BACKGROUND
leukocytes, derived from bone marrow stem cells, are the first line of defense of the immune system.
neutrophils, basophils, and eosinophils are called granulocytes because they have granules in their cytoplasm.
the other two leukocyte categories, lymphocytes and monocytes, belong to the mononuclear cell group.
this means their nucleus is a single piece.
these cells are colorless, but they can be colored with special stains to make them visible under the microscope.
the characteristics of the five leukocyte categories are described as follows.
figure  <dig> shows the micrographic images of the five different leukocytes  <cit> .
neutrophil
this granulocyte has very tiny stained granules with low visibility.
the nucleus is frequently multi-lobed with lobes connected by thin strands of nuclear material.
these cells are capable of phagocytizing foreign cells, toxins, and viruses.
this type of cell is the most commonly found, accounting for 50-70% of all leukocytes.
if the count exceeds this amount, it is usually caused by an acute infection such as appendicitis, smallpox, or rheumatic fever.
if the count is significantly below normal levels, it may be attributed to a viral infection such as influenza, hepatitis, or rubella.
eosinophils
this granulocyte has large granules that are acidophilic and appear pink  after staining.
the nucleus often has two lobes connected by a band of nuclear material.
the granules contain digestive enzymes that are particularly effective against parasitic worms in their larval form.
these cells also phagocytize antigen-antibody complexes.
less than 5% of leukocytes are eosinophils.
the increased amount beyond that may be due to parasitic diseases, bronchial asthma, or hay fever.
eosinopenia may occur when the human body is severely stressed.
basophil
the basophilic granules in this cell are large, stained deep blue to purple, and are often so numerous that they mask the nucleus.
these granules contain histamines  and heparin .
they represent less than 1% of all leukocytes.
if the count shows an abnormally high number of these cells, hemolytic anemia or chicken pox may be the cause.
lymphocyte
the lymphocyte is an agranular cell with a very clear cytoplasm that is pale blue when stained.
this cell is much smaller than the three previous granulocytes that are all about the same size.
the nucleus of the lymphocyte is stained dark purple and almost fills the cell leaving a very thin rim of cytoplasm.
the t-lymphocytes fight against virus infecting cells and tumor cells.
the b-lymphocytes, which make up 25-35% of leukocytes, produce antibodies.
when there is an overexpression of b-lymphocytes, there may be an infectious mononucleosis or a chronic infection.
aids patients are required to keep a careful watch on their t-cell level, an indicator of the aids virus' activity.
monocyte
agranular in shape, this cell type is the largest among the leukocytes.
the nucleus is most often "u" or kidney bean shaped and the cytoplasm is abundant and light blue .
these cells leave the blood stream  to become macrophages.
as a monocyte or macrophage, these cells are phagocytic and defend the body against viruses and bacteria.
3% to 9% of leukocytes are composed of this type of cells.
people suffering from malaria, endocarditis, typhoid fever, and rocky mountain spotted fever will exhibit an increase the number of monocytes.
high leukocyte counts may be due to inflammation, an immune response, or blood diseases.
<cit>
• an increased percentage of neutrophils may result from:
acute infection, eclampsia, gout, myelocytic leukemia, rheumatoid arthritis, rheumatic fever, acute stress, thyroiditis, or trauma.
• decreased percentage of neutrophils could be caused by:
aplastic anemia, chemotherapy, influenza, widespread bacterial infection, or radiation therapy or exposure.
• increasing percentage of lymphocytes may be attributed to:
chronic bacterial infection, infectious hepatitis, infectious mononucleosis, lymphocytic leukemia, multiple myeloma, infectious mononucleosis, mumps, measles, or recovery from a bacterial infection.
• decreased percentage of lymphocytes may be related to:
chemotherapy, hiv infection, leukemia, radiation therapy or exposure, or sepsis.
• increased monocytes could result from:
chronic inflammatory disease, parasitic infection, tuberculosis, infectious mononucleosis, mumps, or measles.
