Digital Signal Processing Reference
In-Depth Information
appearance models for the foreground/background classes can be then learned. Other
works considered both supervised and unsupervised scenarios and the problem of co-
segmentation was focused to detect multiple foreground objects while proposing less
restrictive techniques based on a number of properties such as optimality guarantee
and linear complexity [9]. In this paper, we are interested in the unsupervised co-
segmentation of an image pair. We formulate co-segmentation as an energy
minimization problem based on binary labeling (foreground
vs.
background). Thus,
solving this problem returns to minimize an energy function, which evaluates the
similarity between foreground objects by considering three terms: an intrinsic data
term relating to the two processed images, a smoothness term which promotes a
smooth segmentation of each image, and a correspondence term which penalizes the
dissimilarity between foreground objects in the input images. To assess this
correspondence, which strongly influences the final results, existing techniques
simply compare the intensity histograms without considering the spatial coherence of
neighboring pixels. For this, we propose to integrate the spatial information, by using
the local-entropy during the histogram computing, in order to avoid false detections.
Besides, we proposed a fuzzy classification technique in order to model the ambiguity
of a pixel membership to a histogram bin, especially for pixels on bins' borders. This
permits to optimize the final co-segmentation results, while minimizing noise effects.
The rest of this paper is organized as follows.
In Section 2, we describe the proposed
technique based on fuzzy local-entropy classification. We show the experimental
results in Section 3 and we produce conclusions and perspectives in Section 4
.
2
Proposed Technique
As the co-segmentation goal is to segment common foreground objects from two
images, we start by detecting the correspondence of these objects, which strongly
influences the final results. Thus, given two images,
I
1
and
I
2
,of the same size
M×N
, the
first step in the proposed technique consists to define the local-entropy for each color
channel
C
i
of each image
I
i
(
C
∈
{R,G,B}
and
i
∈
{1,2}
). This is done while considering the
neighborhood of each pixel in order to characterize the texture of the input images,
which provides information about the local variability of the intensity values. The
objective behind the consideration of the local entropy
EC
i
(j)
of each pixel
j
in the color
channel
C
i
, instead of its intensity, is to integrate the spatial information since
neighboring pixels should have in general the same behavior (foreground
vs.
background), what allows particularly to avoid isolated pixels on the co-segmentation
results (
c.f.
Section 3.).
Given the number
K
of bins in the first image, each pixel is then
associated to one of the
K
bins of the corresponding histogram, while producing the
centers of bins to the second image in order to obtain the same classes for both images
(Fig. 2). Then, for each color channel
C
i
, we define a binary matrix
HEC
i
(2) of size
K×S
where
S(=M.N)
denotes the number of pixels in
C
i
.
∀∈
jC
,
∀ ∈
k
{1,...,
K HECjk
},
( ,
)
=
1
⇔
ECj H
( )
∈
,
(2)
i
i
i
k
