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THÔNG TIN TÀI LIỆU
Nội dung
SEGMENTATION OF DIFFERENTIAL
INTERFERENCE CONTRAST CELL IMAGE
TU YAJING
(B.S (Hons.), Beihang University)
A THESIS SUBMITTED
FOR THE DEGREE OF MASTER OF
SCIENCE
DEPARTMENT OF BIOLOGICAL SCIENCE
NATIONAL UNIVERSITY OF SINGPAORE
2012
Declaration
I hereby declare that this thesis is my original work
and it has been written by me in its entirety.
I have duly acknowledged all the sources of
information which have been used in the thesis.
This thesis has also not been submitted for any
degree in any university previously.
____________________________
Tu Yajing
30 May 2012
Acknowledgements
I would like to thank my supervisor, Prof. Paul Matsudaira, for his
mentorship and continued support during my time as a student in NUS, my
co-supervisors, Prof. Peter So and Lisa Tucker-Kellogg, for their guidance
through the time. Thanks to the people in the lab and it was a great time to
be working with them and special thanks to Yip Aikia for providing the DIC
cell images that are used in this paper. Thanks to my brother and all my
friends who gave me the encouragement during the hard times. Finally I
would like to dedicate this thesis to my parents, for their unwavering
support and love.
II
Contents
CHAPTER 1 INTRODUCTION .................................................................................. V
1.1 OVERVIEW OF CELL IMAGE ANALYSIS ................................................................................. 2
1.2 INTRODUCTION TO MICROSCOPY ........................................................................................ 5
Bright Field Microscopy..........................................................................................................................5
Differential Interference Contrast Microscopy.......................................................................................5
Fluorescent microscopy..........................................................................................................................7
1.3 CELL IMAGE SEGMENTATION OVERVIEW ............................................................................. 9
1.3
MOTIVATION......................................................................................................... 12
1.4
REMAINDER OF PAPER ............................................................................................. 13
CHAPTER 2 BACKGROUND OF IMAGE SEGMENTATION ............................ 14
2.1 IMAGE ENHANCEMENT .................................................................................................. 14
2.1.1 Histogram equalization ...............................................................................................................15
2.2 IMAGE DENOISING ........................................................................................................ 16
2.3 WATERSHED................................................................................................................ 20
2.3.1 Basic tools for watershed ............................................................................................................20
The Morphological Gradient[45] is defined as: .............................................................................20
2.3.2 Watershed segmentation ...........................................................................................................23
2.4 ACTIVE CONTOUR ......................................................................................................... 24
2.4.1 SNAKES ................................................................................................................... 25
2.4.2 LEVEL SET APPROACH FOR ACTIVE CONTOURS ................................................................ 26
2.4.3 ACTIVE CONTOURS WITHOUT EDGES ............................................................................. 28
Mumford-Shah model ..........................................................................................................................28
Chan-Vese active contour ....................................................................................................................29
III
CHAPTER 3 ALGORITHMS ..................................................................................... 32
3.1 EXPERIMENT DATA ....................................................................................................... 32
3.2 IMAGE PRE-PROCESSING ................................................................................................ 34
3.3 SEEDED WATERSHED..................................................................................................... 36
3.3 ACTIVE CONTOURS ....................................................................................................... 38
3.4 CELL TRACKING ............................................................................................................ 41
3.5 CELL OVERLAPPING ....................................................................................................... 42
CHAPTER 4 EXPERIMENT RESULTS................................................................... 43
4.1 SEEDED WATERSHED..................................................................................................... 43
4.2 ACTIVE CONTOURS ....................................................................................................... 44
4.3 EXTENSION TO IMAGE SEQUENCE .................................................................................... 46
4.4 DISCCUSSION ............................................................................................................... 49
CHAPTER 5 CONCLUSION ...................................................................................... 50
REFERENCES ................................................................................................................ 52
IV
Abstract
Image segmentation is a complex problem with many practical
applications. In particular cell image segmentation and cell tracking
through a series of images has the potential to increase the throughput of
cell experiments.. This paper addresses the problem with DIC cell images.
In this paper, local contrast enhancement and N-L means image denoising
are proposed for image pre-processing which improves the quality of the
image to a great extend. After that several image segmentation methods
are applied. The first solution is based on a seeded watershed
segmentation technique, and the second one is based on active contours
using level set function. The algorithm is further extended to cell tracking
problems. The active contours produces good results for images with
single cell, and for cell clustering the combination of active contours and
seeded watershed produced good results.
V
List of Figures
Figure 2.1 Illustration of Gaussian function ............................................................... 18
Figure 2.2 Illustration of N-L means.. ........................................................................ 19
Figure 2.5 The level set evolution............................................................................... 26
Figure 2.6 Active contour example 1.......................................................................... 31
Figure 2.7. Active contour example 2 ......................................................................... 31
Figure 3.1 Three datasets for experiment ................................................................... 33
Figure 3.3 Results for three image preprocessing.. ..................................................... 35
Figure 3.4 The procedure of marker-based watershed................................................ 37
Figure 3.5 The effect of initial contour to the final contour.. ..................................... 39
Figure3.6 The effect of choosing different scales for rough outline calculation,. ...... 40
Figure 3.7 The procedure of active contour for DIC image segmentation ................. 41
Figure 3.8 The procedure of active contour for DIC cell tracking ............................. 42
Figure 4.1The procedure for cell segmentation based on marker based watershed. .. 44
Figure 4.2 The procedure for cell segmentation based on active contour .................. 45
Figure 4.3 Additional results using Active Contours.................................................. 46
Figure 4.4 Single cell tracking result using set A. ...................................................... 47
Figure 4.5 Multi-cell tracking result using set B. ....................................................... 48
VI
Chapter 1
Introduction
Humans receive substantial information from the surroundings
everyday and most of the information is obtained by vision. The image,
whether it 2D or 3D, gray or color, is a way of recording such kind of
information. Especially with the advent of computers and the development of
relevant mathematic techniques, digital image analysis and pattern
recognition has drawn a lot of attention from researchers and scientists in
identity recognition, space exploration, remote sensor and many other
industry fields. The image analysis has also become popular in cell biology
study and there is no doubt the application of such quantitative analysis will
prompt new development.
Image segmentation is usually the first step in computer vision tasks
and sometimes it is the most challenging part. It is playing a great role in
image analysis since an accurate segmentation will separate the most
desirable units, which contain certain features, from the background so that
those units can provide more meaningful and easier way to be interpreted by
computer. Many methods of image segmentation have been brought up since
1970’s, however most of them target at some certain problems and no
generic approach is found to solve all segmentation problems.
