| For many applications in the field of computer vision, feature extraction is an important step. In particular, facial feature location is essential to many face recognition algorithms, which are affected by the accuracy and efficiency of landmarks extraction. In this paper, 2D and 3D facial feature extraction techniques for face recognition are summarized briefly and discussed separately. We propose a novel method for 2D facial key-points location, based on fractional differential. And for 3D facial feature extraction, a multi-model approach, that is 3D in conjunction with 2D,is developed.In the first part that discusses 2D facial landmarks detection mainly, we firstly demonstrate how introducing an edge detector based on fractional differential improves the criterion of edge features of 1D signal. According to the amplitude-frequency characteristics of classical fractional differential filter, we reach some conclusions: compared with the first-order derivative of a 1D signal, its fractional differentials with orders between 0 and 1 reserve lots of low-frequency information, and can not upgrade the high-frequency so intensely as the order 1. The function of fractional differentials with higher orders (more than 1) on 1D signal bears some analogy. For 2D signals, a 2D fractional differential filter is a high-pass filter in essence. However, different from first-order and second-order differential filters, it can upgrade the high-frequency and weaken the low-frequency information much more flexibly. We can achieve sub-optimal results by adjusting the changeable orders manually. This kind of property is very appropriate in 2D image processing, because, as 2D signal, the images' own changes possess a great diversity.But through an analysis of the classical fractional derivative function of a parabolic step-type luminance transition, we find that not only does the local-maximum of the derivative appear at the inflexion point of the transition, but it also appears in the right-stationary range. So false edges may be detected, thus the classical fractional differential filter for image's edge extraction is not very satisfactory. Considering that the aim is to improve inflexion point detection selectivity and have no response to the stable signal, we design a new operator, what may be called centre-symmetric fractional differential.According to some simple interpolation approximations, the above formula can be substituted by the following formula, which is expected to deal with the discrete signal. We make the new operator act on the parabolic step-type luminance transition given above. The results demonstrate that there is almost no response to the smooth section but significant response to the changeable range, especially at the inflection point. Then we discuss the derivative order of the new operator and arrive at some clues. The higher the order, the weaker the response to the high-frequency information. Affected by this inspiration, some centre-symmetric fractional differential masks for edge detection of 2D image with noise are designed, i. e. Where,The experiments show that the size and derivative order of the mask play an important rule on edge extraction. When the size is larger, the number of the pixels unprocessed in the image is increasing. The order has influence on the selectivity of edge detection. The edge will be thicker and become blur when the derivative order is becoming higher. In our experiments, the order between 0.5 and 0.8 with mask size between 5 and 7 is a good choice, and in this condition we can extract clear edges. For images with noise, the mask with relatively large size and high order is appropriate. In this paper, we make the size between 7 and 9, the order between 3.5 and 5.0. In short, we can access to relatively satisfactory results through adjusting two parameters of masks, i. e. size and order, for some images with acceptable noise.Then, when dealing with the human face image without good quality, a pre-processing would be better. In this process we make a classical fractional differential mask with low order act on the image. And then, the improved masks proposed in our paper are used in the second-step-processing. At last, we can extract feature counter lines in the processed binary image. For the location of feature points, we combine the processed image above with the corners sharp nature of facial key-points. The computational cost of the algorithm in this paper is very little. What's more, the experimental results also demonstrate the high accuracy of feature extraction and that this algorithm is suitable for handling face images with low quality.In the second part that discusses 3D facial landmarks detection mainly, a multi-modal method, i. e.3D geometric information combined with 2D texture information is proposed. Firstly, in order to determine face symmetric counter and nasal tip and further put right the face mask, 3D face mask is preprocessed. Then, we can obtain the 2D face analog photo through 3D face mask's positive projection. Using the integral projection, the 2D feature region of face picture obtained above is arrived at. Furthermore, the range of 3D landmarks can be reached through the indices that link the 3D points with the 2D pixels. The second, we give corner response factor based on MIC (minimum intensity change) and shape response factor from curvature as the quantitative indicators of 2D and 3D feature points separately. The more the value of corner response and the less the value of shape response, the higher likelihood of a feature point. So, the 3D feature points (eye and mouth corners) extraction algorithm follows. We just carry out the method in the feature region identified in the previous in order to narrow our search. For the 3D points within the region, their shape response values are calculated. The point can be reserved when its value of shape response is less than a certain threshold, and then we calculate corner response function of its corresponding pixel in 2D image. If the corner response is greater than some threshold, the 3D point should be retained as a candidate point. Next, we change the threshold value, and obtain the 3D shape response again. If there is only one point whose shape response value is less than the new threshold, we regard it as the feature point, otherwise the previous steps is repeated. In this process, 2D information and 3D information can be corrected with each other, which make up the defects from the uneven illumination in 2D image and glitches of 3D points set. As we use a method based on voronoi element to calculate the triangular mesh curvature and MIC to reach the 2D corner response, not only can our approach extract accurate facial key points, but also costs little, i. e. in line with the requirements of real-time. Our experiments also show these strong points. |
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