Finding Faces in Gray Scale Images Using Locally Linear ... - CiteSeerX

Finding Faces in Gray Scale Images Using Locally Linear Embeddings Samuel Kadoury1 and Martin D. Levine1 1

McGill University, Department of Electrical and Computer Engineering, 3480 University Street, H3A 2A7, Montreal, Canada

{sakad, levine}@cim.mcgill.ca

Abstract. The problem of face detection remains challenging because faces are non-rigid objects that have a high degree of variability with respect to head rotation, illumination, facial expression, occlusion, and aging. A novel technique that is gaining in popularity, known as Locally Linear Embedding (LLE), performs dimensionality reduction on data for learning and classification purposes. This paper presents a novel approach to the face detection problem by applying the LLE algorithm to 2D facial images to obtain their representation in a subspace under the specific conditions stated above. The low-dimensional data are then used to train Support Vector Machine (SVM) classifiers to label windows in images as being either face or non-face. Six different databases of cropped facial images, corresponding to variations in head rotation, illumination, facial expression, occlusion and aging, were used to train and test the classifiers. Experimental results obtained demonstrated that the performance of the proposed method was similar and sometimes better when compared to other face detection methods, while using a lower amount of training images, thus indicating a viable and accurate technique.

1 Introduction Human face detection has been researched extensively in the past decade due to the recent emergence of applications such as secure access control, visual surveillance, content-based information retrieval, and human/computer interaction. It is also the crucial first task performed in a face recognition system. Simply put, face detection is a two-class decision problem to discriminate facial patterns from background (“nonfaces”) at every location in an image. This is a challenging task because of the high degree of variability in factors that radically change the appearance of the face [1]. This paper proposes an appearance-based method that detects faces subject to a variety of significant conditions present in a static 2D grayscale image defined in a space of dimension D. These conditions include extreme variations in head rotation, illumination, facial expression, occlusion and aging. The approach is predicated on the hypothesis that the LLE method will intrinsically model the face for each of the six individual variations if a specific database that emphasizes a single particular characteris-

tic is used for training. Once the facial data are transformed into a lower-dimensional space d, Support Vector Regression (SVR) is used to define a mapping from the input to the output space for these data. Thus, the SVR provides a new way to compute the location of a point in d-space, given its location in the input D-space. We demonstrate experimentally that, if this very same SVR is used to map previously unseen non-face data, the latter will in general be clustered separately with respect to the specific facial data. An SVM is then used to classify new input patterns as being face or non-face. Six such classifiers were trained using six different databases that were built using different sources. The six decisions were then fused to provide a final decision. Experimental results obtained on common image databases currently referenced in the literature demonstrated that the performance of the proposed method is similar and sometimes better when compared to other face detection methods. The approach described in this paper has the advantage of using significantly less training images than other methods since LLE efficiently models the face space.

2 Locally Linear Embedding (LLE) LLE was designed to solve the problem of many dimensionality reduction methods [2], such as PCA or Multi-Dimensional Scaling (MDS) [3], which would map faraway non-face images to nearby points in the face domain, creating distortions both in the local and global geometry. LLE succeeds by computing a low-dimensional embedding of high-dimensionality data assumed to lie on a non-linear manifold, with the property that nearby face images in the high dimensional space remain nearby, and similarly remain co-located with respect to one another in the low dimensional space.

2.1 LLE algorithm The LLE transformation algorithm is based on simple geometric intuitions, where the input data consist of N points Xi, Xi ∈ RD, i∈[1,N], each of dimensionality D, which were obtained by sampling an underlying manifold. As an output, it provides N points Yi, Yi ∈ Rd, i∈[1,N] where d