Literature reading 002 "Intensive reading"

2002 ICIP face photo recognition using sketch
NET disk link password: if7l

0. ABSTRACT
1. INTRODUCTION
2. SKETCH recognition
   2.1 Conventional Eigenface Method
   2.2 Eigensketch Transformation
3. Experiments
4. SUMMARY

2.1. Conventional Eigenface Method
Eigenface method is one of the effective methods of face recognition, and it shows good performance in Feret (Face database) test.
The method uses KLT (Karhunen-loeve Transform) to extract the representative features of human faces, which is also called PCA method.
PCA algorithm:

输入：样本集D={x1,x2,...,xm}, 低维维数k过程：1.数据中心化/归一化： xi = xi - μi2.计算协方差矩阵： XX^T3.对XX^T做奇异值分解4.取前k个最大的特征值对应的特征向量w1,w2,...,wk输出：投影矩阵W={w1,w2,...,wk}

Qi represents the vector of an image (column vector), Qu represents the mean, and the following is centralized/normalized:


P for all sample vectors normalized and then combined (training set) of the Matrix, W is the covariance matrix (covariance matrix):

By singular value decomposition (SVD), the Matrix VP of eigenvectors is obtained, and the λp of the eigenvalues is composed of diagonal matrices.

Here's a place to "notice": Because W is the N-order matrix (n is the total number of pixels of the image, that is, the length of the Pi), the computational amount is too large for it to be directly SVD. So we can start with the W transpose SVD, because P is nxm matrix, M is the number of vectors (that is, training and size), m<<n, so the computational amount is greatly reduced.

Both sides simultaneously left multiply P:


– Standard orthogonal matrix for ppt:
– We are using SVD to find the PTP standard orthogonal matrix, namely VP,VP-1=VPT. What we are asking for is the standard orthogonal matrix of PPT, such as the above equation, we cannot guarantee that PvP is a standard orthogonal matrix, so we should be able to verify the epept=i by the following standard orthogonality.

Therefore, for a new picture PK, after the conversion of the EP, get the feature vector BP:

2.2. Eigensketch transformation
For the above equation, both sides of the same time to the left by EP, because EP is a standard orthogonal matrix, there is PK=EP*BP, but after the EP dimensionality reduction, the equal sign here is actually a loss, so remember PK for PR, that is, the reconstructed photo:

To substitute EP into:


– What is the relationship between CP and PK here?
Have CP is associated with BP, while BP=EP^TPK.
So we can make a linear combination of the original sample set to approximate the new picture:

In the same vein, we reconstructed the sketch primitive (sketch) in this linear combination as well:

2 (Figure2), we obtain a linear combination of CP from (a), (b), and then use the linear combination (d), (c).

3. Experiments
Use 188 pairs of different faces of the original and sketch map (Photo-sketch pairs).
Training set: Photo-sketch pairs
Test set: Photo-sketch pairs
At the same time, three sets of different methods were compared, namely: Geometrical method (geometry), traditional method (conventional), and the method of this paper.
The test uses FERET test protocol (a face recognition algorithm) to set photo as gallery Set,sketch as probe set. Calculate the similarity, as in the following table.

Similarity calculation process:
Select a PHOTO:PK from the gallery set of the test set, use the 88 photos of the training set to reconstruct the PR, find the CP, and then use the CP to combine the sketches of the training set to represent SR ', finally with the probe of the test set The sketches in set is compared and the similarity is calculated. Such as:

FERET Sep96 Protocol RELATED links:
The_feret_verification_testing_protocol_for_face_recognition_algorithms

Literature reading 002 "Intensive reading"