In this chapter, a few things will be covered. First, we will review the
application of image analysis in cell biology study; then types of microscopy
used in biology research and different segmentation methods regarding that
specific microscopy image will be briefly introduced; in the end, the motivation
for DIC image segmentation will be given and discussed.
1.1 Overview of Cell Image Analysis
Since the invention of the first microscopy in 17th century, biologists
have revealed a micro world that is built up with cells which cannot be
observed by naked eyes. By examining these cells under microscopy,
thousands of hundreds of biological questions have been answered. Even
today it is still a standard and primary way to study cellular function. However,
these images are all inspected and processed by hand, for example, what is
the size of a cell, how fast the cell is moving, or even what the collective
migration pattern of cells is and etc is. The consequences are that the whole
process will not be only laborious but also more error-prone and the results
will be subjective to the person who interprets it. With the advent of the
computer and the development of computer vision theory such kind of image
analysis can be used to supplement and replace human visual inspection
thereby yielding in a more efficient and automatic way. Hence it is no surprise
that this technique is widely used in the fields of studies such as cell shape
changing, collective cell migration and even the recognition of biological
objects.
2
Cancer cells are the cells that have abnormal growth, division and they
may even evade other neighboring tissues. Such cells usually have different
morphological characteristics from normal cells. For example, the cells will
look more round due to the abnormal cytoskeleton structure, the cells lose the
contact inhibition with the substrate and this gives them the ability to move
faster and be more invasive, moreover the cancer cells usually have larger
nuclei with irregular shape[1]. Therefore the final diagnosis or grading for
cancer can be made based on cell morphology and tissue structures, and
these decisions will provide information to further cancer treatment. The
computational visual interpretation was applied for the detection of precursors
of cancer[2, 3] and this has greatly reduced the incidence of those cells
developing into more dangerous disease; in [4] the image analysis was used
to grade transitional cell carcinoma of the bladder. Features of those cells
were extracted and were used for further cell classification, and it achieved a
grading result that is similar to the pathologist while more objective and
reproducible.
The high content screening technology (HCS) is now widely used,
which allows cheap and fast collection of large image data. For example, the
functional genomics is a study that attempts to describe the functions and
interactions of genes and proteins, revealing the relationship between the
genome and its phenotype, to be more specific, how the expression of a
certain gene affects the signaling inside and outside the cells thus lead to
different cell function or behavior. By using HCS thousands of images of cells
3
can be collected. Those cells are stained either by some chemicals, such as
fluorophore, or RNA interference (RNAi), so that the cell shapes could be
screened systematically which indicated how genes controls a specific cellbiological process [5-7]. The collected data can later be used for image
analysis. The HCS is also important in drug discovery [8-11]. In order to study
the effects of drugs on the desired target cell statistically, large quantities of
cell images will be needed. These images will be passed to image analysis
pipeline that automatically extracts cell features, which may not be even
detected by human eyes. Then these features will be trained to build a
classifier that can distinguish those normal and abnormal cells.
Moreover, there is a tendency to study cell functions in a dynamic
way, which captures and tracks the cells using a time-lapsed microscopy.
This is especially helpful in cell migration study, the understanding of which
will give insights into many aspects such as embryonic development, wound
healing as well as tumor cell formation and etc[12, 13]. The image analysis,
such as cell tracking and cell circularity, will again help to provide more robust
and quantitative data and aid in the building of a cell migration model[14, 15].
Down to a more detailed scale, cell migration is always associated with
signaling pathway and protein sub-cellular interaction and transportation.
Tagged with green fluorescent protein (GFP) in living cell, the desired
proteins can be imaged and traced by fluorescence microscopy [16-18],
providing
more
information
in
protein
4
sub-cellular
distribution
and
compartmental transportation and after all how do they determine the cell
migration.
1.2 Introduction to microscopy
Bright Field Microscopy
The bright field microscopy is the simplest and the elementary form of
all optical microscopy techniques. A typical bright field image is a dark sample
with bright background. When a specimen is placed on the stage, light from
the light source passes through a condenser and is focused on the specimen.
The stains, pigmentation, or dense areas of the specimen will absorb some of
the transmitted light so that this contrast allows the user to see the specimen.
The simplicity of bright field microscopy makes it a popular technique
to some extend and. However, this technique still has limitations. For example,
the contrast of most samples is low which makes most details undetectable,
although by sample staining may help to reveal more structures it will also
introduce some other details in the specimen that are not supposed to be
present. Moreover, the technique requires strong light source for high
magnification applications and such intense light may damage the sample
cells by producing lots of heat.
Differential Interference Contrast Microscopy
DIC (differential interference contrast) is a very powerful tool for
visualizing unstained specimens, providing the ability to observe living
5
organisms, tissues or cells. A typical image of DIC gives a 3D look of the
specimen, creating bright light and dark shadows on the respective faces.
The interferometry theory is used to get information about the optical path
length of the sample [19]. The whole process starts with the light passing
through a polarizing filter and this makes the light wave oscillate in only in
direction. After that the light will pass through a two-layered modified
Wollaston prism. The prism will split the light into two beams which are
orthogonally polarized and spatially separated. When the light reaches the
sample plane, the two beams go through different paths. One goes through
the sample while the other one just passes through the background. The two
beams will be combined again by another Wollaston prism located between
objective lens and sample plane. Different segments of the sample have
different refractive indices and thickness. “When the beams are compiled by
the second prism and a second polarizing filter they reconstitute the
vibrational planes of the beams, which causes amplitude variations that are
seen as differences in brightness”[19]. In general, steep gradient in path
length gives high contrast with lines and edges emphasized while regions
having shallow optical path slopes produce insignificant contrast and often
appear as the same intensity level as the background.
It is easy to tell the DIC microscopy has many advantages over the
bright field microscopy, including the capacity to view living and unstained
biological samples in a natural state and providing high-contrast and high-
6
resolution images. Moreover, DIC will not have the halo ring effect and it can
produce very clear images of thick specimens.
Fluorescent microscopy
The fluorescence microscopy[20] is the most used microscope in the
medical and biological fields. It is a more generalized term which could refer
to any microscopy that creates images using fluorescent, such as confocal
fluorescence
microscopy[21],
two-photon
laser
scanning
fluorescence
microscopy[22, 23] or even multi-photon fluorescence microscopy[24]. The
illumination source of these types of microscopes are usually high-powered
light, for example, laser light, thus providing unique image viewing options. All
of the fluorescence microscopy shares the same principle to generate a light
microscope image, which is fundamentally different from transmitted or
reflected white light techniques such as bright field microscopy and differential
interference contrast microscopy.