• increased percentage of eosinophils may be caused by:
allergic reaction, cancer, parasitic infection, or hodgkin's disease.
• basophils percentage reduction may be due to acute allergic reaction.
microscopic leukocyte analysis is very useful for identifying or diagnosing many types of diseases  <cit> .
one can recognize the five different leukocytes via their cytoplasmic granules, staining properties of the granules, sizes and shapes of cells, the proportion of nuclear to cytoplasmic material, and the type of nucleolar lobes.
therefore, developing an automatic leukocyte recognition system is feasible via image processing and pattern recognition techniques.
it is essential to extract the leukocyte image region from a blood smear image for an automatic leukocyte recognition system.
one of the purposes of this paper is to develop an automatic leukocyte nuclei image segmentation method.
a normal neutrophil granulocyte is characterized by the number of nuclear lobes  in the range of two to five.
normally, 10% to 30% of segmented neutrophils have two lobes; the three-lobe type contributes to 40% to 50%, and 10% to 20% are four-lobe type.
five-lobe type constitutes of less than 5%.
when the number of segments is increased to six or more, the cell is hypersegmented.
hypersegmentation is seen most frequently in neutrophils but can also occur in eosinophils and basophils.
hypersegmentation generally represents aging of the cell in the circulation.
corticosteroids usually reduce neutrophil diapedesis into tissues.
as a result, neutrophils remain longer in circulation and may partially become hypersegmented.
a so-called neutrophil right shift , occurs in the cases of leukemias, chronic nephritis, liver diseases, cancer, sepsis, and vitamin b <dig> or folate deficiency.
neutrophil hypersegmentation thus has clinically been widely used as an indicator of b <dig> or folate deficiency.
there were many attempts made to quantify the neutrophil right shift  <cit> .
hence, the other goal of this paper is to develop the automatic method of counting the number of lobes in a cell nucleus.
the experimental results show that the proposed methods resulted in impressive segmentation accuracy.
related works
this section will briefly review some techniques used in this paper as well as some cell segmentation methods.
in this paper, we will compare their performances with the performance of the method provided in this paper by experiments.
mathematical morphology
two basic morphological operations for image shape recognition, dilation, and erosion are introduced in this subsection  <cit> .
erosion can make the objects in a binary image shrink or become thinner.
given an image i ⊆ z <dig> and a structuring element s ⊆ z <dig> , erosion shrinks objects by etching away their boundaries.
the erosion operation ⊙ is defined as
i⊙s={x∈z2|∀s∈s,x+s∈i}.
a binary image contains only two colors: background color and foreground color respectively, described by a 0-bit and a 1-bit.
dilation allows objects' images to expand, thus potentially filling in small holes and connecting disjointed objects.
the dilation operation can be defined as the following:
i⊕s={c∈z2|∃i∈i,∃s∈s,c=i+s}
cell segmentation methods
four cell segmentation methods are reviewed: bone marrow leukocyte segmentation  method  <cit> , nuclei position detection  method  <cit> , fuzzy-based cell detection  method  <cit> , and color and active contour based detection   <cit> .
their performances will be compared to the segmentation method proposed in this paper.
the bmls method  <cit>  was to analyze a set of leukocyte-nucleus-based features using mathematical morphology.
it applies the opening operation  <cit>  on an image and increases the size of the structuring element in order to diminish the objects on the image.
the npd method was developed to automatically segment the cells from genome-wide rnai  screening images.
the nuclei can be separated from dna channel by using a modified watershed algorithm.
the images of cells were then extracted by modeling the interaction between the cells, and by combining both gradient and region information in the actin and rac channels.
a new energy function was formulated based on an interaction model for segmenting tightly clustered cells with significant intensity variance and specific phenotypes, and minimized by using a multiphase level set method.
in npd, otsu's threshold method is first applied to determine a threshold tc to classify all the pixels into two classes.
the distance transform was employed to calculate the shortest distance between each pixel to the non-zero pixel.
