Projection functions are specific types of geometric feature-based approaches that are used in finding intensity variation in an image and extracting the feature vectors. Geng et al.  used the variance projection function for iris localization. Despite the wide application of VPF and MIPF (Mean Integral Projection Function), both have their limitations. MIPF will fail when vertical and horizontal summations of the elements in searching area are unchanged, while VPF will fail in case of the same variance and different mean of the elements. Therefore, the landmarks that have relatively high contrast cannot be properly extracted. To overcome these problems, a new projection function which we called General Projection Function (GPF) is proposed by Bastanfard and Dehshibi . ...view middle of the document...
To identify the problem first must have an accurate definition about projection functions.
In the linear algebra, a projection is a linear transformation P from a vector space to itself such that P2 = P, i.e. it is idempotent. More precisely, an orthogonal projection operator on a vector space is any operator that maps each vector into its orthogonal projection on a hyper-plane (line in ℝ2 and plane in ℝ3) through the origin. (Refer to Figure 1a)
Figure 1(b) demonstrates that a projection functions is not one-to-one. Therefore, all distinct points on the same vertical line are mapped into the same point in the hyper-plane. This defect causes loss of structure in data and the feature extraction process may face problems. Figure 2 shows the result of applying projection function to an image X. As it is obvious, the main horizontal change in the picture occurs in line 3, but the projection cannot highlight that. The proposed method, Linear Principal Transformation, overcomes this weakness. LPT is a linear transformation, which maps a vector space V into a vector space W and highlights the main changes in the image.
3. LPT: Feature Localizer in N-Dimensional Image Space
In , fundamental challenges in the extraction of facial features are summarized in two issues including accuracy and power. Eckhardt et al.  mention that many feature extraction frameworks have been proposed so far, nonetheless, an algorithm that was appropriate for the operating environment, has not been provided. Those algorithms that focus on the power can estimate the position of features in different image conditions with low accuracy. In contrast, algorithms that concentrate on accuracy can extract the features of interest very effective, the number of false positive is high.