Method of pulmonary fissure segmentation based on fuzzy distance transform
Su Gao
University Hospital
Beijing Normal University
Beijing, China
E-mail: gaosu@bnu.edu.cn
Liu Wang
School of Computer
Shenyang Aerospace University
Shenyang 110136, China
E-mail:22659488@qq.com
Abstract—A pulmonary fissure is a boundary between the
lobes in the pulmonary. The segmentation of it plays an
important role in the clinical diagnosis. This paper describes a
new method for the segmentation of pulmonary fissures. A
membership function and a threshold are firstly combined to
segment the contour of pulmonary fissures with fuzzy
boundaries. Then, fuzzy distance transform (FDT) is operated
on the contour image, and the ridges of FDT image accurately
indicate the pulmonary fissures. The key points of fissure are
determined by combining the local maximum of FDT image
and the local minimum gradient of FDT images. Finally, a
continuous pulmonary fissure is obtained by tracking the
maximal neighborhood points.
Keywords: Pulmonary fissure segmentation; Fuzzy
distance transform; Maximal neighborhood point
I. INTRODUCTION
With the emergence of new digital imaging technology,
images are widely used in various fields, and medical
images have a great advantage in diagnosis and treatment.
The computer-aided diagnostic (CAD) system is employed
to assist radiologists in their routine work. It automatically
analyzes CT images and achieves results of diagnosis for
many diseases.
The identification of fissures is crucial for
understanding the anatomy of pulmonary in CT images.
Pulmonary consists of left and right parts. The left
pulmonary has two lobes separated by a major fissure, and
the right one has three lobes separated by two fissures.
There are mainly two problems in the segmentation of
pulmonary fissures by use of thresholding[1,2]: (1) Because
the fissure is a tiny structure in the pulmonary, it is difficult
to find a suitable threshold to segment it. (2) A high noise
level with low contrast would cause a low performance for
the segmentation of pulmonary fissures.
Segmentation for fissures and lobes has attracted a large
of interest over the last few years, which are addressed in
refs.3-6. This paper proposes a new method to detect the
pulmonary fissures based on the fuzzy distance transform
and maximal neighborhood points tracking. Our method
firstly searches the contour of fissure by combining a
membership function and a threshold. Then, the locations
of the main points of fissure are determined by fuzzy
distance transform (FDT). Finally, the main points are
connected by tracking the maximal neighborhood points.
II. FUZZY DISTANCE TRANSFORM
Distance transform (DT) is widely used in target
recognition and image processing. For a binary object, DT
is a process that assigns a value to each location within the
object, which is the shortest distance between the location
and background. However, DT cannot be applied to fuzzy
objects effectively. The notion of DT for a fuzzy object is
called fuzzy distance transform (FDT)[7]. FDT is operated
on a gray image, and it considers the intensity and distance
simultaneously. FDT can be applied in more fields by use
of a membership function, and it is a minimum length of
path between two points in a fuzzy set[8].
Rutovitz proposes a notion of gray-weighted distance in
1968. Later, Saha develops FDT in terms of it. FDT
describes the length of the shortest path between the point p
and q. We will give you some related knowledge about
FDT.
A. Fuzzy subset and membership function
Zadeh proposes a definition of a fuzzy set in 1965. Let
X is a set, and a fuzzy subset A of X is defined as:
{( , ( )) | }, ( ) : [0,1]AAAxxxX xX
μμ
=∈ →
(1)
Where
()A
is the membership function of A.
B. Fuzzy distance between adjacent points
A distance between two adjacent point s p and q in a
fuzzy subset is no longer calculated in terms of Euclidean
distance. A path
π
in a set A from p to q consists of a
sequent points
1, 2,,mppp p q=="
. Where i
A∈
,
1 im≤≤
.
p
is next to
1j
+
.The length of these two
adjacent points is defined as:
() ()()
qpqp −×+ ΟΟ
μμ
2
1
(2)
Where
⋅
denotes the spatial Euclidean distance. In our
study, we used the
1, 2
distance. If p and q are neighbors
in the vertical direction,
⋅
is equal to 1. If they are vertex
neighbors,
⋅
is equal to
2
. We also can use other
2014 International Conference on Virtual Reality and Visualization
978-1-4799-6854-1/14 $31.00 © 2014 IEEE
DOI 10.1109/ICVRV.2014.60
339