finally, the watershed transform was employed to segment the contours of all objects in the image.
the fcd method  <cit>  was to track neural stem cells in a sequence of images.
users can interactively verify and correct the crucial starting segmentation of the first frame, and also inspect the final result while correcting errors if necessary.
all cells are classified into inactive, active, dividing, and clustered cells.
different algorithms are employed to deal with different cell categories.
a special backtracking step was used to automatically correct some common errors that appear in the initial forward tracking process.
the fuzzy threshold method was first applied to classify all the pixels of an image.
two thresholds were calculated.
all pixels with grey-level intensity below the lower threshold were set to  <dig> and all pixels above the higher threshold were set to  <dig>  the gray-level intensities of the remaining pixels, whose gray-level intensities lie between the lower threshold and the higher threshold, are linearly rescaled to the range  <cit> .
then the distance transformed is applied to calculate the shortest distance of any one pixel to the non-zero pixel.
finally, the maximum transform and watershed transform will be applied to determine the contours of all objects in the image.
the cacd method  <cit>  was to cut off the leukocytes from a color blood smear image.
in this method, otsu's threshold method was used to determine a threshold on the green channel of the image.
via the threshold, the initial contours of nucleuses can be detected from the image.
based on the initial contour, active contour method was employed to find the precise boundaries of cytoplasm.
error measure of segmentation
in this paper, four segmentation error measures were used to evaluate the performance of a segmentation method.
over-segmentation rate , under- segmentation rate , and overall error rate  are often applied to evaluate the ability of a segmentation method in severing the roi  from an image  <cit> .
let op be the number of object pixels in the segmentation results but actually not, up be the number of pixels not in the segmentation result but actually included, and dp be the number of pixels in the segmentation result and actually included.
or, ur and er can be described as:
or=opup+dp
ur=upup+dp,
and
er=op+updp.
yang-mao et al.
<cit>  proposed rde  to evaluate object segment results.
let e <dig> e <dig> ...,ene be the pixels on e, and let t <dig> t <dig> ...,tnt be the pixels on t, where e and t are respectively the contour pixels on the segmented object and the ground truth object, and ne as well as nt are the number of pixels on e and t, respectively.
rde is defined as:
rde= <dig>
where dei= min{distance|j =  <dig> , ..., nt},
dtj= min{distance|i =  <dig> , ..., ne}, and
distance is the euclidean distance between ei and tj.
RESULTS
the purpose of this section is to investigate the performances of the lns method in leukocyte nuclei segmentation and the lc method in lobe counting by experiments.
in order to verify the adaptability of the lns method, two image sets are used as the test data.
the two image sets are obtained from different laboratories and different equipments.
there are  <dig> images in set  <dig>  and  <dig> images in set  <dig> .
totally, there are  <dig> leukocytes on all the images in set  <dig> and  <dig> leukocytes on all the images in set  <dig>  these images were taken with optic microscopes at about  <dig> to  <dig> times magnification.
the contours of the leukocyte nuclei manually drawn by a biologist are served as the ground truth.
four of the test images are randomly selected to train the most suitable rs =  <dig> , rg =  <dig> , rt =  <dig> , rr =  <dig> , t <dig> =  <dig>  t <dig> =  <dig>  t <dig> =  <dig>  t <dig> =  <dig>  t <dig> =  <dig> , and t <dig> =  <dig>  via gbpd, where the parameters used are given to nr1=  <dig>  nr2=  <dig>  nr3=  <dig>  nr4=  <dig>  n =  <dig>  n' =  <dig>  and n <dig> = n <dig> = n <dig> = n <dig> = n <dig> = n <dig> =  <dig>  and the lobes in the test images were counted by the biologist in advance.
max_#erosion is set to  <dig>
the first experiment is designed to explore the performance of the lns method and to compare with the performances of the npd, fcd, and cacd methods in segmenting leukocyte nuclei out from a blood smear image.
