Determination of 3-D Image Viewpoint Using Modified Nearest Feature Line Method in Its Eigenspace Domain

Since viewpoint is one of the important information in face recognition system, a viewpoint estimation system is developed to determine the pose position of the 3-D human face images. The system is developed using projection of an unknown viewpoint of a spatial image into its eigenspace representation and calculated its distances to all of available lines connection between every two known viewpoints. We then developed FullyK-LT and SubsetK-LT methods, in order to transform the images from its spatial domain into eigenspace representation. In this paper, we propose a new method that modified the Nearest Feature Line method by adding more feature lines that can be acquired from the projections of every feature point to other feature lines. The developed system is then applied to determine the pose position of 3-D human face of Indonesian people in various positions and expressions. Using our method, it is proved that the increment number of feature lines improved the recognition rate significantly; due to it provide more feature information of an object. The experimental results shown that the highest recognition rate is 96.64% for SubsetK-LT using our Modified Nearest Feature Line method. Key words: Viewpoint recognition system, Feature-line method, Karhunen-Loeve Transformation 1 Introduction The growth of multimedia technology has triggered the needs of 3-D face recognition systems. Face identification is very important problem in law enforcement and forensics, authentication of access into building or automatic transaction machine, and searching for faces in video databases, intelligent user interfaces and others. This face recognition system can hopefully recognize 3-D human face images with various features, such as viewpoints changes, lighting, expression, etc [1]-[4]. Several methods, such as combined feature and template matching [2], template matching using Karhunen-Loeve transformation of large set of face images [3], have developed by many researchers, and good results can be obtained, especially for 2-D frontal or semi-frontal images. Since it is argued that 3-D recognition can also be accomplished by using linear combinations of as few as four or five 2-D viewpoint images [5,6], many researchers are trying to recognize more general view positions of images that cover the entire 3-D viewing sphere. We have developed a 3-D face recognition system using a cylindrical structure of hidden layer neural network [7]. However, since the viewpoints of the given image is a priori unknown, we have assume that the face viewpoints of the given image is already known, which in turn, gave high recognition rate of the developed system [8, 9]. Since these viewpoints are such important information for the 3D face recognition system, we develop pose position or viewpoints estimation system, to determine the pose position of the 2-D image correctly [10]. In this paper, we proposed a new method to estimate the viewpoint of 3-D objects that can also be used as a subsystem in our developed 3-D face recognition system. The developed viewpoint estimation system consists of a viewpoint features extraction subsystem that define the feature-space of the used system, and the viewpoint estimation subsystem that clustered the unknown viewpoint input face by comparing with viewpoints of faces which are stored in a gallery. In the viewpoint features extraction subsystem, a feature-space is developed based on transforming every face in the spatial domain as a vector in the feature-space. As already written in [10], the authors have introduced two kinds of transformation methods, i e the Fully K-LT method and Subset K-LT method as the transformation procedures. Fully K-LT method is the Karhunen-Loeve transformation technique that transforms all of the model images into only one eigenspace, while in Subset K-LT method; every group of images that lies in the same viewpoint will be transformed into every one-subeigenspace. By using this method, we can have many sub-eigenspace related with the number of viewpoints images. In viewpoint recognition subsystem, a Nearest Feature Line method [11] will be used to cluster the unknown viewpoints of images by calculating its nearest distance with all of the feature points. The Nearest Feature Line (NFL) method assumes that at least we should have two feature points of each viewpoint class, and a line that can be draw between two points could represents some changes of faces due to lighting, expression, etc. When there is an unknown face that would be determined its view position, it should be firstly transformed into its eigenspace representation by the K-L transformation. Clustering is then determined by calculating the nearest distance of the transformedunknown point into all available feature lines in the eigenspace. We have proved that by using the conventional NFL techniques, the estimation rate of the system is not high enough. We then developed Subset K-LT method to increase the estimation rate of the system. In order to further increase the viewpoint estimation rate of the system, we propose, in this paper, a new technique of increasing the number of feature lines without making any addition of the number of feature points. The increment of feature lines are accomplished by creating projection lines from each feature point to the other feature lines in the same class. The detail explanation about this technique including with its results will be discussed thoroughly in the next sessions. 2 Feature Extraction Subsystem In this feature extraction subsystem, we use the Karhunen-Loeve transformation to develop a featurespace for higher discrimination power. KarhunenLoeve transformation means to orthogonalize, which in turns increasing the separability of the extracted feature, and reducing its dimensionality [12]. This transformation will be used to project every image in the face gallery, into a feature point that has a smaller vector dimension. As we have discussed earlier in this paper, the transformation process for image vectors is accomplished by the use the two kinds of KarhunenLoeve transformation methods. In the Fully K-LT method, the unknown images that will be estimated its viewpoint should be projected into only one eigenspace. However, when using Subset K-LT method, we should firstly determine the matrix transformation of every viewpoint-class of the images. Suppose we have a class images with a viewpoints of 15, then an eigenspace of 15 is constructed by using all of the images in this viewpoint-class. And this procedure is repeated until all sub-eigenspaces of all viewpoints of the images are completely constructed. Using Subset K-LT method, therefore, the unknown images that will be estimated its viewpoint should be projected into all of the available eigenspaces. By using these two different methods, each image in spatial space is now represented as a feature point in only one eigenspace for Fully K-LT method or as a feature point in every one of the subeigenspaces for Subset K-LT method. The standard analysis using its principal components of image data x(k) ∈ R, k=0,1,. ,m is done by determining a set of hidden linear representation parameters y1(k), . , ym(k), called factors or features. These features could then be used for linear least mean-squared-error reconstruction of the original data. If there is enough correlation between the observation variables x1(k), then we can reconstruct the image with acceptable accuracy using a number of features m which is much smaller than the data dimension n. We often call n is the superficial dimensionality of the image data while m the intrinsic dimensionality of the image data. The Karhunen-Loeve transformation method is firstly done by forming a base vector of image in d dimensions, i.e., zn=[z1,z2, zd]. The next step is computing the average vector of M images through: