序数特征选择在虹膜和掌纹识别中的应用

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"这篇文章主要探讨了虹膜和掌纹识别中的序数特征选择技术，它在生物识别领域具有重要的应用价值。序数特征是衡量图像分析的一种有效方式，但其变体众多，如位置、尺度、方向等参数设置不同，会构建出庞大的特征空间。论文提出了一种新的优化公式来解决这个问题，特别适用于虹膜和掌纹识别的特征选择。" 在"Ordinal Feature Selection for Iris and Palmprint Recognition"这篇研究论文中，作者Zhenan Sun、Libin Wang和Tieniu Tan(均为IEEE成员)深入研究了如何利用序数度量来提高生物识别的准确性和效率。序数特征表示是一种对虹膜和掌纹图像进行建模的有效方法，因为它能够捕捉到生物特征的内在结构和细节。然而，这些特征的多样性导致了特征空间的复杂性，这可能会对识别性能产生负面影响。为了克服这个问题，论文提出了一种新颖的优化框架，旨在从众多的序数特征中选择最有效的子集。该方法的目标函数由两部分组成：一是校正类内和类间匹配样本的误分类误差，这是为了确保所选特征能准确区分不同的虹膜或掌纹；二是考虑特征描述符的加权稀疏性，以实现特征表示的简洁性。通过优化这两个目标，可以得到既准确又稀疏的特征集合。优化过程受到一系列线性不等式约束的制约，这些约束确保所有类内的匹配样本与所有类间的非匹配样本都能得到正确处理。通过这种方法，研究者们成功地减少了特征维度，同时保持了识别系统的性能。这不仅有助于提高识别速度，还有助于降低存储需求，对于实时和大规模的生物识别系统尤其重要。这篇论文为虹膜和掌纹识别提供了新的思路，通过优化序数特征选择，提高了识别系统的准确性和效率，为生物识别领域的未来发展开辟了新的可能。

3924 IEEE TRANSACTIONS ON IMAGE PROCESSING, VOL. 23, NO. 9, SEPTEMBER 2014

to the non-linear objective function. Therefore a three-stage

architecture is necessary to solve a large learning problem [17].

Secondly, the squared sum of regression errors deﬁned in

the objective function makes the feature selection sensitive to

outliers. Thirdly, the class label g can only take the value either

+1or−1, therefore the model could not generate a maximal

margin. Margin analysis is important to the generalization

ability of machine learning algorithms and the most powerful

machine learning methods, e.g. Support Vector Machine and

Boosting are motivated by margins. In addition, the features of

training samples should be normalized to match the class label,

therefore additional computational cost is needed. Fourthly,

the model of Lasso is not ﬂexible so that the optimization

does not take into account the characteristics of image features

and biometric recognition. For example, L1 regularization term

in the optimization function Eqn. 1 assigns an identical

weight to all features and the discriminative information of

each feature is not taken into consideration.

The L1 regularization is a popular technique for feature

selection. For example, Guo et al. proposed a linear program-

ming formulation of feature selection with application to facial

expression recognition [13]. The objective function aims to

minimize misclassiﬁcation error and the L1 norm of feature

weight.

In summary, both Boosting [14], [16] and Lasso [15], [17]

have limitations in ordinal feature selection and it is desirable

to develop a feature selection method with the following

properties.

1) The feature selection process can be formulated as a

simple optimization problem. Here “simple” means that

both the objective function and the constraint terms

can be deﬁned following a well-established standard

optimization problem. So that it is easy to obtain a global

solution of the feature selection problem.

2) A sparse solution can be achieved in feature selection

so that the selected feature set is compact for efﬁcient

storage, transmission and feature matching.

3) The penalty of misclassiﬁcation can not be a high-order

function of regression errors to control the inﬂuence of

outliers.

4) The model of feature selection should be ﬂexible to

take into account the characteristics of the biometric

recognition problem so that the genuine and imposter

matching results can be well separated from each other

and the selected image features are accurate in training

database.

5) The feature selection problem has less dependence on

the training data and it can be solved by a small set of

training samples. It requires the feature selection method

can circumvent the curse of dimensionality problem and

generalize to practical applications.

This paper proposes a novel feature selection method which

meets all requirements listed above. In our method, the fea-

ture selection process of ordinal measures is formulated as

a constrained optimization problem. Both the optimization

objective and the constraints are modeled as linear functions;

therefore linear programming (LP) can be used to efﬁciently

Fig. 2. Problem statement of ordinal feature selection in iris recognition.

solve the feature selection problem. The feature units used

for LP formulation are regional ordinal measures, which are

tested on the training dataset to generate both intra- and inter-

class matching samples. Our feature selection method aims at

ﬁnding a compact subset of ordinal features that minimizes

biometric recognition errors with large margin between intra-

and inter-class matching samples. The objective function of

our LP formulation includes two parts. The ﬁrst part measures

the misclassiﬁcation errors of training samples failing to

follow a large margin principle. And the second part indicates

weighted sparsity of ordinal feature units. Traditional sparse

representation uses L1-norm to achieve sparsity of feature

selection and all feature components have an identical unit

weight in sparse learning. However, we argue that it is better to

incorporate some prior information related to candidate feature

units into sparse representation so that the most individually

accurate ordinal measures are given preferential treatment.

And the linear inequality constraints of LP optimization prob-

lem require that all intra- and inter-class matching results are

well separated from each other with a large margin. Slack

variables are introduced to ensure the inequality constraints of

ambiguous and outlier samples.

III. F

EATURE SELECTION BASED ON

LINEAR PROGRAMMING

The objective of feature selection for biometric recognition

is to select a limited number of feature units from the candidate

feature set (Fig. 2). In this paper, a feature unit is deﬁned as

the regional ordinal encoding result using a speciﬁc ordinal

ﬁlter on a speciﬁc biometric region. We aim to use a machine

learning technique to ﬁnd the weights of all ordinal feature

units. So that feature selection can also be regarded as a

sparse representation method, i.e. most weight values are zero

and only a compact set of feature units have the weighted

contribution to biometric recognition.

In this paper, ordinal feature selection is formulated as a

constrained optimization problem as follows.

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