Intra-Class Threshold Selection in Face Space Using Set Estimation Technique

Intra-Class Threshold Selection in Face Space Using Set Estimation Technique

Madhura Datta (University of Calcutta, India) and C. A. Murthy (Indian Statistical Institute, India)
Copyright: © 2011 |Pages: 16
DOI: 10.4018/978-1-61692-797-4.ch004
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Abstract

Most of the conventional face recognition algorithms are dissimilarity based, and for the sake of open and closed set classification one needs to put a proper threshold on the dissimilarity value. On the basis of the decision threshold, a biometric recognition system should be in a position to accept the query image as client or reject him as imposter. However, the selection of proper threshold of a given class in a dataset is an open question, as it is related to the difficulty levels dictated in face recognition problems. In this chapter, the authors have introduced a novel thresholding technique for a real life scenario where the query face image may not be present in the training database, i.e. often referred by the biometric researchers as the open test identification. The theoretical basis of the thresholding technique and its corresponding verification on several datasets has been successfully demonstrated in the article. The proposed threshold selection is based on statistical method of set estimation and is guided by minimal spanning tree. It has been found that the proposed technique performs better than the ROC curve based threshold selection mechanism.
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1. Introduction

A hypothetical face recognition task can be viewed in general as combinations of two phases i.e. face authentication or verification and face identification. Several evaluation protocols (Philips, 2003; Jain, 2004; Blackburn, 2004) have been designed earlier for measuring the performance of different existing algorithms. Among those popular methods, appearance based methods (Zhao, 2003; Moghaddam, 2004; Solar, 2005; Maltoni 2005) are generally based on dissimilarity, where the query image is either put in the class for which the dissimilarity is minimal or from which the maximum number of matches are found. This is a classical approach of identification and known as closed test identification where the test face always exists in the client database. However, in a real life scenario the identification system may face a situation where the query face image may not be present in the database, i.e. often referred by the biometric researchers as the open test identification. In case of open test identification the system should identify the face as imposter to the system. A way of achieving such a task is to put a threshold on the dissimilarity value at the identification stage. On the basis of the decision threshold, a biometric recognition system should be in a position to accept the query image as client or reject him as imposter. The problem of threshold selection in face recognition has not been properly understood. The understanding has been ambiguous, vague, and imprecise. That problem is modeled as a set estimation problem here. Modeling of ambiguous and imprecise phenomena is one of the subject matters of soft computing, though the usual soft computing techniques are not used here. Additionally, since the feelings of the authors are modeled mathematically, and the subject pertains to human beings, this method of selecting threshold in this article gives the flavor of Kansei Engineering.

Selection of proper threshold of a given class in a dataset is an open question, as it is related to the difficulty levels dictated in face recognition problems. A difficulty level is likely to change from situation to situation. In a face recognition problem for an ideal security system, three difficulty levels may be ascertained. These are (i) zero effort attack, (ii) minimal effort attack and (iii) organized effort attack. Depending on the demand imposed on security system, the difficulty levels are decided.

Mansfield (2002) used a method of selecting threshold based on false acceptance rate (FAR) and false rejection rate (FRR). FAR is defined as the percentage of images which are incorrectly matched by the system and FRR is the percentage of images which are rejected as unknown face images although they exist in the training set. The threshold value is determined using receiver operating characteristic (ROC) curve which in turn, is based on the different values of FAR and FRR. The point on the ROC curve that satisfies the condition of the equal error rate (EER), when FAR = FRR, is selected as the operating threshold for subsequent tests. Martin (1997) proposed the use of detection error trade-off (DET) curve which is nothing but a non-linear transformation of ROC curve. In principle, both the curves for threshold determination work well, if the threshold value is computed over a large number of test images. In practice, however, obtaining recognition results on a large number of test images is computationally expensive.

In any face recognition problem, the given query image may be attributed into one of the following categories with respect to the given training set. These categories are (a) the query image is a non face image, (b) the query image is a face image of a doll or statuette or some such object (c) the query image is that of a human being but no image of that person is in the training set and (d) at least an image of the person in the query image is in the training set. All that is needed for the purpose of face recognition is a procedure to obtain good estimates of FAR and FRR values. Finding a good estimate of FAR is not always possible, as we are supposed to cover ALL or at least a representative set of the images of objects or of living beings falling into categories (a), (b) and (c). In reality, a system can have extremely few examples of genuine access and relatively few imposter accesses as found in the literature. As a result user specific threshold selection is very unreliable to involve FAR and FRR. Again the common practice is to use the global threshold for a system rather than using user dependent versions of ROC.

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