We are all familiar with phosphorescent, which shows a delay in
brightness after the material absorbs energy from an external source. Similar
but a little different from phosphorescent, fluorescent is the process that gives
out the emission light after absorption of energy in a short time, usually on the
scale of nanosecond. Fluorescent microscopy is the equipment that can
visualize materials that are either nature fluorescent or stained by some
chemicals such as fluorephores or gene transition such as GFP. Because of
7
the specificity of fluorephore, fluorescent microscopy is especially useful in
observing sub-cellular compartment or organelles.
The understanding of fluorescent principal the phenomenon of
fluorescent is usually illustrated by Jablonski diagram, and the typical diagram
is shown as figure 1.1A. When the atom absorbs one photon, it will in turn
emit one photon. However, because of the complexity of electronic state
these two photons will carry different energy. The longer the wavelength is
the lower energy a photon carries. Therefore, the wavelength difference
results in the fact that the emitted light is redder, which has longer wavelength
and lower energy, and this is known as the Stroke’s shift (figure 1.1B).
Singlet states
High energy
Triplet states
Excitation ( 10-15 s)
Excited states
S
2
S
1
4
3
2
1
0
4
3
2
1
0
4
3
2
1
0
T
Fluorescence (10-9 s)
2
Phosphorescence (>10-6
4
3
2
1
0
T
1
s)
Internal conversion and
vibration relaxation (10-12
s)
Intersystem crossing
Low energy
S
4
3
2
1
0
Ground state
0
A
8
Stoke’s
shift
100
80
60
40
20
0
400
450
500
550
600
650
700
750
B
Figure 1.1 (A) Jablonski diagram; (B) Stroke’s shift
Although the fluorescent microscopy is now a standard tool for biology
researches, there are still some limitations this technique. The most
prominent one is with photo-bleaching. When a fluorephore is excited by
external energy the structure of this fluorephore is prone to be instable and
degradation. This would bring problems to quantitative image intensity
measurement. Another limitation is that the agents used to make the cell
fluorescent will also have the potential to change the behavior of cells.
1.3 Cell Image Segmentation Overview
The automatic microscopy image analysis is now drawing more and
more attention from the biologists. With the efforts of scientists coming from
both computer science and biology, many image analysis problems are
addressed and there is also some bio-image software ready for use. In
9
following session, we will briefly review the image segmentation methods
applied to different microscopy images.
In fluorescent imaging segmentation, only the desired part or objects
will emit light and be received by the microscopy, so most segmentations are
based on intensity threshold method to separate the object from the
background or intensity gradient to find the edges. However, during the setup
of microscopy or image acquisition the images generated will have uneven
illumination or when in 2D images it is often the case that cells touching each
other. All these scenarios will make the simple algorithms fail and urge
researchers to find a more complex solution. At the nuclear level, the cell
nuclei are more regulated and they are always quite distinct from the
background. In cytometry or HCS applications, numerous algorithms are
suggested, such as watershed and region-grow methods for the clustered
nuclei in cytometry applications[25, 26], in[27] the author addressed the
problems of weak edge information and uneven illumination by combining
several methods in a multi-scale manner. However, at the cell level the
segmentation is more challenging and it is even more difficult if no nuclei
information is available. In[25] the author developed an automatic algorithm
for cell segmentation by combing a number of processing such as watershed,
double thresholds, region merging and quality control. Jones et al.[28] also
suggested using voronoi method to find the boundary between the adjacent
cells. Despite the fact of the variety of fluorescent imaging segmentation,
considerable effort has gone into the quantitative measurement of object
10
features and all these techniques are now packed in standard tools such as
ImageJ[29], CellProfiler[30, 31].
The bright field imaging segmentation poses more difficulties since the
objects are transparent, the shape of cells is usually irregular and moreover
the intensity variation is quite small especially in thin regions. All these
problems require more sophisticated solutions. In [32] Korzynska et al.
presented a semi-automatic solution for the tracking of living cell in image
sequences. The proposed algorithm takes the advantage of texture-base
analysis, the boundary intensity gradient and similarity from consecutive
images in a time series. The algorithm requires manual initialization of the
segmentation and it can only handle the case where no cell overlapping
exists. In [33, 34] Rehan et al. presented another method based on level set
function which requires a derivative image created across different focal
planes. The desired features will be obtained by filtering and divided into
background and cell regions using threshold. However, this method requires
a special image acquisition that the images from different focal plane should
all be taken, which makes this approach not so practical. Wu et al. [35]
presented an early solution to the segmentation of unstained living cells in
their paper. The method is a two stage segmentation in which an approximate
region that the cell resides in is first found by image variance map threshold.
In the second step the cell from the remaining background in the approximate
region is further segmented. [36] also presented a robust segmentation
11
method using multiphase level set to extract candidate markers and these
markers are further used in watershed and region growing process.
While for DIC image segmentation, only a few researches could be
found. D Young et al [37] proposed a general method by constructing cell
templates. In order to fit templates of a range of different sizes and different
orientations to images, Fast Fourier transforms is used and is presented as a
template matching methodology. However, this method is only applicable to
cells which share the same shape characteristic properties. In [38, 39], DIC
microscopy cell image is segmented by a method that removes the gradient
phase. A three-step method is used here. In the first step a reconstruction by
deconvolution is executed on DIC image to get intensity image. In the second
step, the voting method is used to detect the center of the cell. In the final
step, the selected regions are used as seed points of a PDE-based region
growing method. However, the method requires a pre-knowledge of DIC
parameter settings which cannot be generalized.
1.3 Motivation
Despite the fact that there are substantial papers published regarding
the problem of cell image segmentation and many tools available to do
standard processing, they are not able to address all the problems and
meanwhile most of these studies and software are more towards the
application of fluorescent imaging. While fluorescent imaging is essential,
other microscopy imaging approaches, particularly DIC, due to its intrinsic
12
features, supplements the usage of fluorescent microscopy and provides
enhanced information for living cell study.
However, those segmentation methods on DIC images are either based
on model reconstruction or gradient phase removal, and all of them require
the prior-knowledge of DIC microscopy and relevant parameters which make
them not so practical.
Because of the importance of DIC imaging technique and poor
research in its object segmentation currently, we took the effort to explore the
possible way to solve the problem of DIC cell image segmentation.
1.4 Remainder of paper
The remainder of the paper is organized as follows: Chapter 2 contains
the background information on a variety of common segmentation and
clustering algorithms; Chapter 3 contains a description of the algorithms;
Chapter 4 has the results of all algorithms presented and finally Chapter 5 is
the conclusion of this paper.
