Digital Signal Processing Reference
In-Depth Information
dictionary and the foreground is sparse in the sense that majority pixels of the frame
belong to the background. The given frame
x
can be decomposed into sparse coded
background
x
B
=
D
α
and a sparse foreground
x
F
=
x
−
D
α
The foreground objects are not only sparse but also have grouped pixels i.e. the
foreground pixels are spatially correlated which is calculated by confidence score
given below
x
F
(
x
F
(
score
(
i
)
=
i
)
+
j
)
j
∈
Neighbor
(
i
)
The dictionary is formed by collecting a few background training samples. It is not
robust to outliers when the training samples contains foreground objects. To make
the learning algorithm robust against outliers, a Robust Dictionary Learning (RDL)
approach is developed. In matrix factorization form,
X
=
DA
+
E
where,
X
is the matrix of training data each stacked as a column,
A
is the matrix of
coefficient vectors stacked in a similar way,
E
is a sparse matrix of outliers and
D
is
the dictionary given by
1
+
λ
1
D
=
arg min
D
X
−
DA
A
,
A
D and A optimized by keeping each other constant known as robust sparse coding
and robust dictionary update.
Table
12.2
shows different PCA methods which have been discussed earlier.
12.4.2 Background Modeling Using Independent
Component Analysis
Independent Component Analysis (ICA) is a statistical data analysis method which
finds application in Image Processing and Computer Vision [
58
]. The input images
observed by stationary cameras consists of the background and moving objects, so
we can consider a particular image in an image sequence as the sum of a reference
image containing the background and a difference image containing the moving
objects, but not the background. The reference image and difference images can be
obtained as the independent components of input images by ICA. ICA generalizes
the technique of Principal Component Analysis (PCA) and has also proven to be a
good tool of feature extraction.
