增强DT-CWT特征与正则化邻域投影的人脸识别

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"这篇研究论文探讨了一种基于增强的离散小波变换(DT-CWT)特征的人脸识别方法，该方法结合了正则化邻域投影判别分析(Regularized Neighborhood Projection Discriminant Analysis, RNDA)。文章指出，这种方法可以有效提升人脸识别的性能和准确性。" 在计算机视觉和模式识别领域，人脸识别是一项重要的任务，广泛应用于安全、监控、身份验证等场景。离散小波变换(DT-CWT)是一种多分辨率信号分析工具，能够捕获图像的频率和位置信息，对于图像特征提取尤其有用。在人脸识别中，DT-CWT可以帮助提取人脸图像的局部和全局特征，这些特征通常包含人脸的形状、纹理和结构信息。然而，仅仅依赖于DT-CWT特征可能不足以达到最优的识别效果，因为原始特征可能存在冗余或噪声。为了优化特征并提高分类性能，论文提出了使用正则化邻域投影判别分析(RNDA)。RNDA是一种统计学习方法，它通过正则化技术减少特征之间的相关性，同时保持类间差异最大化，从而提高分类器的辨别能力。在人脸识别中，RNDA可以进一步降低维度，减少过拟合风险，并且更好地保留特征间的判别信息。该研究可能包括以下步骤： 1. **DT-CWT特征提取**：首先，对人脸图像进行离散小波变换，得到不同尺度和方向的系数，这些系数包含了人脸图像的多种频率成分。 2. **特征增强**：对提取的DT-CWT特征进行处理，可能包括选择具有高区分度的系数，或者利用某种增强策略来突出关键特征。 3. **RNDA特征选择与降维**：将增强后的DT-CWT特征输入到RNDA模型中，通过正则化手段去除冗余特征，同时保留最大化类间距离的特征子集。 4. **分类器训练与测试**：使用降维后的特征训练分类器（如支持向量机、神经网络等），并在独立测试集上评估识别性能。论文作者通过实验验证了该方法的有效性，可能比较了不同特征提取方法和分类器的性能，以及正则化参数对结果的影响。此外，他们可能还讨论了与其他现有方法的比较，以及该方法在实际应用中的潜在优势和挑战。总结来说，这篇论文提供了一个融合DT-CWT特征和RNDA的创新人脸识别框架，旨在通过优化特征表示和减少特征空间的复杂性，提高人脸识别的准确性和鲁棒性。这对于推动人脸识别技术的发展具有重要意义，尤其是在复杂环境和有限数据条件下的应用。

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in less computation, it still has two limitations when applied in

human face recognition. Firstly, DT-CWT does not consider the

structural information in human face. As we know, the different

facial regions have different degrees of importance, especially the

eyes, mouth, face contour, etc. [14]. In order to distinguish two

faces, the differences at these important regions should be

emphasized. However, traditional DT-CWT representation does

not consider the relative importance between the different facial

regions, and make no distinction between different parts of the

face. Secondly, DT-CWT does not consider the statistical

distribution of the transformed features. It treats each element

equally and cannot emphasize those elements with high statistical

probabilities which may play an important role in discrimination.

Extracting proper features is crucial for satisfactory design of

any pattern classiﬁer, and how to develop a general procedure for

effective feature extraction remains an interesting and challenging

problem [15,16]. One usually starts with a given set of features and

then attempts to derive an optimal subset (under some criteria) of

features leading to high classiﬁcation performance with the

expectation that similar performance can also be displayed on

future trials using novel (unseen) test data [17]. Principal

Component Analysis (PCA) [18] is a popular technique used to

derive a starting set of features for both face representation and

recognition. As it is based on the optimal representation criterion in

the sense of mean-square error, PCA does not consider the

classiﬁcation aspect. To improve the classiﬁcation performance,

one needs to combine further this optimal representation criterion

with some discrimination criterion. One widely used criterion in

the face recognition community is the Fisher Linear Discriminant

(FLD, a.k.a. Linear Discriminant Analysis, or LDA) [19], which tries

to maximize the ratio

FLD

ðW

opt

Þ¼argmax



ð1Þ

where S

is the between-class scatter matrix, and S

is the within-

class scatter matrix. Thus, by applying LDA, we can ﬁnd the optimal

feature vectors that on the one hand maximize the Euclidean

distance between the face images of different classes and on the

other minimize the distance between the face images of the same

class. This ratio is maximized when the column vectors of the

projection matrix W are the eigenvectors of S

1

There are two limitations for LDA when used for pattern

classiﬁcation. One is the so-called small sample size (SSS) problem.

