experimental results are reported only for academic research
without any commercial use.
Related Knowledge and Methods
2.1 Pre processing palmprint image s
Image preprocessing is a prerequisite for image retrieval and
recognition, especially for palmprints [15] and fingerprints [6].
Recognition results can be substantially improved via the
preprocessing procedure which can deal with many troubling
problems, e.g. rotation and translation alignment, region of
interest (ROI), and so forth. In this paper, the PolyU palmprint
database is used as test material for our method. The palmprint
images are captured by a CCD device [17], which can remove
rotation and translation phenomena to some extent. In addition,
in Ref. [15], a segmentation method was proposed for palmprint
images captured using CCD devices to obtain the regions of
interest. Thus, these methods are directly used in our paper. Fig. 1
shows an illustration of palmprint image preprocessing. The
obtained ROI contains 128|128 pixels with 256 gray levels per
pixel.
2.2 Image blur theory
Image blur can be considered to be equivalent to having a clear,
non-distorted image convoluted with a degradation function in the
spatial domain. The general concept is illustrated in Fig. 2. If the
image remains space-invariant in the process of degradation, we
can write
d i,jðÞ~f i,jðÞh i,jðÞzn(i,j) ð1Þ
where i,jðÞdenotes the position in the image, d i,jðÞthe blurred
image, f i,jðÞthe non-blurred image, h i,jðÞthe degradation
function, and n i,jðÞis additive noise. The operator ‘’ denotes
convolution.
We can see from Fig. 2 and Eq. (1) that h i,jðÞplays an
important role in the process of degradation. There are many
kinds of degradation function and in Ref. [24] Wang et al. list
several of the more common ones. The Gaussian defocus
degradation model (GDDM) is one of the most effective models
for simulating image blur, as proved by a large number of
researchers. GDDM is expressed using the following equation:
h x,yðÞ~
1
2ps
exp {
x
2
zy
2
2s
2
, ð2Þ
where s is the sampling width of the filter which controls the
degree of image degradation. As the value of s increases, image
degradation becomes more obvious and the image becomes more
blurred. In Ref. [25], several methods of evaluating blur are
defined which have proved to be effective and correct. Here, in
order to clearly show the relationship between blurriness and s,we
select one of those effective methods to use as our evaluation
standard, the Robert gradient energy (RGE). The definition of this
measure is described as follows
RGE~
X
i,j
Ii,jðÞ{Iiz1,jz1ðÞ
jj
z Iiz1,jðÞ{Ii,jz1ðÞ
jj
ðÞ: ð3Þ
Here, Ii,jðÞstands for the gray value of the image at position i,jðÞ.
The RGE value reflects the definition of the image. As the RGE
value increases, the image becomes sharper. Conversely, if the
RGE value wanes, the image becomes more blurred. If we use the
GDDM with different s values to simulate image blur, the
corresponding RGE values can be obtained to reflect the degree of
blurriness. Fig. 3 shows a ROI with different degrees of blurring
(i.e. different s values) and Fig. 4 shows the blurriness curve
corresponding to Fig. 3.
In Fig. 4, as the s value varies from 1 to 15, the RGE value
becomes smaller. However, when the s value is greater than 10,
the RGE value seems to be constant. Therefore, we can use the s
value (e.g. in the range from 1 to 10) to represent the blurriness of
an image. We considered this to be an approximate standard by
which to measure the level of blur in a palmprint in this paper.
2.3 VO decomposition model
Meyer pointed out that an image can be divided into a structure
layer and a texture layer using image decomposition. This can be
expressed as
f ~uzv, ð4Þ
where f is the original image, and u and v are the structure and
texture layers of the image, respectively. On this basis, Meyer [26]
introduced the concept of a G space which is substituted for the L
2
-
norm used in the total variation (TV) model to describe the
oscillating component of the image. This established the total
variation based on G space (TV–G) model for image decompo-
sition applications. The TV–G model is defined as follows
inf
u
E uðÞ~ +ujjzl vkk
G
,f ~uzv
: ð5Þ
In Eq. (5), the oscillating component of the image (which contains
texture and noise) is described using the G space.
Meyer did not propose a method for solving the corresponding
TV–G model. Therefore, based on Meyer’s thoughts, many
numerical methods were proposed to solve the TV–G model. The
results proved that G space is effective for describing the oscillating
component of images. Among these methods, Vese and Osher
Figure 3. The ROI with different degrees of blurring (
s
). (a)–(f) correspond to the ROI with blurring set to 1, 2, 3, 4, 5, and 6,
respectively.
doi:10.1371/journal.pone.0101866.g003
VO Model for Blurred Palmprint Recognition
PLOS ONE | www.plosone.org 3 July 2014 | Volume 9 | Issue 7 | e101866