the segmentation errors are shown in figures  <dig>   <dig>   <dig>   <dig> and tables  <dig> and  <dig>  the experimental results illustrate that the lns method produces much better ur, er, and rde than the npd, fcd, and cacd methods by using the images in sets  <dig> and  <dig> as the test images.
or
ur
er
rde
<dig>
<dig>
<dig>
<dig>
<dig>
<dig>
<dig>
<dig>
<dig>
<dig>
<dig>
<dig>
<dig>
<dig>
<dig>
<dig>
or
ur
er
rde
<dig>
<dig>
<dig>
<dig>
<dig>
<dig>
<dig>
<dig>
<dig>
<dig>
<dig>
<dig>
<dig>
<dig>
<dig>
<dig>
the second experiment is designed to scrutinize the performance of the lc method in splitting the leukocyte nuclei into lobes.
the lc method is used to detect whether a leukocyte nucleus comprises more than one lobe or not, and then to separate those seemed-multi-lobe image of the nucleus into clear lobes.
if the area ratio r of the leukocyte nucleus to its mbr is less than a threshold ra, the leukocyte nucleus is considered to be the nucleus containing more than one lobe.
the r's of  <dig> leukocyte nuclei to their mbrs is shown in figure  <dig>  where the  <dig> leukocyte nuclei have to be split further.
the curve in figure  <dig> displays that its r is almost less than  <dig>  for each leukocyte nuclei.
therefore, in this experiment, ra is set to  <dig> .
the lc method is used to split the leukocyte nuclei into lobes with ra =  <dig> .
in this experiment, the biological expert figures out  <dig> leukocyte nucleus lobes in the  <dig> test images.
the leukocyte nuclei were split into lobes and counted that there are  <dig> leukocyte nucleus lobes in the  <dig> test images.
the accuracy rate of  <dig> % resulted from counting the leukocyte nucleus lobes on the blood smear images by the lc method.
discussion
the first experimental results show that the lns method is inferior to the npd and fcd methods but worse than the cacd method in or by using the images in set  <dig> as test data.
with set  <dig> as test data, the lns method performed better or than the cacd method but worse than the fcd method, and as excellently as the npd method.
the results of this experiment revealed that the lns method resulted in much better ur, er, and rde and is much less sensitive to the variation of images.
in the primary stage of a continued "right shift" , a leukocyte nucleus was twisted and slightly indented, such as the regions indicated by the black dashes in figure  <dig>  the experimental results show that lc method can provide a good lobe split for most leukocyte nuclei, except the leukocyte nuclei with a slight indentation.
CONCLUSIONS
insensitive to the variance of images, the lns method functioned well to isolate the leukocyte nuclei from a blood smear image with much better ur, er, and rde.
the presented lc method is capable of splitting leukocyte nuclei into lobes.
the experimental results illuminated that both methods can give expressive performances.
in addition, three advanced image processing techniques were proposed as weighted sobel operator, gdw, and gbpd.
in a weighted sobel operator, a user can give the most suitable rs to satisfy his requirement.
a bigger rs is required for the user to accentuate the objects with a more definite contour.
to highlight the objects with an indistinct contour, a smaller rs has to be assigned.
gdw can not only enhance the object's contour, but also suppress the noise's contour.
gbpd was used to determine the optimal parameters that were used in lns method.

