Digital Signal Processing Reference
In-Depth Information
x
j
,
y
j
)
placed and
(
is the location of the document. Besides the word value
w
ji
,the
location
(
x
i
,
y
i
)
and image index
g
i
of a word
i
are observed and stored in variable
c
i
=(
g
i
,
x
i
,
y
i
)
. The generative procedure is as following:
1. For a topic
k
, a multinomial parameter
φ
k
is sampled from Dirichlet prior
φ
k
∼
.
2. For a document
j
, a multinomial parameter
Dir
(
β
)
π
j
over the
K
topics is sampled from
.
3. For a word (image patch)
i
, a random variable
d
i
is sampled from prior
p
Dirichlet prior
π
j
∼
Dir
(
α
)
(
d
i
|
η
)
indicating to which document word
i
is assigned. We choose
p
(
d
i
|
η
)
as a uniform
prior.
4. The
image
index
and
location
of
word
i
are
sampled
from
distribution
c
d
i
,
σ
)
(
|
p
c
i
. We may choose this as a Gaussian kernel.
⎨
⎬
x
d
i
−
x
i
2
y
d
i
−
y
i
2
p
g
d
i
,
y
d
i
+
x
d
i
,
(
g
i
,
x
i
,
y
i
)
,
σ
∝ δ
g
d
i
(
g
i
)
exp
−
,
⎩
2
⎭
σ
c
d
i
,
σ
)=
0 if the word and the document are not in the same image.
5. The topic label
z
i
of word
i
is sampled from the discrete distribution of document
d
i
,
z
i
∼
p
(
c
i
|
.
6. The value
w
i
of word
i
is sampled from the discrete distribution of topic
z
i
,
w
i
∼
Discrete
Discrete
(
π
d
i
)
(
φ
z
i
)
.
In [
11
] both LDA and SLDA were evaluated on the MSRC data set [
2
] with
240 images for object segmentation. The detection rate and false alarm rate of four
classes (cows, cars, faces, and bicycles) are shown in Table
3.2
. Some examples
are shown in Fig.
3.11
. The segmentation results of LDA were noisy since spatial
information was not considered. The patches in the same image were likely to have
the same labels. SLDA achieved better results.
In [
11
] SLDA was also used to segment objects from a video sequence. All the
frames were treated as a collection of images and their temporal order was ignored.
Figure
3.12
shows results on two sampled frames. LDA could not segment out any
objects. SLDA clustered image patches into tigers, rock, water, and grass.
Tabl e 3. 2
Detection(Det) rate and False Alarm (FA) rate of LDA and SLDA on MSRC [
2
]. The
results are from [
11
]
Cows
Cars
Faces
Bicycles
Det rate
FA rate
Det rate
FA rate
Det rate
FA rate
Det rate
FA rate
LDA
0.3755
0.5576
0.5552
0.3963
0.7172
0.5862
0.5563
0.5285
SLDA
0.5662
0.0334
0.6838
0.2437
0.6973
0.3714
0.5661
0.4217
