10-04-2017, 09:26 PM
feature extraction using curvelet transform
Introduction
Designing a completely automatic and efficient face recognition system is a grand challenge for biometrics, computer vision and pattern recognition researchers. Generally, such a recognition system is able to perform three subtasks: face detection, feature extraction and classification. We ll put our focus on feature extraction, the crucial step prior to classification. The key issue here is to construct a representative feature set that can enhance system-performance both in terms of accuracy and speed. At the core of machine recognition of human faces is the extraction of proper features. Direct use of pixel values as features is not possible due to huge dimensionality of the faces. Traditionally, Principal Component Analysis (PCA) is employed to obtain a lower dimensional representation of the data in the standard eigenface based methods [Turk and Pentland 1991]. Though this approach is useful, it suffers from high computational load and fails to well-reflect the correlation of facial features. The modern trend is to perform multiresolution analysis of images. This way, several problems like, deformation of images due to in-plane rotation, illumination variation and expression changes can be handled with less difficulty.Multiresolution ideas have been widely used in the field of face recognition. The most popular multiresolution analysis tool is the Wavelet Transform. In wavelet analysis an image is usually decomposed at different scales and orientations using a wavelet basis vector. Thereafter, the component corresponding to maximum variance is subjected to further operation . Often this further operation includes some dimension reduction before feeding the coefficients to classifiers like Support Vector Machine (SVM), Neural Network (NN) and Nearest Neighbor. This way, a compact representation of the facial images can be achieved and the effect of variable facial appearances on the classification systems can also be reduced. The wide-spread popularity of wavelets has stirred researchers interest in multiresolution and harmonic analysis. Following the success of wavelets, a series of multiresolution, multidimensional tools, namely contourlet, curvelet, ridgelet have been developed in the past few years. In this chapter, we ll concentrate on Digital Curvelet Transform. First, the theory of curvelet transform will be discussed in brief. Then we'll talk about the potential of curvelets as a feature descriptor, looking particularly into the problem of image-based face recognition. Some experimental results from recent scientific works will be provided for ready reference
Face Recognition has been studied for over 20 years in computer vision. Since thebeginning of the 1990s, the subject has become a major issue, mainly due to theimportant real-world applications of face recognition like smart surveillance, secureaccess, telecommunications, digital libraries and medicine. Faces are very specificobjects whose most common appearance (frontal faces) roughly look alike but subtlechanges make the faces different.The different face recognition techniques have been discussed in the work of Zhaoet al [1]. In the recent years, the success of wavelets in other branches of computervision, inspired face recognition researchers to apply wavelet based multiresolutiontechniques for face recognition [2, 3].Over the past two decades, following wavelets, other multiresolution tools likecontourlets [4] , ridgelets [5] and curvelets [6], to name a few, were developed. Thesetools have better directional decomposition capabilities than wavelets. These newtechniques were used for image processing problems like image compression [7] anddenoising [8], but not for addressing problems related to computer vision.In some recent works, Majumdar showed that a new multiresolution tool curvelets can serve as bases for pattern recognition problems. Using curvelets, heobtained very good results for character recognition [9]. In a comparative study [10]Majumdar showed that curvelets can indeed supersede wavelets as bases for facerecognition. In this paper we propose to go one step further towards a curvelet based face recognition system by fusing results from multiple classifiers trained withcurvelets coefficients from images having different gray scale resolutions.In Section 2 Curvelet Transform and our proposed feature extraction technique willbe discussed. A brief overview of Support Vector Machine (SVM), the classifier wehave used is given in Section 3. In Section 4 the three databases we have carried outour experiments on are covered. Finally, Section 5 lists the experimental results andSection 6 concludes the future prospects of this technique.