 leukocytes, derived from bone marrow stem cells, are the first line of defense of the immune system. neutrophils, basophils, and eosinophils are called granulocytes because they have granules in their cytoplasm. the other two leukocyte categories, lymphocytes and monocytes, belong to the mononuclear cell group. this means their nucleus is a single piece. these cells are colorless, but they can be colored with special stains to make them visible under the microscope. the characteristics of the five leukocyte categories are described as follows. figure shows the micrographic images of the five different leukocytes. neutrophil this granulocyte has very tiny stained granules with low visibility. the nucleus is frequently multi-lobed with lobes connected by thin strands of nuclear material. these cells are capable of phagocytizing foreign cells, toxins, and viruses. this type of cell is the most commonly found, accounting for 50-70% of all leukocytes. if the count exceeds this amount, it is usually caused by an acute infection such as appendicitis, smallpox, or rheumatic fever. if the count is significantly below normal levels, it may be attributed to a viral infection such as influenza, hepatitis, or rubella. eosinophils this granulocyte has large granules that are acidophilic and appear pink after staining. the nucleus often has two lobes connected by a band of nuclear material. the granules contain digestive enzymes that are particularly effective against parasitic worms in their larval form. these cells also phagocytize antigen-antibody complexes. less than 5% of leukocytes are eosinophils. the increased amount beyond that may be due to parasitic diseases, bronchial asthma, or hay fever. eosinopenia may occur when the human body is severely stressed. basophil the basophilic granules in this cell are large, stained deep blue to purple, and are often so numerous that they mask the nucleus. these granules contain histamines and heparin. they represent less than 1% of all leukocytes. if the count shows an abnormally high number of these cells, hemolytic anemia or chicken pox may be the cause. lymphocyte the lymphocyte is an agranular cell with a very clear cytoplasm that is pale blue when stained. this cell is much smaller than the three previous granulocytes that are all about the same size. the nucleus of the lymphocyte is stained dark purple and almost fills the cell leaving a very thin rim of cytoplasm. the t-lymphocytes fight against virus infecting cells and tumor cells. the b-lymphocytes, which make up 25-35% of leukocytes, produce antibodies. when there is an overexpression of b-lymphocytes, there may be an infectious mononucleosis or a chronic infection. aids patients are required to keep a careful watch on their t-cell level, an indicator of the aids virus' activity. monocyte agranular in shape, this cell type is the largest among the leukocytes. the nucleus is most often "u" or kidney bean shaped and the cytoplasm is abundant and light blue. these cells leave the blood stream to become macrophages. as a monocyte or macrophage, these cells are phagocytic and defend the body against viruses and bacteria. 3% to 9% of leukocytes are composed of this type of cells. people suffering from malaria, endocarditis, typhoid fever, and rocky mountain spotted fever will exhibit an increase the number of monocytes. high leukocyte counts may be due to inflammation, an immune response, or blood diseases. • an increased percentage of neutrophils may result from: acute infection, eclampsia, gout, myelocytic leukemia, rheumatoid arthritis, rheumatic fever, acute stress, thyroiditis, or trauma. • decreased percentage of neutrophils could be caused by: aplastic anemia, chemotherapy, influenza, widespread bacterial infection, or radiation therapy or exposure. • increasing percentage of lymphocytes may be attributed to: chronic bacterial infection, infectious hepatitis, infectious mononucleosis, lymphocytic leukemia, multiple myeloma, infectious mononucleosis, mumps, measles, or recovery from a bacterial infection. • decreased percentage of lymphocytes may be related to: chemotherapy, hiv infection, leukemia, radiation therapy or exposure, or sepsis. • increased monocytes could result from: chronic inflammatory disease, parasitic infection, tuberculosis, infectious mononucleosis, mumps, or measles. • increased percentage of eosinophils may be caused by: allergic reaction, cancer, parasitic infection, or hodgkin's disease. • basophils percentage reduction may be due to acute allergic reaction. microscopic leukocyte analysis is very useful for identifying or diagnosing many types of diseases. one can recognize the five different leukocytes via their cytoplasmic granules, staining properties of the granules, sizes and shapes of cells, the proportion of nuclear to cytoplasmic material, and the type of nucleolar lobes. therefore, developing an automatic leukocyte recognition system is feasible via image processing and pattern recognition techniques. it is essential to extract the leukocyte image region from a blood smear image for an automatic leukocyte recognition system. one of the purposes of this paper is to develop an automatic leukocyte nuclei image segmentation method. a normal neutrophil granulocyte is characterized by the number of