

![0_image_0.png](0_image_0.png)

4) Leaf Area: The value of leaf area is easy to evaluate, just counting the number of pixels of binary value 1 on smoothed leaf image. It is denoted as A.

5) Leaf Perimeter: Denoted as P, leaf perimeter is calculated by counting the number of pixels consisting leaf margin.

## B. 12 Digital Morphological Features

Based on 5 basic features introduced previously, we can define 12 digital morphological features used for leaf recognition.

1) Smooth factor: We use the effect of noises to image area to describe the smoothness of leaf image. In this paper, smooth factor is defined as the ratio between area of leaf image smoothed by 5 × 5 rectangular averaging filter and the one smoothed by 2 × 2 rectangular averaging filter.

2) Aspect ratio: The aspect ratio is defined as the ratio of physiological length Lp to physiological width Wp, thus Lp/Wp.

3) Form factor: This feature is used to describe the difference between a leaf and a circle. It is defined as 4**πA/P**2, where A is the leaf area and P is the perimeter of the leaf margin.

4) Rectangularity: Rectangularity describes the similarity between a leaf and a rectangle. It is defined as LpWp/A, where Lp is the physiological length, Wp is the physiological width and A is the leaf area.

5) Narrow factor: Narrow factor is defined as the ratio of the diameter D and physiological length Lp, thus D/Lp.

6) Perimeter ratio of diameter: Ratio of perimeter to diameter, representing the ratio of leaf perimeter P and leaf diameter D, is calculated by P/D.

7) Perimeter ratio of physiological length and physiological width: This feature is defined as the ratio of leaf perimeter P and the sum of physiological length Lp and physiological width Wp, thus P/(Lp + Wp).

8) Vein features: We perform morphological opening [25]
on grayscale image with falt, disk-shaped structuring element of radius 1,2,3,4 and substract remained image by the margin. The results look like the vein. That is why following 5 feature are called vein features. Areas of left pixels are denoted as Av1, Av2, Av3 and Av4 respectively. Then we obtain the last 5 features: Av1/A, Av2/A, Av3/A, Av4/A, Av4/Av1.

Now we have finished the step of feature acquisition and go on to the data analysis section.

## Iv. Proposed Scheme A. Principal Component Analysis (Pca)

To reduce the dimension of input vector of neural network, PCA is used to orthogonalize 12 features. The purpose of PCA
is to present the information of original data as the linear combination of certain linear irrelevant variables. Mathematically, PCA transforms the data to a new coordinate system such that the greatest variance by any projection of the data comes to lie on the first coordinate, the second greatest variance on the second coordinate, and so on. Each coordinate is called a principal component.

In this paper, the contribution of first 5 principal components is 93.6%. To balance the computational complexity and accuracy, we adopt 5 principal components.

When using our algorithm, one can use the mapping f :
R

12 → R
5 to obtain the values of components in the new coordinate system.

## B. Introduction To Probabilistic Neural Network

An artificial neural network (ANN) is an interconnected group of artificial neurons simulating the thinking process of human brain. One can consider an ANN as a "magical" black box trained to achieve expected intelligent process, against the input and output information stream. Thus, there is no need for a specified algorithm on how to identify different plants.

PNN is derived from Radial Basis Function (RBF) Network which is an ANN using RBF. RBF is a bell shape function that scales the variable nonlinearly.

PNN is adopted for it has many advantages [26]. Its training speed is many times faster than a BP network. PNN can approach a Bayes optimal result under certain easily met conditions [24]. Additionally, it is robust to noise examples. We choose it also for its simple structure and training manner.

The most important advantage of PNN is that training is easy and instantaneous [24]. Weights are not "trained" but assigned. Existing weights will never be alternated but only new vectors are inserted into weight matrices when training. So it can be used in real-time. Since the training and running procedure can be implemented by matrix manipulation, the speed of PNN is very fast.

The network classfies input vector into a specific class because that class has the maximum probability to be correct. In this paper, the PNN has three layers: the Input layer, Radial Basis Layer and the Competitive Layer. Radial Basis Layer evaluates vector distances between input vector and row weight vectors in weight matrix. These distances are scaled by Radial Basis Function nonlinearly. Then the Competitive Layer finds the shortest distance among them, and thus finds the training pattern closest to the input pattern based on their distance.