A local feature-based facial expression recognition system from depth video - Emerging Trends in Image Processing, Computer Vision, and Pattern Recognition - page 342

(2)
where n is the number of the LDP histogram bins (normally n = 256) for an image I . Then, the
histogram of the LDP map is presented as
(3)
To describe the LDP features, a depth silhouete image is divided into nonoverlapping rect-
angle regions and the histogram is computed for each region. Furthermore, the whole LDP
feature F is expressed as a concatenated sequence of histograms
(4)
where s represents the number of nonoverlapped regions in the image. After analyzing the
LDP features of all the face depth images, there are some positions from all the positions cor-
responding to all the face images have values > 0 and hence these positions can be ignored.
Thus, the LDP features from the depth faces can be represented as D .
3.2 PCA on LDP Features
PCA is very popular method to be used for data dimension reduction. PCA is a subspace pro-
jection method which transforms the high-dimensional space to a reduced space maintaining
the maximum variability. The principal components of the covariance data matrix Y of the
LDP features D can be calculated as
(5)
where λ represents the eigenvalue matrix and P the eigenvector matrix. The eigenvector as-
sociated with the top eigenvalue means the axis of maximum variance and the next one with
the second largest eigenvalue indicates the axis of second largest variance and so on. Thus, m