13
Chapter 2
Background of Image Segmentation
There are many approaches to solve segmentation problems: the
threshold method based on the difference in intensities of background and
object, level set methods rely on PDE’s, while the watershed method treats
the image as topography. This chapter will discuss some background
algorithms that are useful for DIC image segmentation, such as image preprocessing, namely local contrast image enhancement and N-L means image
denoising, as well as active contours and watershed methods.
2.1 Image Enhancement
Image enhancement is an important part in image processing. It aims
to improve the image quality, give more interpretability for human viewers,
remove or reduce redundant information and facilitate with further image
analysis. There are several approaches for Image enhancement techniques
and they can be categorized into spatial domain and frequency domain
methods [40]. The frequency domain methods adopt flourier transform, either
blurring the image by a low pass filter or sharpening the image by a high pass
filter. On the contrast, the spatial domain methods operated directly on pixels,
and these methods will be covered in more detail.
14
2.1.1 Histogram equalization
Histogram
equalization
is
a
common
technique
for
image
enhancement [40, 41]. By applying statistic theory it transforms the image by
stretching the original histogram to uniformly distribution. Such adjustment
will change the pixel value and therefore improves the image contrast.
Consider an image whose intensity levels is in the range of [0, L-1], the
total number of pixels is n, and nk is the total number of pixels of intensity level
rk . The proportion of pixels with value rk is given by:
Prk
nk
(2.1)
n
Where k 0,1...L 1 , and the function for histogram equalization is
given by:
k
k
nk
j 0 n
Sk T (rk ) Prk
j 0
(2.2)
The whole entropy is also given by:
L 1
L 1
k 0
k 0
I I (rk ) Prk lnPrk
(2.3)
When Pr0 Pr1 Pr2 ... PrL1 , it reaches the maximum entropy and the
image carries the maximum information.
The traditional histogram equalization adjusts the range of pixel values
and is easy and fast. However, it is a global method and would lose detailed
information as a result of combine intensity values that have a low occurrence.
15
Therefore, the local enhancement[42] can help to improve the appearance of
images and still preserve the most detailed information.
The local image enhancement is given as:
f (i, j ) mx (i, j ) k ( x(i, j ) mx (i, j ))
(2.4)
Where, x(i, j ) is the original pixel value at point (i, j ) and f (i, j ) is the
output value; mx (i, j ) is the mean value of the neighboring regions with
center (i, j ) ; k is some co-efficiency. When k 1 , if x(i, j ) mx (i, j ) then
f (i, j ) x(i, j ) so that the value is increased; whereas if x(i, j ) mx (i, j ) , then
f (i, j ) x(i, j ) the value is decreased. Overall, the local enhancement can
improve the local details.
2.2 Image Denoising
The image could always be corrupted by noise, either during
acquisition or transmission. Image denoising is the process to remove or
reduce noise in the image.
So that the image noise model could be
presented as:
g x, y f x, y vx, y
(2.5)
Where f x, y is the ideal image, vx, y is noise and g x, y is the
observed values.
There are many ways for image denoising and they can also be
categorized into frequency domain and spatial domain methods.
16
For the spatial domain method, the median filter is the most common
one. It is a non-linear filter, which assigns a pixel with the median number of
pixels in a mask. To illustrate, suppose there is an image that is of size m*n, a
mask of k*l is defined and moves across the whole image. Let (i,j) be the
center of the mask when it moves to a certain region of the image, and also
let T be the median value of all the pixels that are covered by the mask. So
that (i,j) is assigned to the value T.
In frequency domain methods, a typical way to smooth an image is
Gaussian filter. It is a convolution in the spatial domain and a low pass filter
which attenuating high frequency in frequency domain. The 2D Gaussian
function has the equation as:
G( x, y )
1
2
2
e
x2 y 2
2 2
(2.6)
Where x and y are the distances from the center point respectively,
is the standard deviation of the Gaussian distribution which determines the
shape of Gaussian function (figure 2.2 (a)). Theoretically, the Gaussian
distribution is non-zero everywhere. However, in practical only the points
within three times standard deviation are used and the rest points are
truncated. This distribution is presented as Gaussian Convolution Kernel in
discrete space. Figure 2.2 (b) is an example when is 1;
17
Figure 2.1 Gaussian function with =1.0. (a) Gaussian curve in continuous space; (b)
Discrete Gaussian approximation or Gaussian Convolution Kernel
Both median and Gaussian filters have the advantage of simple
calculation; however they will also bring the problem of blurring to the resulted
images. For example, they can’t preserve the fine structures, details and
textures since this information all behave like noise in frequency domain. The
N-L means method is a way to address this problem.
Given a noisy image v {v(i) | i I } , and define Nk as a square
neighborhood of a certain size with center point at pixel k. i and j are two
pixels so the Euclidean distance between i and j in the noisy image model has
the following equation:
E || v(i ) v( j ) ||22,a || u( i ) u( j ) ||2,2 a 2 2
(2.7)
Where is the standard deviation of Gaussian white noise distribution.
So the similarities between pixel i and j is defined as:
18
|| v( Ni ) v( N j ) ||2,
1
w(i, j )
exp(
)
Z (i)
h2
2
Where z (i ) exp(
|| v( N i ) v( N j ) || 22,
h2
j
(2.8)
) is a normalizing constant.
h controls the smoothness, determining the decay of the exponential function,
and here it refers to the change of weights as a function of Euclidean
distances. For example, when h is small, the decay of exponential is more
distinctive and the resulted image will preserve more detailed information.
Meanwhile, the weights w(i, j ) also satisfy the conditions 0 (i, j ) 1 and
(i, j) 1.
jI
Therefore the final value of each pixel is give by the weighted average
of all the pixels in the image:
NL(v)(i) w(i, j )v( j )
(2.9)
jI
Figure 2.2 illustration of N-L means. When calculate the value in region 4, since region
3 more resembles to 4 more weight is give to 3, whereas 1 and 2 are given smaller
weights.
19
2.3 Watershed
The first watershed was brought up in geography, but now it is widely
used in image segmentation. This method is a regional segmentation based
on mathematical morphology. In[43] and Lantu_ejoul gave the first definition
to watershed: suppose that the landscape is flooded by falling rain. The water
will come to the lowest point first and starts to go up the surface. When water
comes from different regions about to meet, a dam is built along the ridge. In
[44] Vincent and Soille gave an alternative way to descried the process: treat
each pixel value in the image as the height on that point, drill holes in every
local minima and immerse the region in a lake. Therefore the water will come
from these holes and will fill up the catchment basins. Similarly, a dam is built
at the points where water coming from different basins would meet. The
whole process will stop when the water immersed the whole landscape.
