正交局部判别样条嵌入技术在植物叶片识别中的应用

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"正交局部判别样条嵌入用于植物叶片识别的研究论文" 这篇研究论文探讨了使用正交局部判别样条嵌入(Orthogonal Local Discriminant Spline Embedding, OLDE)方法在植物叶片识别中的应用。在生物多样性研究、农业科学以及生态保护等领域，植物叶片的识别是至关重要的。传统的叶片识别方法通常基于形状、纹理或颜色特征，但这些方法可能在处理复杂背景、光照变化或叶片损伤时效果不佳。 OLDE是一种先进的机器学习技术，旨在提高样本的分类性能和数据表示能力。它结合了局部判别分析（LDA）和样条函数的概念，通过正交化处理来减少特征之间的共线性，同时保持数据的局部结构。这种方法能够提取更具有判别性的特征，从而在复杂的数据集中提高识别精度。在植物叶片识别中，OLDE首先对原始图像进行预处理，如去噪、增强和分割，以获取叶片的特征区域。接着，利用样条函数对叶片的形状、边缘和纹理信息进行建模，样条函数可以灵活地适应叶片的不规则形状。然后，通过正交化过程，OLDE能有效降低特征空间的维度，同时最大化类间距离，最小化类内距离，实现样本的有效分类。该论文的实验部分可能包括了与其他传统方法（如PCA、LDA、SVM等）的比较，展示了OLDE在处理植物叶片数据集上的优越性能。此外，论文可能还讨论了OLDE的参数选择、鲁棒性以及在不同光照条件和损伤叶片上的表现。作者们可能还探讨了OLDE算法的未来改进方向，例如集成深度学习技术来进一步提升识别准确率，或者探索如何利用多模态信息（如光谱和结构数据）来增强识别效果。同时，他们可能提到了版权和学术使用的规定，强调了论文副本的使用限制，并提供了关于Elsevier的作者权利和存档政策的链接，以供需要进一步信息的作者参考。这篇研究对于理解植物叶片识别的挑战和解决方案提供了深入见解，同时也为相关领域的研究者提供了新的工具和技术，有助于推动植物识别技术的发展和应用。

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Moreover, most of these methods are computationally expensive,

thus limiting their utility in plant leaf image data sets.

1.2. Feasibility of plant leaf recognition based on manifold learning

Over the last decade, a large number of nonlinear manifold

learning algorithms have been proposed under the assumption

that the input data set lies on or near some low-dimensional man-

ifold embedded in a high-dimensional unorganized Euclidean

space. Among the most well known are isometric feature mapping

(ISOMAP) [14], locally linear embedding (LLE) [15–16], Laplacian

eigenmaps (LE) [17], Hessian-based locally linear embedding

(HLLE) [18], maximum variance unfolding (MVU) [19], local tan-

gent space alignment (LTSA) [20], and local spline embedding

(LSE) [21]. Each manifold learning algorithm attempts to preserve

a different geometrical property of the underlying manifold. Local

approaches such as LLE, HLLE, LE, LTSA, and LSE aim to preserve the

proximity relationship among the data, while global approaches

like ISOMAP aim to preserve the metrics at all scales. These nonlin-

ear methods yield impressive results on some benchmark artiﬁcial

and real world data sets due to their nonlinear nature, geometric

intuition, and computational feasibility.

