A Geometrc Approach To Fully Automatc Chromosome Segmentaton Shervn Mnaee ECE Department New York Unversty Brooklyn, New York, USA shervn.mnaee@nyu.edu Mehran Fotouh Computer Engneerng Department Sharf Unversty of Technology Tehran, Iran mehran.fotouh@gmal.com Babak Hossen Khalaj Electrcal Engneerng Department Sharf Unversty of Technology Tehran, Iran khalaj@sharf.edu arxv:1112.4164v5 [cs.cv] 1 Sep 2014 Abstract A fundamental task n human chromosome analyss s chromosome segmentaton. Segmentaton plays an mportant role n chromosome karyotypng. The frst step n segmentaton s to remove ntrusve objects such as stan debrs and other noses. The next step s detecton of touchng and overlappng chromosomes, and the fnal step s separaton of such chromosomes. Common methods for separaton between touchng chromosomes are nteractve and requre human nterventon for correct separaton between touchng and overlappng chromosomes. In ths paper, a geometrc-based method s used for automatc detecton of touchng and overlappng chromosomes and separatng them. The proposed scheme performs segmentaton n two phases. In the frst phase, chromosome clusters are detected usng three geometrc crtera, and n the second phase, chromosome clusters are separated usng a cut-lne. Most of earler methods dd not work properly n case of chromosome clusters that contaned more than two chromosomes. Our method, on the other hand, s qute effcent n separaton of such chromosome clusters. At each step, one separaton wll be performed and ths algorthm s repeated untl all ndvdual chromosomes are separated. Another mportant pont about the proposed method s that t uses the geometrc features of chromosomes whch are ndependent of the type of mages and t can easly be appled to any type of mages such as bnary mages and does not requre multspectral mages as well. We have appled our method to a database contanng 62 touchng and partally overlappng chromosomes and a success rate of 91.9% s acheved. I. INTRODUCTION Chromosome karyotypng s an essental task n cytogenetcs and s usually performed n clncal and cancer cytogenetc labs and can be used n the dagnoss of genetc dsorders. The normal human karyotypes contan 22 pars of autosomal chromosomes and one par of sex chromosomes. Chromosome karyotypng s meant to dentfy and assgn each chromosome n the mage to one of the 24 classes. Chromosome karyotypng has three man steps: pre-processng, segmentaton and classfcaton. Among these steps, chromosome segmentaton s very mportant, snce t affects performance of classfcaton whch s the fnal goal. Chromosome mages may have some defects; they may be bent, they may touch or overlap and ther bands may be spread. In addton, snce touchng and overlappng chromosomes exst n almost every metaphase mage, the soluton of ths problem s vtal. The frst step n analyzng a chromosome mage s segmentaton of chromosomes from the mage background, the man methods used n ths step are based on the evaluaton of a global threshold by means of the Otsu method [1], or on a re-thresholdng scheme [2]. Due to the fact that long chromosomes may touch and overlap, the frst segmentaton step s usually unable to dentfy each chromosome as a sngle object, and presents a number of clusters. So far, attempts have been made to deal wth clusters of touchng (but not overlappng) chromosomes [3], [4], [5], and for clusters of overlappng (but not touchng) chromosomes [6], [7], where both of geometrc and ntensty based features have been used to resolve segmentaton ambgutes. Lerner [8] proposed a method to combne the choce of correct cluster dsentanglement wth the classfcaton stage, resultng n a classfcaton-drven segmentaton. Grsan [9] proposed a smlar method. There are many other methods for separaton between touchng and overlappng objects [10], [11]. Schwartzkopf [12] proposed a method for jont segmentaton and classfcaton that used statstcal method. Snce ths method was appled to multspectral chromosome mages, t does not work for bnary mages. So far, most of chromosome analyss systems have a common fault: ther poor automatc chromosome ncson ablty. Most of current systems for automatc chromosome segmentaton are nteractve and need human nterventon. We have to menton that the orgnal mages are pre-processed and the chromosomes are segmented from the background and the ntrusve objects and noses are removed from the background. Therefore, our man effort s to detect and separate touchng or overlappng chromosomes. It s worth mentonng that there are dfferent approaches for segmentaton and classfcaton of medcal mages. One man approach s to the geometrc characterstcs of the object of nterest, the other one s usng spatal and transform doman features of the mage, etc. The rght set of features depends on the applcaton. For example, n bometrc recognton area, there are a lot of works based on spatal and frequency doman nformaton of mages. One such work s presented n [13], where the author uses the spatal and wavelet doman features of mages to perform palmprnt recognton. However, some of those approaches requres a very large dataset to tran the model properly so they may not be applcable to small datasets, because they could be very prone to over-fttng. A good work for dealng wth small dataset s presented n [14], where the author explans how to jontly maxmze the model