nuclear lobes in the range of two to five. normally, 10% to 30% of segmented neutrophils have two lobes; the three-lobe type contributes to 40% to 50%, and 10% to 20% are four-lobe type. five-lobe type constitutes of less than 5%. when the number of segments is increased to six or more, the cell is hypersegmented. hypersegmentation is seen most frequently in neutrophils but can also occur in eosinophils and basophils. hypersegmentation generally represents aging of the cell in the circulation. corticosteroids usually reduce neutrophil diapedesis into tissues. as a result, neutrophils remain longer in circulation and may partially become hypersegmented. a so-called neutrophil right shift, occurs in the cases of leukemias, chronic nephritis, liver diseases, cancer, sepsis, and vitamin b or folate deficiency. neutrophil hypersegmentation thus has clinically been widely used as an indicator of b or folate deficiency. there were many attempts made to quantify the neutrophil right shift. hence, the other goal of this paper is to develop the automatic method of counting the number of lobes in a cell nucleus. the experimental results show that the proposed methods resulted in impressive segmentation accuracy. related works this section will briefly review some techniques used in this paper as well as some cell segmentation methods. in this paper, we will compare their performances with the performance of the method provided in this paper by experiments. mathematical morphology two basic morphological operations for image shape recognition, dilation, and erosion are introduced in this subsection. erosion can make the objects in a binary image shrink or become thinner. given an image i ⊆ z and a structuring element s ⊆ z, erosion shrinks objects by etching away their boundaries. the erosion operation ⊙ is defined as i⊙s={x∈z2|∀s∈s,x+s∈i}. a binary image contains only two colors: background color and foreground color respectively, described by a 0-bit and a 1-bit. dilation allows objects' images to expand, thus potentially filling in small holes and connecting disjointed objects. the dilation operation can be defined as the following: i⊕s={c∈z2|∃i∈i,∃s∈s,c=i+s} cell segmentation methods four cell segmentation methods are reviewed: bone marrow leukocyte segmentation method, nuclei position detection method, fuzzy-based cell detection method, and color and active contour based detection. their performances will be compared to the segmentation method proposed in this paper. the bmls method was to analyze a set of leukocyte-nucleus-based features using mathematical morphology. it applies the opening operation on an image and increases the size of the structuring element in order to diminish the objects on the image. the npd method was developed to automatically segment the cells from genome-wide rnai screening images. the nuclei can be separated from dna channel by using a modified watershed algorithm. the images of cells were then extracted by modeling the interaction between the cells, and by combining both gradient and region information in the actin and rac channels. a new energy function was formulated based on an interaction model for segmenting tightly clustered cells with significant intensity variance and specific phenotypes, and minimized by using a multiphase level set method. in npd, otsu's threshold method is first applied to determine a threshold tc to classify all the pixels into two classes. the distance transform was employed to calculate the shortest distance between each pixel to the non-zero pixel. finally, the watershed transform was employed to segment the contours of all objects in the image. the fcd method was to track neural stem cells in a sequence of images. users can interactively verify and correct the crucial starting segmentation of the first frame, and also inspect the final result while correcting errors if necessary. all cells are classified into inactive, active, dividing, and clustered cells. different algorithms are employed to deal with different cell categories. a special backtracking step was used to automatically correct some common errors that appear in the initial forward tracking process. the fuzzy threshold method was first applied to classify all the pixels of an image. two thresholds were calculated. all pixels with grey-level intensity below the lower threshold were set to and all pixels above the higher threshold were set to the gray-level intensities of the remaining pixels, whose gray-level intensities lie between the lower threshold and the higher threshold, are linearly rescaled to the range. then the distance transformed is applied to calculate the shortest distance of any one pixel to the non-zero pixel. finally, the maximum transform and watershed transform will be applied to determine the contours of all objects in the image. the cacd method was to cut off the leukocytes from a color blood smear image. in this method, otsu's threshold method was used to determine a threshold on the green channel of the image. via the threshold, the initial contours of nucleuses can be detected from the image. based on the initial contour, active contour method was employed to find the precise boundaries of cytoplasm. error measure of segmentation in this paper, four segmentation error measures