2012美国大学生数学建模竞赛A题一等奖论文

2012美国大学生数学建模竞赛A题一等奖论文

A Small Leaf Tell You All: Modeling in Leaves

Classification and Mass Estimation

Control #16263

Abstract

The paper carries the research on the issues of leaves classification and mass estimation. Shape difference function combined with BP neural network is built to classify the leaves shape and a tree shape—density mathematical model is done to estimate the mass and quantity of leaves.

As for classifying leaves, we firstly set up leaves included-angle model which makes the smallest overlapping part and greatest possibility to reach sunshine when the included-angle is near to golden section.

Then, we establish shape difference function to describe the difference between leaves in the surface and ektonexine of the same tree. The value of shape difference function can be acquired by weighting circularity and boundary energy, and it shows chi-square distribution with the tree-crown thickness, thus, leaves distribution information in the canopy can be obtained from leaves shape information.

In order to investigate the tree shapes and contours, we focus on 5 basic tree contours and select 20 tree species(Jennifer，2009), make an account on the leaves shape situation of certain relative tree contour, and find the relation between the tree shape and contour.

For the purpose of calculating the tree leaves mass, we have gotten a mathematical model, which is canopy volume formula of the 5 basic contours, after estimating the volume of a leave and density of leave distribution, the model has been used to get the number of leaves, and the total leaves mass can be gotten by multiplying the average leaves mass.

Finally, the classification modeling and mass calculation modeling are both empirical. In the prediction results of classification model, leaves shape identification accuracy reaches 75%, the surface and ektonexine distribution accuracy is 100%. We also select a mango tree in campus to make empirical study on the leave quality modeling. According to the modal calculation, the mass of leaves is approximately equal to 15500, and the quality is about 77.5kg.

2012美国大学生数学建模竞赛A题一等奖论文

Page 1 of 28

Control#16263

2012美国大学生数学建模竞赛A题一等奖论文

I. Introduction

1.1Background：Why are there so many different shapes of leaves?

The shapes of leaves are influenced by two factors: gene and environment. As for gene of leaves, the decisive factor, this article will not mainly talk about it although Japanese scientists have recently discovered the gene clusters of leaves while the environment is analyzed here. (Lan jianzhong,2011) The main functions of leaves are photosynthesis and transpiration, so the mainly affective factors are sunshine, moisture and the amount of carbon dioxide.

Firstly, the earth can be pided into five zones according to the reach of the sun and each zone has typical climate features. Hence, respective plants in these areas show different shapes:

Figure 1. Plant feature in five zones（This picture is from Google）

frigid zone is represented by coniferous forest; temperate zone is well-known as deciduous broad-leaved forest; tropical zone is full of evergreen broad-leaved forest.

It is found that leaves in tropical zone are more circular and thicker than those in temperate area after comparison. Meanwhile, the border of a leaf is more incised in former zone. Consequently, tropical leaves are tougher than temperate ones—the former ones can always keep green all over the year while the latter ones only stay for a season.

2012美国大学生数学建模竞赛A题一等奖论文

The different cover of the sunshine in five zones causes different shapes of leaves. But in the same tree, the leaves can show variable styles because of unequal amount of the sunshine. The crown of a tree and the surface leaves can receive the largest amount of sunshine whereas the lower and the inside leaves can only obtain less. In order to make sunshine reach the inside and photosynthesis function from top to down, the crown and surface leaves are often smaller but inside ones are bigger and rounder, which can keep a balance to recycle.( Wei Ming,2011)

Secondly, moisture can influence the shape of leaves. Tropical zone is hot and rainy so the plants with big and broad leaves are contributed to evaporate extra water moisture. However, in dry dessert or Frigid Zone, leaves have to be smaller and even coniferous so as to maintain enough water moisture.

Lastly, the spread of carbon dioxide in the global is even, which doesn’t affect the shape of leaves obviously. In addition, other plants have various functions. For example, some hairy plants can slow down the air and reduce transpiration, also stop harmful insects.

The shape of leaves is various and its classification can be perse. But this article aims at studying leaves by shapes, further conferring subjects such as their distribution in distinct areas, category and weight in order to provide some new ideas and methods for scientific research.

1.2 Problem process

The leaves have many shapes, and can represent different species, at the same time, it also can reflect in the structure of tree.(Dengler et al,1982) began to study palm leaves. Along with the further study of the leaf, more and more people pay attention to the leaf and the relationship between the climates. Hironori Fujita, et, al(2006)establish a positive and negative feedback model to explain the leaves persity from the point of view of the veins.( Benjamin Blonder, et al 2010)used with factors such as light, explains why the leaves have a different shape. In addition, in 1986, Ingrouille et. al used 27 leaves’ characteristics, classified for 40 plants. In 2001, Osikar et. al the BP neural network to clas …… 此处隐藏：23373字，全部文档内容请下载后查看。喜欢就下载吧 ……