Leaves Classification and Leaf Mass Estimation美国大学生数模竞赛二等奖.docVIP

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Leaves Classification and Leaf Mass Estimation美国大学生数模竞赛二等奖.doc

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Contents Contents 0 Ⅰ. Introduction 1 Ⅱ. Some Definitions 1 Ⅲ. General Assumptions 1 Ⅳ. Symbols 2 Ⅴ. Problem analysis 2 Ⅵ. Models 3 6.1 Neural network model to classify tree leaves 3 6.1.1 Neuromime 3 6.1.2 Multi-layer perceptron network 4 6.1.3 Back-propogation 5 6.1. 4 NN’s use to classify leaves 6 6.2 Studying the reasons of the various shapes that leaves have. 6 6.2.1 Set up a AHP model to value these base factors 6 6.2.2 Paired comparison matrix structure 7 6.2.3 Calculation of the weight vector and the consistency test 8 6.3 Optimize leaves shape for maximize exposure 9 6.3.1 Explain and answer requirment 9 6.3.2 Set up a Elastic mechanics model 9 6.4 Tree profile and branching structure’s influence on leaf shape. 10 6.4.1 Analysis about the impact of tree profile to leaf shape 10 6.4.2 Electric tree branch angle’s impact analysis 13 6.5 Estimation of the leaf mass 14 6.5.1 Build up a volumetric model 14 6.5.2 The correlation of leaf mass vs. mean crown radius’s cubic 15 6.5.3 The correlation between the leaf mass and the height of the tree 16 6.5.4 The dry leaf mass vs. the volume of the tree 17 6.5.5 The relationship between the leaf mass and mean crown radius 18 Ⅶ. Conclusions 19 Ⅷ. Strengths and Weakness of the Model 19 Ⅸ. Future Work 20 Ⅹ. References 20 Key Findings 21 Ⅰ. Introduction As is known to all，there are not two leaves exactly alike. Plant leaves have diverse and elaborate shapes and venation patterns. The beauty of them has attracted curiosity of many people involving biologists, physicists, mathematician, artists, computer scientists, etc. for a long time. The leaf study of forests and of individual tree is important to understand resource allocation of trees, atmosphere—biosphere exchange processes, and the energy budget, it would also be valuable for individual tree growth. The aim of this article is to develop models for leaf shapes classification and to figure out the main factors which lead to the various leaf shapes. At the same time