accuracy and relablty. In ths paper, a geometrc method for segmentaton of the touchng and partally overlappng chromosomes s presented. Frst, we ntroduce an approach to evaluate whether an object s a sngle chromosome or a chromosome cluster. By chromosome clusters, we mean a group of chromosomes whch overlap and touch each other. Subsequently, for each cluster, we use geometrc features of chromosome boundary whch help separate touchng or partally overlappng chromosomes. Chromosome segmentaton s performed n two phases. In the frst phase, touchng or overlappng chromosomes are detected usng the approach whch s ntroduced n Secton II where we deal wth the chromosomes shape and ther geometrc features. If two or more chromosomes overlap, the resultng cluster would not have the usual long and thn shape and we can use such dfference to detect chromosome clusters. In the second phase, we use other geometrc features to separate touchng or partally overlappng chromosomes. We wll dscuss about ths step n Secton III whch deals wth boundary pattern of chromosomes. Our method has three advantages over earler schemes: 1) Frst, t can be appled to any type of mages, even bnary mage, and t does not need multspectral or grayscale mages. Therefore t can reduce the cost of photography and the amount of computaton. 2) Second, t can easly separate chromosome clusters that contan more than two chromosomes where most earler schemes fal. 3) Thrd, our method s fully automatc and does not need any human nterventon. II. DETECTION OF TOUCHING OR OVERLAPPING CHROMOSOMES In order to detect chromosome clusters, we use three crtera whch deal wth the geometry of chromosomes. The frst method s surroundng ellpse method (Secton II.A), whch s based on the rato of the length of mnor axs of surroundng ellpse to the length of ts major axs. The second method s convex hull method (Secton II.B) whch s based on the number of pxels n the orgnal chromosome to the number of pxels n ts convex hull rato. An mportant pont about ths method s ts robustness n detectng small chromosomes that may produce error n the frst method. The thrd method s skeleton and end ponts (Secton II.C), whch uses the skeleton of each chromosome (ether sngle chromosome or a chromosome cluster) to fnd the end ponts of skeleton and decdes based on the number of end ponts. All of these methods have some lmtatons, but through proper ntegraton, we can detect all chromosome clusters (ether touchng or overlappng chromosomes) as shown through our smulaton results. Each chromosome passes through these three methods and n case t satsfes the crtera of all three methods, t wll be detected as a chromosome cluster. We wll dscuss the detals of each method n the followng parts. A. Surroundng ellpse method Surroundng ellpse of a shape s an ellpse whch surrounds that. Sngle chromosome s usually long and thn (unless those chromosomes whch belong to 20th, 21st or 22nd group) so ts surroundng ellpse wll be long, but the overlappng chromosomes have a surroundng ellpse close to a crcle. We can use ths dfference for detecton of overlappng chromosomes. In order to take advantage of such dfference, the rato of the length of mnor to major axs of the surroundng ellpse has to be found. If the label s overlappng, we expect ths rato to be close to 1, because the surroundng ellpse would be close to a crcle, but f the chromosome s sngle t wll have a smaller rato. Therefore, a threshold can be determned to dstngush between chromosome clusters and sngle chromosomes. We propose the below algorthm for ths step: 1) Fnd the surroundng ellpse of each chromosome label 2) Fnd the rato of mnor axs length to major axs length of surroundng ellpse for each chromosome (ether a sngle chromosome or chromosome cluster) 3) Determne a threshold (we smply set ths threshold to the average of all ratos, but f we have a large dataset, we can use a tranng set to determne ths threshold) 4) Compare rato of each label wth ths threshold. For each label, f the rato s less than the threshold, remove t, but f the rato s more than the threshold, keep ths chromosome Ths method s very fast, but t has problems wth two types of chromosomes: 1) Small chromosomes 2) Bent chromosomes The shape of small chromosomes s dfferent from usual chromosomes as they have a round shape where the rato of mnor axs length to major axs length of ther surroundng ellpse wll be smlar to overlappng chromosomes. Bent chromosomes also have ratos smlar to overlappng chromosomes so they may wrongly be detected as overlappng chromosomes, an ssue that needs to be addressed properly. As the proposed algorthms are appled to each chromosome n a cascade fashon, each step has to remove those sngle chromosomes whch are not removed n the prevous steps. B. Convex hull method In Eucldean space, an object s convex f for every par of ponts wthn the object, every pont on the straght lne segment that jons them s also wthn the object. The convex hull of a set C s the smallest convex set that contans C. Convex hull have been used n several applcatons n computer vson, mage analyss, and dgtal mage processng, ncludng object recognton, mage and vdeo codng. As a normal chromosome has a relatvely convex shape, ts convex hull would approxmately have the same number of pxels as the orgnal chromosome. If we fnd the convex hull of the chromosomes, we wll notce that the convex hull of chromosome clusters have much more pxels than chromosome clusters themselves, whereas the sngle chromosomes have almost the
same number of pxels as ther convex hulls. Consequently, we can detect chromosome clusters usng such dfference. In order to acheve ths goal, we should fnd the rato of the number of pxels n each chromosome to number of pxel n ts convex hull for all chromosomes and then compare these ratos wth a threshold. For each chromosome, f the rato s less than a gven threshold, we expect that ths label would be an overlappng chromosomes and vce versa. The proposed algorthm for ths method s gven below: 1) Fnd convex hull of each chromosome label. 2) Calculate the rato of the number of pxels n the orgnal chromosome to the number of pxel n ts convex hull for each chromosome. 3) Determne a threshold (ths threshold can be determned usng tranng set, or t can smply set to the average of these ratos for all chromosomes) 4) Compare ths rato for each chromosome wth ths threshold, for each label f the rato was more than the threshold elmnate ths chromosomes. 5) The remanng chromosomes wll be sent to the next step. One advantage of ths method s that we can elmnate small sngle chromosomes remanng from the prevous step. Snce for these chromosomes the convex hull s almost concdent wth orgnal chromosome, the rato wll be more than the gven threshold. However, as we stll have problem wth bent chromosomes, we should elmnate them n the next step. Fg.1 represents an mage of chromosomes wth convex hulls of two chromosomes. Fg. 1. A chromosome mage wth convex hull of two chromosomes C. Skeleton and end ponts Skeletonzaton s the transformaton of a component n a dgtal mage nto a subset of the orgnal component. Skeleton has been used n several applcatons n computer vson, mage analyss, and dgtal mage processng. We used ths method as one step of the chromosome clusters detecton algorthm. If we fnd the skeleton of each chromosome and then fnd the end ponts of ths skeleton (end ponts are those pont whch are the last pont n any sde of a lne) we wll notce that the overlappng chromosomes usually have more than 2 end ponts. Therefore, we can use ths dea for detecton of overlappng chromosomes. Skeletons and end ponts of a set of chromosomes are represented n Fg.2. End ponts of chromosomes are shown wth red ponts. We observe that all chromosomes clusters n ths pcture have more than two end ponts. Fg. 2. An example of skeletons and end ponts of a chromosome mage The proposed algorthm for ths method s: 1) Fnd the skeleton of each chromosomes. 2) Fnd the end ponts of each skeleton. 3) In the case more than two ponts are found, classfy them as a chromosome clusters. Ths method s robust for fndng overlappng chromosomes. However, because of the teratve structure of the skeleton algorthm, t s tme-consumng and we should mprove ts computatonal complexty. In the next part, we combne these three methods n a proper way. D. Integraton Step In order to solve the problem of the skeleton method, we decded to apply ths method to a fewer number of chromosomes, ntally 40 to 46 chromosomes, some of whch are overlappng. Frst, we apply convex hull and surroundng ellpse methods and elmnate a large number of sngle chromosomes. After these two steps we usually have about 8 to 14 chromosomes. Subsequently, the skeleton method can be appled to detect chromosome clusters from the remanng ones and because the number of chromosomes has been reduced from 46 to between 8 and 14, we wll mprove the tme effcency of the algorthm by a factor of 4. On the other hand, the surroundng ellpse method can not elmnate small sngle chromosomes and t s better to apply surroundng ellpse method after convex hull method. The block dagram for the drecton of overlappng chromosomes shown n Fg.3 : Each chromosome passes through these three methods and f t satsfes all three crtera, t wll be consdered as a chromosome cluster. After detecton of all chromosome clusters, they wll be used as the nput of the second phase, whch s separaton of chromosome clusters.
