# A New Face Recognition Method for Intelligent Security
## 3 Related Work  
### Optimized Goldstein Branching Method  
The four-step phase-shift method is used as the demodulation method of the fringe phase in this paper, which modulates the grating fringe pattern projected onto the surface of the object, and then the phase unwrapping [22] is calculated. Common spatial phase algorithms for phase unwrapping include: row and column expansion, Goldstein branching [23], discrete cosine transform least squares (DCT), and Fourier transform least squares. Traditional Goldstein branching methods can eliminate the inconsistency of the phase unwrapping results due to the different integral paths and thus avoid the propagation of errors. However, the established branching tangent line is relatively long, and the phase may be incapable of unfolding due to the formation of a loop in areas with denser residual points. Therefore, to reduce the sum of the lengths of all branch tangent lines, we propose an improved Goldstein branching method, which combines the positive and negative residual points in the interferogram and uses the sum of the lengths of the tangent lines as the evaluation value to replace and re-establish the positive and negative residual points in the interferogram, which can effectively overcome the \"island phenomenon\" that is prone to occur in areas with denser residual points when the phase is unwrapped. The Goldstein branching method connects and balances the residual points on the interferogram to find the branching tangent lines that need to be avoided when the phase is unwrapped. When  
Figure 1: General process of face recognition. Figure 3: Overall flowchart of software. Figure 2: Hardware system block diagram. the strategy of connecting residual points to branches differs, the branching tangent lines differ, and phase unwrapping will also have different results. To create a better effect on phase unwrapping, the length of branching tangent lines should be as short as possible, and the connection distance between the positive and negative residual points should be short as well. The probability of residual point occurrence is 1/100 to 1/1000 of the two interference images with a correlation value between 0.3 and 0.5. Assuming that the number of positive and negative residual points is \(N\), then there are \(N!\) combinations. If the image is large, there will be many calculations for the optimal combination. The steps of the optimized Goldstein branching method are as follows:  
1. Identify the positive and negative residual points in the two-dimensional interferogram and mark the position of the residual points in the residual point map. 2. Take the positive residual point as the center and search within the radius of 5. If a negative residual point is found within the range, the pair of positive and negative residual points is defined as a \"near-point pair\". If there is not any corresponding negative residual point within the range, this positive residual point is defined as a \"far point\". 3. Center on the \"far point\" and gradually expand the search radius until all \"far points\" have found their negative residual points to become \"far point pairs\". 4. Take the positive residual point of the \"far point pair\" as the center and carry out the search again. The search radius here is the length of the branching tangent line of the \"far point pair\". Replace and re-establish all \"near-point pairs\" and \"far point pairs\" within the radius. The principle of replacement is based on whether the value of the function (fitness) is reduced, and the evaluation value (fitness) is shown in Equation (1). 5. If the evaluation value does not decrease after the replacement, replace the combination of the positive and negative residual points in the search radius and repeat step (4). 6. Perform steps (4) and (5) for all \"far point pairs\". As the fitness continues to decrease, the length of the branching tangent line also decreases.