Information Technology Reference
In-Depth Information
The Gaussianized vector representation is closely connected to the classic his-
togram of keywords representation. In the traditional histogram representation, the
keywords are chosen by the k-means algorithm on all the features. Each feature
is distributed to a particular bin based on its distance to the cluster centroids. The
histogram representation obtains rough alignment between features vectors by as-
signing each to one of the histogram bins. Such a representation provides a natural
similarity measure between two images based on the difference between the corre-
sponding histograms. However, the histogram representation has some intrinsic limi-
tations. In particular, it is sensitive to feature outliers, the choice of bins, and the noise
level in the data. Besides, encoding high-dimensional feature vectors by a relatively
small codebook results in large quantization errors and loss of discriminability.
Gaussianized vector representation enhances the histogram representation in the
following ways. First, k-means clustering leverages the Euclidean distance, while
the GMM leverages the Mahamalobis distance by means of the component posteri-
ors. Second, k-means clustering assigns one single keyword to each feature vector,
while the Guassinized vector representation allows each feature vector to contribute
to multiple Gaussian components statistically. Third, histogram-of-keywords only
uses the number of feature vectors assigned to the histogram bins, while the Gaus-
sianized vector representation also engages the weighted mean of the features in
each component, leading to a more informative representation.
2.1
GMM for Feature Vector Distribution
We estimate a GMM for the distribution of all patch-based feature vectors in an im-
age. The estimated GMM is a compact description of the single image, less prone to
noise compared with the feature vectors. Yet, with increasing number of Gaussian
components, the GMM can be arbitrarily accurate in describing the underlying fea-
ture vector distribution. The Gaussian components impose an implicit multi-mode
structure of the feature vector distribution in the image. When the GMMs for dif-
ferent images are adapted from the same global GMM, the corresponding Gaussian
components imply certain correspondence.
In particular, we obtain one GMM for each image in the following way.
First, a global GMM is estimated using patch-based feature vectors extracted
from all training images, regardless of their labels. Here we denote
z
as a feature
vector, whose distribution is modeled by a GMM, a weighted linear combination of
K
unimodal Gaussian components,
K
k
=
1
w
k
N
(
z
; μ
global
k
p
(
z
;
Θ
)=
,
Σ
k
)
.
global
1
Θ
=
{
w
1
,
μ
,
Σ
1
, ···}
,
w
k
,
μ
k
and
Σ
k
are the weight, mean, and covariance ma-
trix of the
k
th Gaussian component,
Search WWH ::
Custom Search