were used to evaluate the performance of a segmentation method. over-segmentation rate, under- segmentation rate, and overall error rate are often applied to evaluate the ability of a segmentation method in severing the roi from an image. let op be the number of object pixels in the segmentation results but actually not, up be the number of pixels not in the segmentation result but actually included, and dp be the number of pixels in the segmentation result and actually included. or, ur and er can be described as: or=opup+dp ur=upup+dp, and er=op+updp. yang-mao et al. proposed rde to evaluate object segment results. let e e...,ene be the pixels on e, and let t t...,tnt be the pixels on t, where e and t are respectively the contour pixels on the segmented object and the ground truth object, and ne as well as nt are the number of pixels on e and t, respectively. rde is defined as: rde= where dei= min{distance|j =,..., nt}, dtj= min{distance|i =,..., ne}, and distance is the euclidean distance between ei and tj.  the purpose of this section is to investigate the performances of the lns method in leukocyte nuclei segmentation and the lc method in lobe counting by experiments. in order to verify the adaptability of the lns method, two image sets are used as the test data. the two image sets are obtained from different laboratories and different equipments. there are images in set and images in set. totally, there are leukocytes on all the images in set and leukocytes on all the images in set these images were taken with optic microscopes at about to times magnification. the contours of the leukocyte nuclei manually drawn by a biologist are served as the ground truth. four of the test images are randomly selected to train the most suitable rs =, rg =, rt =, rr =, t = t = t = t = t =, and t = via gbpd, where the parameters used are given to nr1= nr2= nr3= nr4= n = n' = and n = n = n = n = n = n = and the lobes in the test images were counted by the biologist in advance. max_#erosion is set to the first experiment is designed to explore the performance of the lns method and to compare with the performances of the npd, fcd, and cacd methods in segmenting leukocyte nuclei out from a blood smear image. the segmentation errors are shown in figures and tables and the experimental results illustrate that the lns method produces much better ur, er, and rde than the npd, fcd, and cacd methods by using the images in sets and as the test images. or ur er rde or ur er rde the second experiment is designed to scrutinize the performance of the lc method in splitting the leukocyte nuclei into lobes. the lc method is used to detect whether a leukocyte nucleus comprises more than one lobe or not, and then to separate those seemed-multi-lobe image of the nucleus into clear lobes. if the area ratio r of the leukocyte nucleus to its mbr is less than a threshold ra, the leukocyte nucleus is considered to be the nucleus containing more than one lobe. the r's of leukocyte nuclei to their mbrs is shown in figure where the leukocyte nuclei have to be split further. the curve in figure displays that its r is almost less than for each leukocyte nuclei. therefore, in this experiment, ra is set to. the lc method is used to split the leukocyte nuclei into lobes with ra =. in this experiment, the biological expert figures out leukocyte nucleus lobes in the test images. the leukocyte nuclei were split into lobes and counted that there are leukocyte nucleus lobes in the test images. the accuracy rate of % resulted from counting the leukocyte nucleus lobes on the blood smear images by the lc method. discussion the first experimental results show that the lns method is inferior to the npd and fcd methods but worse than the cacd method in or by using the images in set as test data. with set as test data, the lns method performed better or than the cacd method but worse than the fcd method, and as excellently as the npd method. the results of this experiment revealed that the lns method resulted in much better ur, er, and rde and is much less sensitive to the variation of images. in the primary stage of a continued "right shift", a leukocyte nucleus was twisted and slightly indented, such as the regions indicated by the black dashes in figure the experimental results show that lc method can provide a good lobe split for most leukocyte nuclei, except the leukocyte nuclei with a slight indentation.  insensitive to the variance of images, the lns method functioned well to isolate the leukocyte nuclei from a blood smear image with much better ur, er, and rde. the presented lc method is capable of splitting leukocyte nuclei into lobes. the experimental results illuminated that both methods can give expressive performances. in addition, three advanced image processing techniques were proposed as weighted sobel operator, gdw, and gbpd. in a weighted sobel operator, a user can give the most suitable rs to satisfy his requirement. a bigger rs is required for the user to accentuate the objects with a more definite contour. to highlight the objects with an indistinct contour, a smaller rs has to be assigned. gdw can not only enhance the object's contour, but also suppress the noise's contour. gbpd was used to determine the optimal parameters that were used in lns method. 
