Facial feature extraction is one of the most important challenges in the area of facial image processing. This step is the first in applications like Face Recognition , Facial Expression Recognition , Face Detection , Gender Classification , Age Classification , Animation  etc.
Facial feature extraction, in general, refers to the detection of eyes, mouth, nose and other important facial components. Various techniques have been proposed in the literatures for this purpose and can be mainly classified in four groups: geometric feature-based, template-based, color segmentation-based and appearance-based approaches.
In geometric feature-based approaches, the features are ...view middle of the document...
Methods such as Hidden Markov Model , SVM , and AdaBoost ,  are used to extract the feature vector containing the facial components. Although these methods have a good success rate, in one hand, they have a high training time and in the other hand, their accuracy depends on the diversity of test data.
Regarding facial feature extraction, there is a general agreement that says eyes are the most important facial features, thus a great research effort has been devoted to their detection and localization . This is due to several reasons, among which:
• Existence of eyes verifies that the interest object is human.
• Factors which influence on the face appearance have less affect on the appearance of eyes. For instance, the eyes are unaffected by the presence of facial hair, and are little altered by small in-depth rotations.
• Knowledge about the eyes’ position helps to estimate the face scale and degree of its in-plane rotation.
• Accurate localization of the eyes, allows identifying all other interest facial features.
Researchers utilize different methods to solve this problem. These methods include: filtering techniques , morphology operations , applying neural networks on color images , horizontal and vertical projections of the edge image , wavelet decompositions  or discrete cosine transformed mean subtracted face images . The success of AdaBoost for face detection  may have motivated    to apply AdaBoost to eye localization as well.
In the most literatures indicate that eye localization is not yet a solved problem. Due to this agreement, we concentrated our method on eye features localization. The proposed method is a linear one-to-one transform which works on an n-dimensional image space. The subsequent discussion has been organized into the following six sections: Section II explains the background of projection functions and their defects, Section III focuses on definition of the new n-dimensional space for representing an...