbody></table>

<figure><img src="image_3.png" /><figcaption>Figure 1. The SPSS components eigenvalue scatter diagram</figcaption></figure>

## (5) Determine the principal components

From cumulative variance contribution ratio of table 3 and each component eigenvalue scatter diagram of figure 1 show that 1-6 cumulative variance contribution
rate has reached 87.1 percent. After the sixth component feature value is going to be more smaller, and the transform slow. Therefore, here take first 6 comprehensive variables as main component.

(6) Determine the principal component loading matrix L

$$l_{ij} = p(z_i, x_j) = \sqrt{\lambda_i} e_{ij} (i, j = 1,2, \dots, p)$$

In this paper data loading matrix results are as follows:

<table><caption>**Table 4.** Principal component loading matrix L about SPSS</caption><thead><tr><th rowspan="3">Shape descriptor</th><th colspan="6">Component Matrix(a)</th></tr><tr><th colspan="6">Component</th></tr><tr><th>F1</th><th>F2</th><th>F3</th><th>F4</th><th>F5</th><th>F6</th></tr></thead><tbody><tr><td>Perimeter area ratio</td><td>0.502</td><td>-0.492</td><td>0.070</td><td>-0.208</td><td>0.225</td><td>-0.243</td></tr><tr><td>Fineness ratio</td><td>-0.560</td><td>0.410</td><td>0.387</td><td>0.314</td><td>-0.026</td><td>-0.061</td></tr><tr><td>Appearance ratio</td><td>-0.633</td><td>0.550</td><td>0.320</td><td>-0.314</td><td>0.003</td><td>0.208</td></tr><tr><td>Eccentricity</td><td>0.594</td><td>-0.568</td><td>-0.322</td><td>0.295</td><td>-0.011</td><td>-0.221</td></tr><tr><td>Skeleton eccentricity</td><td>0.536</td><td>-0.449</td><td>-0.113</td><td>0.272</td><td>0.055</td><td>0.071</td></tr><tr><td>Bounding rectangle compactness</td><td>-0.745</td><td>0.059</td><td>-0.430</td><td>0.302</td><td>0.018</td><td>0.125</td></tr><tr><td>Bounding polygon compactness</td><td>-0.536</td><td>0.476</td><td>0.055</td><td>0.564</td><td>-0.120</td><td>0.004</td></tr><tr><td>Centroid offset rate</td><td>0.223</td><td>0.357</td><td>0.318</td><td>-0.070</td><td>0.772</td><td>-0.103</td></tr><tr><td>Area symmetric rate</td><td>-0.274</td><td>0.243</td><td>-0.569</td><td>0.334</td><td>0.481</td><td>0.257</td></tr><tr><td>Perimeter symmetric rate</td><td>-0.314</td><td>-0.121</td><td>0.406</td><td>0.548</td><td>0.033</td><td>-0.499</td></tr><tr><td>Hu1 Moment</td><td>0.643</td><td>-0.430</td><td>0.328</td><td>0.215</td><td>0.102</td><td>0.338</td></tr><tr><td>Hu2 Moment</td><td>0.395</td><td>-0.464</td><td>0.487</td><td>0.308</td><td>-0.041</td><td>0.475</td></tr><tr><td>Hu3 Moment</td><td>0.860</td><td>0.479</td><td>-0.048</td><td>0.024</td><td>-0.047</td><td>-0.049</td></tr><tr><td>Hu4 Moment</td><td>0.863</td><td>0.476</td><td>-0.045</td><td>0.030</td><td>-0.045</td><td>-0.050</td></tr><tr><td>Hu5 Moment</td><td>0.793</td><td>0.545</td><td>-0.035</td><td>0.123</td><td>-0.093</td><td>0.019</td></tr><tr><td>Hu6 Moment</td><td>0.846</td><td>0.495</td><td>-0.021</td><td>0.110</td><td>-0.080</td><td>0.022</td></tr><tr><td>Hu7 Moment</td><td>0.843</td><td>0.518</td><td>-0.039</td><td>0.082</td><td>-0.069</td><td>-0.011</td></tr></tbody></table>
(7) Calculate the feature vectors to determine the linear expression of the principal component index of the original data.

<table><caption>Table 5. Characteristic vector of correlation matrix about SPSS</caption><thead><tr><th></th><th colspan="6">Eigenvectors</th></tr><tr><th></th><th>F1</th><th>F2</th><th>F3</th><th>F4</th><th>F5</th><th>F6</th></tr></thead><tbody><tr><td>P/Area</td><td>0.19</td><td>-0.27</td><td>0.06</td><td>-0.18</td><td>0.23</td><td>-0.26</td></tr><tr><td>Fineness ratio</td><td>-0.22</td><td>0.22</td><td>0.32</td><td>0.26</td><td>-0.03</td><td>-0.07</td></tr><tr><td>Min/MaxLen</td><td>-0.24</td><td>0.30</td><td>0.26</td><td>-0.26</td><td>0.00</td><td>0.23</td></tr><tr><td>Eccentricity</td><td>0.23</td><td>-0.31</td><td>-0.26</td><td>0.25</td><td>-0.01</td><td>-0.24</td></tr><tr><td>Skeleton eccentricity</td><td>0.21</td><td>-0.25</td><td>-0.09</td><td>0.23</td><td>0.06</td><td>0.08</td></tr><tr><td>Bounding rectangle compactness</td><td>-0.29</td><td>0.03</td><td>-0.35</td><td>0.25</td><td>0.02</td><td>0.14</td></tr><tr><td>Bounding polygon compactness</td><td>-0.21</td><td>0.26</td><td>0.04</td><td>0.48</td><td>-0.12</td><td>0.00</td></tr><tr><td>Centroid offset rate</td><td>0.09</td><td>0.20</td><td>0.26</td><td>-0.06</td><td>0.80</td><td>-0.11</td></tr><tr><td>Area symmetric rate</td><td>-0.11</td><td>0.13</td><td>-0.46</td><td>0.28</td><td>0.50</td><td>0.28</td></tr><tr><td>Perimeter symmetric rate</td><td>-0.12</td><td>-0.07</td><td>0.33</td><td>0.46</td><td>0.03</td><td>-0.54</td></tr><tr><td>Hu1 Moment</td><td>0.25</td><td>-0.24</td><td>0.27</td><td>0.18</td><td>0.11</td><td>0.37</td></tr><tr><td>Hu2 Moment</td><td>0.15</td><td>-0.25</td><td>0.40</td><td>0.26</td><td>-0.04</td><td>0.52</td></tr><tr><td>Hu3 Moment</td><td>0.33</td><td>0.26</td><td>-0.04</td><td>0.02</td><td>-0.05</td><td>-0.05</td></tr><tr><td>Hu4 Moment</td><td>0.33</td><td>0.26</td><td>-0.04</td><td>0.03</td><td>-0.05</td><td>-0.05</td></tr><tr><td>Hu5 Moment</td><td>0.30</td><td>0.30</td><td>-0.03</td><td>0.10</td><td>-0.10</td><td>0.02</td></tr><tr><td>Hu6 Moment</td><td>0.32</td><td>0.27</td><td>-0.02</td><td>0.09</td><td>-0.08</td><td>0.02</td></tr><tr><td>Hu7 Moment</td><td>0.32</td><td>0.28</td><td>-0.03</td><td>0.07</td><td>-0.07</td><td>-0.01</td></tr></tbody></table>

$$ (8) \quad F_{1*6} = X_{1*17} * E_{17*6} $$

$E_{17*6}$ as eigenvector matrix in table 5, $F_{1*6}$ as the principal component vector, $X_{1*17}$ as the original shape descriptor vector
## 5. Experiments and results

The first principal component eigenvalue is 6.783, the variance contribution rate is 39.9%, the entire data of standard variant is 39.9%, only relying on the first principal component can not reflect most information of original data. The first principal component in geometric invariant feature has high positive loads, in Appearance ratio and bounding rectangle compactness has high negative loads, the centroid offset rate has low positive loads, in the area and perimeter symmetric rate has a low negative loads, in other variables have similar secondary loads. That is to say, large (small ) to the first principal components tend to be large ( small ) geometric moment invariants, then appearance ratio and bounding rectangle compactness tend to have smaller values ( large). As a result of invariant moments are based on the regional global statistical feature, with similar but different sets of images ( like the fruit with similar to leaves ) has better identification of. Therefore, the first principal component can be used to characterize the morphology of the more slender, not completely symmetrical, with concave boundary, and the global features of difference image sets with strong discernment.

The second principal component feature value is 3.334, the variance contribution rate of 19.614%, the entire data of standard variation is 19.614%. Through the observation to load factor matrix in table 4, we find that the second principal component in most variables are approximately equal to the load, so can be used as a comprehensive metric variables, reflect almost all the features of the original nature. In addition, because the main components in the bounding rectangle of compactness and area symmetrical rate have a low normal load and the perimeter symmetric rate with a low negative load. Therefore, while the second principal component analysis in comprehensive measure all the features, it slightly weak impact of foliage bending on region side.