therefore, the development of an automatic leukocyte recognition system is feasible and necessary. it is essential to extract the leukocyte region from a blood smear image in order to develop an automatic leukocyte recognition system. the experimental results demonstrated impressive segmentation accuracy. the experimental results illuminated that both methods can give expressive performances. the five types of leukocytes can be distinguished by their cytoplasmic granules, staining properties of the granules, size of cell, the proportion of the nuclear to the cytoplasmic material, and the type of nucleolar lobes. the number of lobes increased when leukemia, chronic nephritis, liver disease, cancer, sepsis, and vitamin b or folate deficiency occurred. clinical neutrophil hypersegmentation has been widely used as an indicator of b or folate deficiency.biomedical technologists can currently recognize abnormal leukocytes using human eyes. clinical neutrophil hypersegmentation has been widely used as an indicator of b or folate deficiency. an increased percentage of neutrophils may be caused by an acute infection, while an increased percentage of lymphocytes can be caused by a chronic bacterial infection. the purpose of this paper is to contribute an automatic leukocyte nuclei image segmentation method for such recognition technology. insensitive to the variance of images, the lns method functioned well to isolate the leukocyte nuclei from a blood smear image with much better ur, er, and rde. the presented lc method is capable of splitting leukocyte nuclei into lobes. in addition, three advanced image processing techniques were proposed as weighted sobel operator, gdw, and gbpd. any infection or acute stress may increase or decrease the number of leukocytes. the other goal of this paper is to develop the method of counting the number of lobes in a cell nucleus.
 leukocytes play an important role in the human immune system. the family of leukocytes is comprised of lymphocytes, monocytes, eosinophils, basophils, and neutrophils. any infection or acute stress may increase or decrease the number of leukocytes. an increased percentage of neutrophils may be caused by an acute infection, while an increased percentage of lymphocytes can be caused by a chronic bacterial infection. it is important to realize an abnormal variation in the leukocytes. the five types of leukocytes can be distinguished by their cytoplasmic granules, staining properties of the granules, size of cell, the proportion of the nuclear to the cytoplasmic material, and the type of nucleolar lobes. the number of lobes increased when leukemia, chronic nephritis, liver disease, cancer, sepsis, and vitamin b or folate deficiency occurred. clinical neutrophil hypersegmentation has been widely used as an indicator of b or folate deficiency.biomedical technologists can currently recognize abnormal leukocytes using human eyes. however, the quality and efficiency of diagnosis may be compromised due to the limitations of the biomedical technologists' eyesight, strength, and medical knowledge. therefore, the development of an automatic leukocyte recognition system is feasible and necessary. it is essential to extract the leukocyte region from a blood smear image in order to develop an automatic leukocyte recognition system. the number of lobes increased when leukemia, chronic nephritis, liver disease, cancer, sepsis, and vitamin b or folate deficiency occurred. clinical neutrophil hypersegmentation has been widely used as an indicator of b or folate deficiency.  the purpose of this paper is to contribute an automatic leukocyte nuclei image segmentation method for such recognition technology. the other goal of this paper is to develop the method of counting the number of lobes in a cell nucleus. the experimental results demonstrated impressive segmentation accuracy.  insensitive to the variance of images, the lns method functioned well to isolate the leukocyte nuclei from a blood smear image with much better ur, er, and rde. the presented lc method is capable of splitting leukocyte nuclei into lobes. the experimental results illuminated that both methods can give expressive performances. in addition, three advanced image processing techniques were proposed as weighted sobel operator, gdw, and gbpd. 