2.3.1 Basic tools for watershed
Morphological Gradient
The Morphological Gradient[45] is defined as:
g ( f ) B ( f ) B ( f )
(2.10)
Where B ( f ) and B ( f ) are dilation and erosion of f with the
elementary structuring element B. In the close neighborhood of a pixel, the
20
contrast intensity is indicated by each pixel value; hence the morphological
gradient is an image from each of these pixels.
Figure 2.3, morphological gradient (b) of image(a) with element
size 12.
Distance function
The distance function is defined as “the distance from every pixel of
the object component to the nearest background pixel” [46]. The distance
between two pixels [i1, j1] and [i2, j2] in a digital image is defined in several
ways, e.g.:
“Euclidean:
d Euclidean ([i1 , j1 ],[i2 , j2 ]) (i1 i2 )2 ( j1 j2 )2
(2.11)
City Block:
dcityblock ([i1 , j1 ],[i2 , j2 ]) | i1 i2 | | j1 j2 |
(2.12)
Chessboard:
dchessboard ([i1 , j1 ],[i2 , j2 ]) max(| i1 i2 | | j1 j2 |)
Minima of an image
21
(2.13)”
The minima, in watershed context, are one of the primary important
features that are extracted from an image. The topographic surface S can be
defined as set of all the points {x, f ( x)} belonging to X. The altitude of surface
point {x, f ( x)} can be corresponded to the gray value at point x.
The minima of an image, also called regional minima, are defined
as[47]:
Consider two points
s1 and s2
of S, the path between s1 ( x1 , f ( x1 )) and
s2 ( x2 , f ( x2 )) is defined as any sequence points {si } on surface S. A non
ascending path is:
si ( xi , f ( xi )), s j ( x j , f ( x j ))i j
f ( xi ) f ( x j )
(2.14)
A point belongs to minima only if there exists no ascending path
starting from s. In another word, minima can be considered as a sink of the
topographic surface. The set M of all the minima of f is made of various
connected components M i ( f ) .
Figure 2.4, A topographic minima
22
2.3.2 Watershed segmentation
The concept of watershed derives from geography. In image
segmentation, it takes the value of a pixel as the height of that point in a 3D
landscape. There are mainly two ways to achieve watershed, one is based on
immersion simulation and the other is by the rain falling model.
Similarly, the water dropping simulation gives another way of the whole
process. The rain will drop on the landscape and due to the gravity it will fall
along a path which leads to the local minima most quickly. So if drops
eventually come to the same region then the points where they landed on the
landscape belong to the same region. Only the water drops on the ridge has
the equal potential to fall into any adjacent regions.
The immersion simulation approach describes a scenario that in a
uneven landscape the water begins to immerse the region from each local
minima; As the water rises up, the water comes from different basins will
meet. So a dam will be built on that point and in the end the landscape will be
divided into different regions by these dams. The dam on the ridge is celled
watershed.
However, the traditional watershed is very sensitive to the noise which
leads to a serious image over segmentation. Therefore, many improved
watershed have been proposed and have achieved good experimental result.
These methods aim to minimize the influence of noise and fine textures,
preserve essential contours, reduce the number of regions and avoid region
merging. In the following, methods based on markers will be discussed.
23
The watershed segmentation is quite sensitive to image quality. An
image with noise and other factors would always lead to over segmentation,
resulting in the desired contour be overlaid by many other irrelevant contours.
An effective way to solve this problem is to use marker-based watershed. The
seeds are selected either manually or automatically. They will be assigned as
the lowest points in the image, as in the gradient image, and then watershed
method will be applied to this image.
2.4 Active Contour
The active contours model is now widely used in image segmentation
and object tracking. The main idea of active contours is to evolve a curve to fit
the boundary and the curve moves under internal and external forces and in
the end stops when energy function is minimized. Active contour models have
the advantage that the final curve will always be a closed and smooth area
regardless of the image quality, to illustrate, blurred images, spurious edges
or broken edges.
There are two main types of active contour models: parametric active
contours[48, 49] and geometric active contours[50-54]. Parametric explicitly
defines the curve is by curves points, so that it only needs to move the points
according to some energy function. The geometric active contours, on the
other hand, implicitly define the curve by transforming the curve to a higher
dimension function, for example, 2d curve line to 3d curve surface .
24
2.4.1 Snakes
The snake model was first proposed by Kass et al. [48]. It is widely
used in image segmentation and edge detection in computer vision. In this
model, an initial contour has to be given and then the contour will evolve to
reduce energy. In the end the contour will reach a final status after several
iterations. The snake is given as a closed curve given as:
C (s) ( x(s), y(s))
(2.15)
And the energy function is described as:
1
1
1
0
0
0
E (C ) | C '( p) |2 dp | C ''( p) |2 dp | IC '( p) | dp
(2.16)
Where controls the “tension” controls the “rigidity”, therefore the
first two terms are internal forces and they control the smoothness of the
contour, the third term is the external force.
Although effective in giving continuous boundary detection, the snake
still possessed some defects. For example, the segmentation result is largely
depended on the selection of initial contour and local, therefore when an
image is contaminated with noise it will yield a false boundary; moreover, this
method cannot handle with topological changes which means it is hard to
segment multiple objects.
25
2.4.2 Level Set Approach for Active Contours
The level set method was first introduced by Osher and Sethian [53] as
a way to describe the shape changes of flame. The fire shape is highly
dynamic and uncertain in topology, so that the traditional parametric
representation is very hard. Therefore they proposed level set approach and
its main idea is to transform the curve from n dimensions to n+1 dimensions
and the curve is embedded as 0 level set. The curve will get evolved under
some constrains and in the end reach the level set 0.
Figure 2.5 the level set evolution
First of all, let’s define the signed distance function (SDF):
( x, t 0) d
(2.17)
Where d is the shortest distance from point x to the curve, and the sign
is determined on whether x is inside or outside the curve, normally outside is
26
positive inside is negative and only the points at the curve surface have the
values of zero.
The level set function is given as:
F | |, (0, X , Y ) 0 ( x, y)
t
(2.18)
Where F is the speed term and is in the normal direction to the curve
surface. 0 is the zero level set of the function and represents the boundary
of the current segmentation. So the problem now becomes the analysis and
calculations of curve surface evolution under F. It can be seen that if the
change of F is smooth then (t , X , Y ) will always be a smooth function as well
so that the description of surface topological change can be easy. Depending
on different models, the expression of F also varies. For example, in image
segmentation, the level set function can be defined as an anisotropic diffusion
model:
g (| u0 |) | | (div(
t
| |
(2.19)
Where is a constant, u0 is the intensity gradient, g (| u0 |) is a
function and it is inversely proportional to | u0 | , which is when | u0 | is small
g (| u0 |) gets large. That means if the curve reaches a sharp change in
intensity, the evolve speed will also decrease sharply or even stop.