In face recognition tasks, the dimension of the sample space is

typically larger than the number of samples in the training set. As a

consequence, S

is singular and we cannot compute S

1

directly.

In the past few decades, various approaches have been proposed to

solve this problem. A common way to deal with the singularity

problems is to apply an intermediate dimension reduction

stage such as PCA to reduce the dimension of the original data

before classical LDA is applied. The algorithm is known as PCA+LDA

[19–21]. In this two-stage PCA+LDA algorithm, the discriminant

stage is preceded by a dimension reduction stage using PCA.

The dimension of the subspace transformed by PCA is chosen

such as the ‘‘reduced’’ within scatter matrix in the subspace is

nonsingular, so that classical LDA can be applied. A limitation is that

the optimal value of the reduced dimension for PCA is difﬁcult to

determine. Moreover, the PCA stage may lose some useful

information for discrimination. Howland and Park [22] solved

the singularity problem of LDA by using Generalized Singular

Value Decomposition (GSVD). GSVD aims to ﬁnd the optimal

transformation W

opt

, which can preserve the dimension of the

spaces spanned by the centroids in the original and transformed

spaces. The drawback is the optimal solutions are obtained by

applying the SVD decomposition of the data matrix, which is

computationally expensive in both time and memory for high

dimensional large scale data sets. Ye [23] extended such

approach by solving the optimization problem using

simultaneous diagonalization of the scatter matrices.

Another limitation of LDA is that it works under the condition that

the sample vectors of each class are generated from underlying

multivariate normal distributions of common covariance matrix but

different means [24]. Hence, if the data of a class are multimodal, LDA

will not generally work. It may even collapse the data samples of the

different class into a single cluster. Over the years, authors have

deﬁned several extensions to the basic formulation of LDA. One such

method is to use a weighted version of LDA, such as the approximate

Pairwise Accuracy Criterion (aPAC) [25] or Penalized DA (PDA) [26].In

this method, weights are introduced in the deﬁnition of the metrics,

which can reduce (or penalize) the role of the least stable features and

thus it can make the metrics of DA a bit more ﬂexible. He et al. [27]

proposed Locality Preserving Projection (LPP) method that seeks for

an embedding transformation such that nearby data pairs in the

original space close in the embedding space. Thus, LPP can reduce

the dimensionality of multimodal data without losing the local

structure. Zhu et al. [28] proposed Subclass Discriminant Analysis

(SDA) method, which aims to adapt to a large variety of data

distributions. In this method, multimodal data can be divided into

a set of subclasses whose representation can be used to adapt to

different types of class distributions. We proposed Neighborhood

Preserving Discriminant Analysis (NPDA) method [29],whichcan

maximize the between-class separability while preserve the within-

class local structure. However, NPDA is still affected with the SSS

problem.

The points below highlight the contributions of this paper:

1. A new Augmented DT-CWT (ADT-CWT) method is presented to

extract multi-scale facial features. In this approach, a new

mapping function is deﬁned and used to emphasize those

features having higher statistical probabilities and spatial

importance for face images. After this nonlinear mapping, the

transformed features could have a higher discriminating power.

2. A new dimensionality reduction method is presented called the

Regularized Neighborhood Projection Discriminant Analysis

(RNPDA). In this method, linear projective functions can be

obtained directly using a simple regression framework. Tradi-

tional eigen-problem computation is not involved in our

approach and thus it can avoid SSS problem.

3. Extensive experiments have been made to compare the face

recognition performance of the proposed method with some

popular dimensionality reduction methods on the FERET data-

base [30], the extended YALEB database, [31] and the CMU PIE

database [32]. The results verify the effectiveness of our method.

This paper is organized as follows. ADT-CWT and RNPDA are

introduced in Sections 2 and 3, respectively. Experimental results are

presented in Section 4. Finally, conclusions are drawn in Section 5.

2. Augmented Dual-Tree Complex Wavelet Transform

In this section, we ﬁrstly make a brief review of DT-CWT. Then

we present ADT-CWT method which fully considers the statistical

property of the input features and the spatial information about

human faces. For convenience, we present in Table 1 the important

notations used in the rest of the paper.

2.1. Dual-Tree Complex Wavelet Transform

In DT-CWT, two real discrete wavelet transforms

ðtÞ and

ðtÞ

are employed in parallel to generate the real and imaginary parts of

H. Hu / Pattern Recognition 44 (2011) 519–531520

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