2 Curvelet Based Feature Extraction
Wavelets and related classical multiresolution ideas exploit a limited dictionary madeup of roughly isotropic elements occurring at all scales and locations. Thesedictionaries do not exhibit highly anisotropic elements and there are only a fixednumber of directional elements (The usual orthogonal wavelet transforms havewavelets with primarily vertical, primarily horizontal and primarily diagonalorientations), independent of scale. Images do not always exhibit isotropic scaling andthus call for other kinds of multi-scale representation.Computer Vision researchers of the 80s and early 90 s [11, 12] were inspired bytwo biological properties of the visual cortex, that it functions in a) multi-scale b)mutli-orientational mode. The multi-scale aspect has been captured by the scale-spaceanalysis as well as wavelet transform. However standard wavelet transforms for two-dimensional functions f(x1, x2) have only very crude capabilities to resolve directionalfeatures. The limitations of the wavelet transform inspired the vision researchers tofind new transforms proposed that had improved directional representation; such as the Steerable Pyramids and Cortex Transforms . Curvelet transform by Candes andDonoho [6] is the latest multi-directional multi-scale transform.Field and Olshausen [13] did set up a computer experiment for empiricallydiscovering the basis that best represents a database of 16 by 16 image patches.Although this experiment is limited in scale, they discovered that the best basis is acollection of needle shaped filters occurring at various scales, locations andorientations. The interested reader will find a stark similarity between curvelets,which derive from mathematical analysis, and these empirical basis elements arisingfrom data analysis [14].It is not possible to go into the details of digital curvelet transform within thispaper. The interested reader can refer to the works of Candes and Donoho [16]. Abrief procedural definition of curvelet transform is provided here for ready reference.
Curvelets are good at representing edge discontinuities in two dimensionalfunctions. In this work we will exploit this property of curvelets in a novel way forfacial feature extraction. Human faces are three dimensional objects that arerepresented in two-dimensions in ordinary images. As a result when a face isphotographed different parts of the face reflect the incident light differently and wefind differential shades in the face image. We, human beings are able to get a roughidea of the three-dimensional structure from this differential shades.Black and white digital images are represented in 8 bits or 16 bits resulting in 256or 65536 gray levels. Let us suppose that the images are represented by 256 graylevels (actually the image databases we used are all 8 bit images). In such an imagetwo very near regions in can have differing pixel values. Such a gray scale image willhave a lot of edges and consequently the curvelet transform will capture this edgeinformation. But if we quantize the gray levels, say to 128 or 64, nearby regions thathad very little differences in pixel values and formed edges in the original 256 bitimage will be merged and as a result only more bold edges in face image will berepresented. Now if these gray-level quantized images are curvelet transformed, thetransformed domain coefficients will contain information of these bolder curves.Images of the same person from the AT&T face database, quantized to 4 bits and 2bits from the original 8 bit representation are shown below.
Support Vector Classification
Support Vector Machine (SVM) [17] models are a close cousin to classical neuralnetworks. Using a kernel function, SVM s are an alternative training method forpolynomial, radial basis function and multi-layer perceptron classifiers in which theweights of the network are found by solving a quadratic programming problem withlinear constraints, rather than by solving a non-convex, unconstrained minimizationproblem as in standard neural network training.The two most popular approaches are the One-Against-All (OAA) Method and theOne-Against-One (OAO) Method. For our purpose we used a One-Against-All(OAA) SVM because it constructs g binary classifiers as against g(g-1)/2 classifiersrequired for One-Against-One SVM while addressing a g class problem.
Face recognition has been studied extensively for more than 20 years now. Since the beginning of 90s the subject has became a major issue. This technology is used in many important real-world applications, such as video surveillance, smart cards, database security, internet and intranet access. This report reviews recent two algorithms for face recognition which take advantage of a relatively new multiscale geometric analysis tool - Curvelet transform, for facial processing and feature extraction. This transform proves to be efficient especially due to its good ability to detect curves and lines, which characterize the human's face. An algorithm which is based on the two algorithms mentioned above is proposed, and its performance is evaluated on three data bases of faces: AT&T (ORL), Essex Grimace and Georgia-Tech. k-nearest neighbour (k-NN) and Support vector machine (SVM) classifiers are used, along with Principal Component Analysis (PCA) for dimensionality reduction. This algorithm shows good results, and it even outperforms other algorithms in some cases.
Curvelet Transform
Before getting started with curvelet transform, the reader is suggested to go through the theory of multiresolution analysis, especially wavelet transform. Once the basic idea of wavelets and multiresolution analysis is understood, curvelets will be easier to comprehend.
Theory and Implementation
Motivated by the need of image analysis, Candes and Donoho developed curvelet transform in 2000 [Candes and Donoho 2000]. Curvelet transform has a highly redundant dictionary which can provide sparse representation of signals that have edges along regular curve. Initial construction of curvelet was redesigned later and was re-introduced as Fast Digital Curvelet Transform (FDCT) [Candes et al. 2006]. This second generation curvelet transform is meant to be simpler to understand and use. It is also faster and less redundant compared to its first generation version. Curvelet transform is defined in both continuous and digital domain and for higher dimensions. Since image-based feature extraction requires only 2D FDCT, we ll restrict our discussion to the same.