The application of level set method in image processing and analysis
shows great advantages, especially in the problem of image segmentation
such advantages are more prominent. For example, if the speed term is
27
smooth, the level set function could change its topological structures easily,
such as separation, merging and sharp corner; second, since the curve is
handled implicitly, the solution of this problem becomes a PDE question
which can be solved more easily; thirdly, the level set method is not only
useful in 2d and 3d but this application can also be extended to higher
dimensions.
2.4.3 Active Contours without Edges
Since the traditional snake is an edge-based model, it will often yield
bad results to blurred or noisy images. In order to overcome this difficulty,
Chan and Vese proposed a new model for active contours to detect objects in
a given image[51]. It is a region-based level set model, which attracts the
curve to the desired boundary using some regional information. The CV
model is actually derivative from Mumford-Shah model and it has achieved
great success in blurred image segmentation.
Mumford-Shah model
The Mumford-Shah model is first proposed in 1989 in their influential
paper[55]. It aims to find the minimum function energy in order to get the
image segmentation. Its main form can be given as:
E (u, C ) | u u0 |2 dxdy
| u |
2
\C
28
dxdy length(C )
(2.20)
Where and are non-negative constants, is the region of whole
image, C is the boundary, u0 is the initial image, u is a piecewise smooth
image. Therefore, the first term makes sure the similarity between the original
and resulted images, the second term is called the smooth term which
ensures the contour is smooth and continuous; the third term is a constraint to
minimize the length of the curve. The Mumford-Shah model is to find u and
C when E (u, C ) reaches its minimum.
Chan-Vese Active Contour
The Chan-Vese active contour applies the level-set method to solve
Mumford-Shah model. It simplifies the u to a piecewise constant which means
in every region u is a constant. The CV model is usually given as:
E (c1 , c1 , C ) Length(C ) 1
| u0 ( x, y ) c1 |2 dxdy
inside ( C )
2
| u0 ( x, y ) c2 |2 dxdy
(2.21)
outside ( C )
Where , 1 and 2 are positive constants, usually fix 1 2 1 , 0 ,
C is a variable curve on the image, and the constants c1 and c2 are the mean
intensities of u0 inside and outside C respectively.
The CV model uses the level set method and replaces the unknown
evolving curve C with function ( x, y) , and it is defined as:
0if ( x, y )insideC
( x, y ) 0if ( x, y )onC
0if ( x, y )outsideC
29
(2.22)
Furthermore, using Heaviside function:
1if 0
H ( )
0if
(2.23)
The CV active contour can be represented as:
F (c1 , c2,C ) ( ) | | H ( )dxdy
1
inside ( C )
(u0 c1 ) 2 H ( )dxdy
2
outside ( C )
(2.24)
(u0 ( x, y ) c2 ) 2 (1 H ( ))dxdy
The solution can be obtained by Euer-Lagrange function and by
solving the following three equations:
c1
u H ( )dx
H ( )dx
0
(2.25)
c2
u0 (1 H ( ))dx
(1 H ( ))dx
(2.26)
( ) div(
) | u0 c1 |2 | u0 c2 |2
t
| |
(2.27)
Figure 12 and 13 present some examples of active contours without
edges. Especially that figure 13 shows the method is successfully able to find
non-convex shapes in a noisy image.
30
Figure 2.6 An example showing that the energy function is minimized only if the curve
is on the edge of the object[51].
Figure 2.7. Results for[51] on a noisy, non-convex image
31
Chapter 3
Algorithms
In the previous chapter, we introduced some algorithms for image
preprocessing and segmentation, and this chapter will present the proposed
algorithms for
DIC cell image segmentation. These approaches include
the use of watershed as well level set active contour. In addition, we have
also address the problem of DIC cell tracking by active contour.
3.1 Experiment Data
In order to better understand the problem of DIC image segmentation,
it is necessary to give some illustration about the dataset. All the image data
were obtained from the Center of Biological Image Science of National
University of Singapore.
In this database, there are three datasets (figure 3.1). Set A is cell
migration image sequence, which is composed of both DIC cell image and
fluorescent cell nucleus image, and in each frame there is only one single cell.
Similar to set A, set B is also cell migration image serial which is collected by
both fluorescent and DIC microscopy, however in this dataset each frame
contains multiple cells which possesses the problem of touching with other
32
cell. For set C, it is a collection of cell images using DIC microscopy only, but
compared with set A and B these cells show more variety in shapes.
Besides the difficulty of segmenting DIC image itself, there are some
more problems existing in these three datasets that make the task more
complicated: first, the contrast between object and background is not distinct
due to the fact some part of a cell is too thin, therefore an unclear boundary
makes most edge-based methods fail in this problem; second, the
background is not homogenous in a way that the illumination is not even
across the field of view and the background texture is not clean either which
contains some other impurities.
Figure 3.1 Three datasets for experiment
33
3.2 Image Pre-processing
It is shown from figure 3.1 the DIC images have major problems such
as uneven background and low image contrast which make the segmentation
even hard for human eyes. In order to achieve better result, it is necessary to
have some image pre-processing.
In order to tackle with the low contrast issue, the local contrast image
enhancement introduced in chapter 2 will be applied. This method is superior
to the normal image enhancement methods such as global histogram
equalizations in the sense that it will also eliminate the problem of uneven
background.
However after the local contrast image enhancement, more noise is
brought into the resulting image (figure 3.2 B). Although the image is easier to
view, in the context of signal processing, noise is redundant and unwanted
information and most of time it will be harmful to the processing that follows.
So the N-L means image denoising is taken to remove the noise. Figure 3.2
shows the results of different image denoising techniques and it is obvious
that N-L means is better than the other two methods in term of fine details
preserving.
To be more explainable figure 3.3 gives the results of original image
after local contrast image enhancement and N-L means. It is obvious to see
that the image after such preprocessing is now much easier for computation.
34
Figure 3.2 comparisons among image denoising methods: a. original image;
b. denoised image by N-L means; c. denoised image using Gaussian filtering;
d.denoised image by mean filtering.
Figure 3.3 results for image preprocessing. (A) original image; (B) image after local
contrast image enhancement; (C) image after N-L means image denoising.
35
3.3 Seeded Watershed
After some necessary image preprocessing, such as the local contrast
enhancement and N-L means image denoising. The image is now ready for
the next step segmentation.
The first method we will try is watershed. As described in chapter 2,
marker based watershed, or seeded watershed, is the most popular
watershed algorithms. The main idea of marker based watershed is that
instead of letting water rise from every minimum in the image, “water can be
allowed to rise only from places marked as seeds”[44]. This method avoids
the issue of image over-segmentation and will give the right amount of
segmented objects since the number of objects is constraint to the number of
seeds. Therefore, the problem now becomes how to find the seeds.
