Image Processing Reference

In-Depth Information

(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

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