An important advantage of manifold learning [14–21] com-

pared with conventional approaches concerns how the data are

treated mathematically. Conventional approaches typically pro-

duce a smaller data space from linear combinations of the original

data. One common example is PCA which seeks a low-dimensional

linear subspace spanned by the eigenvectors corresponding to the

largest eigenvalues of the covariance matrix of all samples. How-

ever, for plant leaf images, the assumption of global linearity is a

severe constraint since they are sensitive to period, location, and

illumination conditions and there is no reason to believe that the

leaf image data are linearly separable from each other. Manifold

learning approaches recognize this fact and allow the data to be

nonlinearly related, which results in the fact that manifold learning

approaches can much more accurately capture the proper informa-

tion relationships among the data thus allowing for accurate recog-

nition. Fig. 1 shows a simple example that 150 leaf images of two

kinds of plants are mapped into two-dimensional subspace by local

spline embedding (LSE). The size of each image is 32  32 pixels,

with 256 gray-levels per pixel. Thus, each leaf image is represented

by a point in the 1024-dimensional ambient space. The left and

right leaf images respectively correspond to the points with green

and cyan circles in the two-dimensional embedding subspace. As

can be seen, the leaf images are divided into two parts. The circles

and the asterisks represent leaf images of different classes. It can

be clearly seen that the sample points of each class exhibit a

sub-manifold distribution. The results demonstrate that LSE can

successfully ﬁnd the discriminative directions, but the directions

are not optimal for leaf recognition task. This is because in trying

to preserve local structure in the embedding, the LSE implicitly

emphasizes the natural clusters in the data. More importantly,

LSE is capable of capturing the intrinsic leaf manifold structure to

some extent.

1.3. Contribution of the paper

In this study, we take an alternative view of manifold learning

to develop two orthogonal locally discriminant spline embedding

methods (OLDSE-I and OLDSE-II) for plant leaf recognition. The

goal of OLDSE-I or OLDSE-II is to map the plant leaf images into a

plant leaf subspace for analysis. Different from principal compo-

nent analysis (PCA) [22] and linear discriminant analysis (LDA)

[23] which can only deal with ﬂat Euclidean structures of plant leaf

space, The OLDSE-I/OLDSE-II ﬁnds an embedding that not only

inherits the advantages of local spline embedding (LSE) [21] which

uses local neighborhoods as a representation of the local geometry

so as to preserve the local structure, but makes full use of class

information to improve discriminant power by introducing trans-

lation and rescaling models. In this way, a plant leaf subspace that

best detects the essential plant leaf manifold structure can be ob-

tained. It is worthwhile to highlight several aspects of the proposed

approaches here:

(1) An efﬁcient subspace learning algorithm for plant recogni-

tion should be able to discover the nonlinear manifold struc-

ture of the leaf image space. Our proposed OLDSE-I and

OLDSE-II algorithms explicitly considers the intrinsic leaf

manifold structure which is modeled by an adjacency graph.

(2) OLDSE-I/OLDSE-II takes local structure and discriminant

information into consideration simultaneously and attempts

to manage the trade-off between LSE, which is based mainly

on preserving local geometry and maximum margin crite-

rion (MMC), which emphasizes discriminant power.

(3) OLDSE-I/OLDSE-II shares some similar properties to LSE,

such as a local neighborhood preserving character. However,

their objective functions are ultimately different. OLDSE-I/

OLDSE-II computes an explicit linear mapping from the

input space to the reduced space, while in LSE, the mapping

is implicit and it is not clear how new data samples can be

embedded.

(4) Although OLDSE-I and OLDSE-II seek to ﬁnd a set of orthog-

onal basis functions and further improve their recognition

accuracy, they use different orthogonalization processes in

which their fundamental difference lies.

1.4. Paper organization

The rest of this paper is organized as follows: Section 2 brieﬂy

describes the LSE algorithms. In Section 3, the OLDSE-I and

OLDSE-II algorithms are developed. A variety of the experimental

results are presented in Section 4. Finally, we provide some con-

cluding remarks and future work in Section 5.

2. A brief review of local spline embedding

Given a data set of n data points X ¼½x

; x

; ...; x

2R

Dn

the goal of dimensionality reduction is to project the high-

dimensional data into a low-dimensional feature space. Let us

denote the corresponding set of n points in the reduced space as

-5 -4 -3 -2 -1 0 1 2 3 4

-1

Fig. 1. Two-dimensional embedding of plant leaf images by LSE.

Y.-K. Lei et al. / Computer Vision and Image Understanding 119 (2014) 116–126

117

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