Many seeded watershed applications rely on manual seed selection
but this doesn’t give the benefit of computational segmentation. However, in
our dataset, especially dataset A and B, each frame of image sequence
contains both the location of nucleus in fluorescent image and shape of cells
in DIC image. Therefore it is no surprise that the nucleus is the ideal seed for
each cell. Thus the method of seeded watershed in this case involves
processing of two images and the main steps for the algorithms are given as
figure 3.4.
36
Figure 3.4 the procedure of marker-based watershed
As for the nucleus fluorescence image, it is thresholded to binary
image followed by some necessary morphological transforms, such as holes
filling inside the object and binary dilation, so that we will get the seed for the
object itself; However we also need a seed for the background, and it is also
generated by reverting the binary nucleus image obtained before and image
morphology to get the background; after that, the binary image containing
foreground and background seeds will be imposed to the DIC image and this
seeded image will be ready to use for watershed.
37
3.3 Active Contours
The second method is level set active contours. Because of the special
image acquisition method for set A and B, the watershed seems to be a good
choice. However, images like set C, which doesn’t have the supplement
nucleus fluoresce image, is not that simple and needs a different treatment.
Likewise, we will need some image preprocessing as described in the
first method before apply active contour. Figure 3.5 shows some results of
this method with different initial contour boundaries. It is noted that a good
initial contour for this dataset using active contour is essential. The first
column gives a scenario when the initial contour is far away from the cell, and
the computed result ended up with including some regions which don’t belong
to the cell object; The middle one is the case that the contour is initialized
inside the cell, but still this gives the wrong segmentation; For the third case
presented in the last column, the initial contour is outlined in a way that it
enclosed the whole cell while still very closed to the boundary of the cell, and
this one yields the best segmentation. So now the problem becomes how to
obtain a good initial contour.
38
Figure 3.5 the effect of initial contour to the final contour. A. The initial contour is a bit
far from the cell boundary; B. the initial contour is inside the cell boundary; C. the
initial contour is close to the boundary. A and B end up with inaccurate final
segmentation while C yields right result.
To get an ideal initial contour, one can do it manually. Still this doesn’t
give much credit to computational image segmentation since when dataset is
becoming huge, manual selection is impossible. After some examination it is
noticed that there is more morphological variance inside and at the edge of
the cell than the background, in another word the background is more
homogeneous than the interior of cells. To get the variance map, the original
image is transformed to the morphology gradient map.
Figure 3.6 gives the result of such transformation and each of them is
the result from different image scale. It can be seen that choosing an
39
appropriate image scale is also important to obtain the initial contour. For
example, in figure 3.6 the initial size of the image is 500*500 pixels and the
transformed image is C, in A the 100*100 pixel-size image is used, and image
B is at the scale of 200*200. It can be clearly seen that B gets the best
approximation in terms of that the computed foreground covers the whole cell
yet no other unwanted objects. Such difference is due to the fact different
image scales will give different level of information. Although a high resolution
will give fine details such as texture, in this case a low scaled image is good
enough for a rough outline computation.
Figure3.6 the effect of choosing different scales for rough outline calculation, A. the
image is at scale 0.2; B, the image is at scale 0.4; C the image at scale 1.
The
whole
procedure
for
active
segmentation can be given as figure 3.7.
40
contour
based
DIC
image
Figure 3.7 the procedure of active contour for DIC image segmentation
3.4 Cell Tracking
The DIC microscopy is powerful in observing living cells and is widely
used in the study of cell migration. To fully take advantage brought by DIC
microscopy and computational image analysis, there is also a need to extend
the static cell segmentation to dynamic cell tracking.
Intuitively, the methods designed for static image segmentation can
also be applied to image sequence since the video is nothing more than a
collection of static images in a time serial. However, for each neighboring
image frame there is some spatial correlation between them, since the cells
will not move very far within a certain time interval. Such kind of time interval
can be manually determined because it is possible to increase the rate at
41
which images are taken. Also if the cell moves too far in between frames,
even a human will not be able to track the cells. Because of such spatial
correlation active contour method is a good choice so that each computed
outline in the current frame will be the initial contour for the next frame. The
main procedure for cell tracking is also given in figure 3.8.
Figure 3.8 the procedure of active contour for DIC cell tracking
3.5 Cell Overlapping
In our dataset, particularly in set B, a group of cells will always have
the problem of cell clustering and this is also one of the goals of image
segmentation. So far watershed is still the popular way to address the
overlapping problem. There are also two ways to do watershed. The first one
is based on the distance map. In this method the binary image will be
converted to the distance map and the minima of watershed will be identified
as the peak point in that distance map function. The other one is seeded
watershed which has been covered in segmentation as well and the nucleus
will still be used as markers.
42
Chapter 4
Experiment Results
After giving the necessary illustration of proposed methods in chapter 3,
this chapter will test and show the results. All the computation was done
under MATLAB.
4.1 Seeded Watershed
Figure 4.1 gives the image version of figure 3.4. Each image shows the
results of each step. From image A to image C, the contrast of the image is
greatly improved and the background noise is also maximally removed. In
image F the binary image E is imposed on C as a marker and this makes the
watershed local minimum only exists in the region covered by E. However,
the result is not satisfactory.
43
Figure 4.1the procedure for cell segmentation based on marker based watershed. A,
the original image; B. Image after local contrast transform; C, the image is further
processed by N-L denoisng; D. the fluorescence image of nucleus; E. the binary
image of D after some morphological processing; F. the seed E is imposed on the
image C and is applied to watershed segmentation; G the final segmentation
4.2 Active Contours
Figure 4.2 demonstrate the usage of level set active contours in DIC
image segmentation. Similarly the original image is preprocessed by image
enhancement and noise removal, then the 0.2 image scale is chosen to get
the rough outline of the cell and this outline is set as the initial contour. Image
44
E is the computed results, some small objects are included but they can be
removed by some area size criteria. Figure 4.3 gives more results by this
method. It is obvious that active contour is far better than seeded watershed,
regardless the variety of cell shapes.
Figure 4.2 the procedure for cell segmentation based on active contour A initial image;
B after image processing; C morphology gradient of B at the scale of 0.2; D the binary
image of C; E. The final segmentation
45
Final zero level contour, 110 iterations
Figure 4.3 Additional results using Active Contours. From the top to the bottom: the
original image and binary image of segmented cell.
4.3 Extension to Image Sequence
For algorithm of cell tracking, the dataset A and B are tested
separately. For each set, an initial contour of the first frame is manually drawn.