The third principal component feature value is 1.504, showing that the entire data of standard variation is 8.847% separately. The third principal component in the area of symmetric rate ratio has high loads, in circumference symmetrical ratio, fineness rHu1 and Hu2 moments have high positive load. To the leaf image, if the edge has some curl, it may not affect the perimeter circumference, but it changed the blade on the imaging surface of two-dimensional area, causing the image has high perimeter symmetric rate, and low rate of area of symmetry. Therefore, the higher of the third principal component values tend to express has an elongated oval blades, and the
blade edge may appear in curling.

The fourth principal component feature value is 1.405, showing the entire data of standard variation is 8.264% separately. The fourth principal component in encircle polygon compactness and perimeter symmetric rate have high positive loads, in appearance ratio and the circumference area ratio have high negative loads, in the centroid offset ratio with low negative loads, at the moment invariant part has lower positive load. High bounding polygon compactness and perimeter symmetric ratio both show that the region is filling full, is more symmetrical convex polygon, and the appearance ratio and perimeter area ratio with higher load, the principal component has higher differentiate different width of the ability to target. To a certain extent, the fourth principal components can be associated with the first principal component is complementary, it weakens the global moment invariant statistical characteristics influence, but strengthen the shape complexity and symmetry as well as the appearance of the elongated convex characteristics.

The fifth principal component feature value is 0.933, showing the entire data of standard variation is 5.489% separately. On the center of mass migration rate of fifth principal components have significantly high positive loads the area of symmetric rate has high positive load, in addition, the other variables with have smaller load value. In general, low centroid rate figure centroid bias top right (according to the centroid offset rate calculation formula can be seen ), high centroid rate figure centroid bias bottom left. Value of the larger of the fifth principal components tend to say mass at the bottom left of the symmetrical region.

The sixth principal component feature value is 0.848, showing the entire data of standard variation is 4.985% separately. In the perimeter symmetric rates on sixth principal components have higher negative loads, and in $Hu_1$ and $Hu_2$ with higher positive load, in other variables are not high load. Because $Hu_1$ and $Hu_2$ are calculated by using image moment of order two, and the image of two order moment is not included details of the general information, in the geometry mean variance, if we consider only the order for 2 sets of the moment, the original image is completely equivalent to the image centroid as the center and has the same two order moments of the ellipse. Therefore, the higher of the sixth principal component values tend to express elliptical rather than circular, may have side edges curled area, but the direction and size of the show is weak.

From the above analysis we can see that the first six principal components of the cumulative variance contribution ratio reach to 87.1%, it can be very good summary
of the data group. And the six main component covers the area of concave and convex
of elongated, the complexity symmetry of shape, the centroid position and direction,
as well as statistics based on geometric moment invariants and other aspects of
information, a reasonable description of the region shape characteristic, the original
17 features integrated into 6, while retaining the original variables most of the
information under the premise, realize dimension compression of the data.

6. Conclusion

This article from the 17 dimensions of the quantitative describe the single plane shape
characteristics, including the target boundary geometric description (perimeter area
ratio, fineness ratio, eccentricity and so on), the target area and its surrounding
polygon metric (bounding rectangle compactness, encircle polygon compact degree
and so on), the target area (centroid offset ratio, area of symmetry, perimeter
symmetry degree and so on) invariant moment (Hu), covering graphics elongated,
convexity, complexity, symmetry, centroid direction, ellipse, compact plumpness,
number of shape, geometric invariant moment etc.. Then through by the method of
principal component analysis to do variable compression on these characteristics,
explaining the first six principal components which cumulative variance
contribution rate reach to 87.1%, in which elongated, convexity and geometric
invariant moment contributed to the first principal component is larger; the second
principal component can be used as a comprehensive measure factor, each
characteristics of second main components in the contribution rate is almost equal; the
third principal component more reflect the region of the ellipse and elongated; the
fourth principal component in global invariant moment statistical properties of the
performance is not outstanding, but focused on the expression of slim and compact
plumpness; the higher of the fifth principal component values tend to areas near left
lower direction of the center of mass, which leaves the image on the right is fine, but
left is wide, image centroid shift; sixth main components on the ellipse has stronger
descriptive power, but the direction and size of the description of is a little weak.
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