For single cell tracking using set A (figure 4.4) the proposed method is
adequate and shows accurate cell segmentation for each frame. However, in
set B (figure 4.5) such method is insufficient to solve the cell overlapping
problem during migration, therefore we used the distance (figure 4.4 C) and
seeded watershed (figure 4.4 D) to separate the cells.
46
Figure 4.4 single cell tracking result using set A.
47
Figure 4.5 the multi-cell tracking result using set B. a. the binary image after the cell
tracking method; b. the nucleus; c. the final segmentation after distance watershed; d
the final segmentation after seeded watershed
48
4.4 Discussion
In this chapter, we see the results of the suggested methods and there
are advantages and disadvantages for each method.
For static cell segmentation, the level set active contour outperforms
the seeded watershed for set A, B and C. The results yielded by the level-set
can nicely found a closed curve to fit the cell boundary, while for watershed it
gives an inaccurate segmentation.
For cell tracking issue, when dealing with a single cell case the level
set alone is enough. However, when multiply cells are involved, the initial
results require post processing and two different watershed schemes are
considered. After comparison it can be concluded that seeded watershed is
better than the distance map watershed. The distance map one still tends to
get more segmented objects than expected, and this is because when the
image of irregular-shaped cell is converted into binary and later transformed
to distance map, it tends to get many local peak points which serves like
markers when using seeded watershed. In practice, distance map watershed
is usually adopted in the case when the number of objects is unknown and
the shapes of objects resemble each other.
49
Chapter 5
Conclusion
Differential
interference
contrast
(DIC)
microcopy
has
many
advantages over other microscopy in cell biology research. However, the
segmentation of DIC images of cells have not draw much attention from the
researchers, partly because the segmentation alone is a challenging problem,
but also because the DIC imaging itself has some features that makes the
segmentation job even harder, such as poor image contrast, broken boundary
and overlapping. Several methods aiming at this problem is not practical in
use therefore we tried to explore the possible solutions to provide a automatic
DIC cell image segmentation.
To facilitate with the segmentation, some image pre-processing
techniques are used. As the sampled image featured in bad image quality,
image enhancement based on local-contrast and image denoising using N-L
means are provided to get a better image for further image analysis.
After the image with a better quality is obtained, we further used two
approaches to segment cells. The first was based on a seeded watershed
method, in which the fluorescence nucleus image is used as the seed. The
resulting algorithm was able to provide some segmentation but yet not good
enough. The second solution involves the use of active contours based on
50
level-set, concentrating on pulling apart the background and object. This
method was able to provide accurate results regardless of cell shapes.
In the extension to cell tracking in image sequence, it is no surprise to
use active contour based on the evolution characteristic of such method.
Each computed outline is passed as the initial contour to the next frame. In
order to overcome the problem of cell overlapping, distance map watershed
and seeded watershed are used for image post processing. The comparisons
show
that
the
seeded
watershed
provides
better
overlapping
cell
segmentation when the number of cells is known.
Our experiment was based on DIC image data obtained from the
Center of Biological Image Science of National University of Singapore. So
possible future work would includes testing the algorithms on other datasets,
or testing the robustness of the methods when using other microscopy cell
images, such as bright field and phase contrast, and moreover how to
improve the separation of clustered cell.
51
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[...]... quantitative image intensity measurement Another limitation is that the agents used to make the cell fluorescent will also have the potential to change the behavior of cells 1.3 Cell Image Segmentation Overview The automatic microscopy image analysis is now drawing more and more attention from the biologists With the efforts of scientists coming from both computer science and biology, many image analysis... quantities of cell images will be needed These images will be passed to image analysis pipeline that automatically extracts cell features, which may not be even detected by human eyes Then these features will be trained to build a classifier that can distinguish those normal and abnormal cells Moreover, there is a tendency to study cell functions in a dynamic way, which captures and tracks the cells using... method treats the image as topography This chapter will discuss some background algorithms that are useful for DIC image segmentation, such as image preprocessing, namely local contrast image enhancement and N-L means image denoising, as well as active contours and watershed methods 2.1 Image Enhancement Image enhancement is an important part in image processing It aims to improve the image quality, give... helpful in cell migration study, the understanding of which will give insights into many aspects such as embryonic development, wound healing as well as tumor cell formation and etc[12, 13] The image analysis, such as cell tracking and cell circularity, will again help to provide more robust and quantitative data and aid in the building of a cell migration model[ 14, 15] Down to a more detailed scale, cell. .. details 2.2 Image Denoising The image could always be corrupted by noise, either during acquisition or transmission Image denoising is the process to remove or reduce noise in the image So that the image noise model could be presented as: g x, y f x, y vx, y (2.5) Where f x, y is the ideal image, vx, y is noise and g x, y is the observed values There are many ways for image denoising... is an edge-based model, it will often yield bad results to blurred or noisy images In order to overcome this difficulty, Chan and Vese proposed a new model for active contours to detect objects in a given image[ 51] It is a region-based level set model, which attracts the curve to the desired boundary using some regional information The CV model is actually derivative from Mumford-Shah model and it has... during the setup of microscopy or image acquisition the images generated will have uneven illumination or when in 2D images it is often the case that cells touching each other All these scenarios will make the simple algorithms fail and urge researchers to find a more complex solution At the nuclear level, the cell nuclei are more regulated and they are always quite distinct from the background In cytometry... ImageJ[29], CellProfiler[30, 31] The bright field imaging segmentation poses more difficulties since the objects are transparent, the shape of cells is usually irregular and moreover the intensity variation is quite small especially in thin regions All these problems require more sophisticated solutions In [32] Korzynska et al presented a semi -automatic solution for the tracking of living cell in image. .. background and cell regions using threshold However, this method requires a special image acquisition that the images from different focal plane should all be taken, which makes this approach not so practical Wu et al [35] presented an early solution to the segmentation of unstained living cells in their paper The method is a two stage segmentation in which an approximate region that the cell resides... Those cells are stained either by some chemicals, such as fluorophore, or RNA interference (RNAi), so that the cell shapes could be screened systematically which indicated how genes controls a specific cellbiological process [5-7] The collected data can later be used for image analysis The HCS is also important in drug discovery [8-11] In order to study the effects of drugs on the desired target cell ... particular cell image segmentation and cell tracking through a series of images has the potential to increase the throughput of cell experiments This paper addresses the problem with DIC cell images... on the desired target cell statistically, large quantities of cell images will be needed These images will be passed to image analysis pipeline that automatically extracts cell features, which... is composed of both DIC cell image and fluorescent cell nucleus image, and in each frame there is only one single cell Similar to set A, set B is also cell migration image serial which is collected