Fg. 3. Block dagram of chromosome clusters detecton algorthm III. SEPARATION OF TOUCHING OR PARTIALLY OVERLAPPING CHROMOSOMES USING CUT-LINE METHOD As dscussed prevously, after detecton of overlappng chromosomes we need to separate them. We ntroduce another geometrc-based method for separaton of touchng or partally overlappng chromosomes. Frst, we fnd the cross-ponts of overlappng chromosomes. Crossponts are those ponts on the boundary of a chromosome cluster where two chromosomes touch or overlap. We wll dscuss the methods whch can be used to fnd these crossponts n Sectons III.A and III.B. Through the applcaton of the proposed method, varous touchng or partally overlappng chromosomes can be handled n the same way. Two chromosome clusters and ther cross-ponts are shown n Fg.4: Fg. 4. Cross-ponts of chromosome clusters Once the cross-ponts are found, we should separate chromosome clusters usng these cross-ponts. If the chromosome cluster conssts of two chromosomes, t can then be cut from the lne between cross-ponts resultng n two sngle chromosomes. However, f t conssts of more than two chromosomes, we should repeat the whole algorthm multple tmes. In the followng sectons, we wll ntroduce some approaches to fnd such cross-ponts. In order to fnd these cross-ponts, we only need to search on the boundary of the chromosomes. Therefore, n order to reduce the amount of computatons, we can extract the boundary of chromosomes and search for the cross-ponts only n the boundary locatons. Once the boundary extracton s done, we can sort the pxels on the boundary n a clockwse fashon. Suppose that the sorted boundary pxels are located n an N 2 matrx n whch each row contans the coordnates of the -th pxel on the boundary and N s the total number of pxels on the boundary. Ths boundary matrx wll be denoted by B. Fg.5 llustrates the result of boundary extracton n a chromosome cluster. In order to fnd the cross-ponts, we use two crtera based on the geometry of the boundary. The crtera are: 1) Varatons n the Angle of Moton Drecton (VAMD) 2) Sum of Dstances among Total Ponts (SDTP) Fg. 5. A chromosome cluster and ts boundary The frst crteron, VAMD, s explaned n Secton III.A. It tres to fnd the cross-ponts based on the varaton n the angle of moton. The second crteron s SDTP as explaned n Secton III.B. Ths crteron uses the fact that cross-ponts are usually located n the mddle of a chromosome cluster. All pxels of the boundary pass through these two crtera, and at each step, some of boundary ponts wll be elmnated and the total crossponts wll be selected wth a cost functon whch takes nto account both these crtera. A. Varatons n the Angle of Moton Drecton (VAMD) In order to understand the meanng of VAMD, suppose that an object s movng on the boundary of a chromosome. At each pxel, t has to move n a drecton called moton drecton whch leads t to the next pxel. The angle between ths drecton and the horzontal axs s called the angle of moton drecton. Ths angle can be calculated as the angle of connectng lne between -th and (+1)-th pxels. We denote ths angle wth θ. ( ) y(+1) y() θ = tan 1 x(+1) x() It should be noted that due to nose on the boundary, t s better to use more pxels to fnd a better estmaton of the angle of moton drecton. One can use angle of the connectng lne between -th pxel and j-th pxel as: θ (j) ( ) y(j) y() = tan 1 x(j) x() Subsequently, we can use a weghted average of θ (j) dfferent j s to fnd a robust estmaton of θ. θ = +N1 j=+1 β(j) θ (j) j= N 2 α (j) θ (j) + 1 +N1 j=+1 β(j) + 1 j= N 2 α (j) usng the forthcomng pxels and the second summaton s the estmated θ (j) and α (j) can be set to The frst summaton s the estmated θ (j) usng prevous pxels. The weghts β (j) a fxed value or can be adaptve. The adaptve choce usually works better and t has to be a functon of the Eucldean dstance between the -th and j-th pxels. For example, one possble choce of β (j) and α (j) could be e (d(b,bj))2, where d(b,b j ) denotes the Eucldean dstance between -th and j-th (1) (2) for (3)
pxels. As can be verfed from the above formula, for pxels wth long dstance from the current pxel, d(b,b j ) would be large, therefore the correspondng weghts would be very small, whch s reasonable. Based on our smulaton we deduced that f j=+4, +5 are used, the result wll be the most satsfactory. Therefore, we used the followng formula to fnd θ : θ = (1/2) (θ (+4) Fg.6 depcts ths method on a curve. Fg. 6. +θ (+5) ) (4) Representaton of boundary pxel s angle After fndng θ for all pxels on the boundary, we have to calculate the varaton of angle n the -th pxel as the dfference of the (+1)-th pxel angle and the -th pxel. θ = θ +1 θ (5) We expect to have a larger θ n cross-ponts compared to the other ponts of the boundary. We can use the followng algorthm to remove superfluous ponts on the boundary: 1) Fnd the varaton of angle n each pxel on the boundary. N =1 2) Calculate the average of θ : θ avg = θ N. 3) For each pxel f θ < λ 1 θ avg then remove ths pxel from canddate pxels for cross-ponts (we used λ 1 =1 whch s found by tral and error). The result of ths step s shown n Fg.7. n the cross-ponts to be less than the other ponts. We can fnd the sum of dstances from each pxel to other pxels as: Ds() = M d(b,b j ) for = 1 : M (6) j=1 j where d(b,b j ) s the Eucldean dstance between -th and j-th pxels on the boundary. We can select two pxels wth the mnmum amount of Ds() as cross-ponts. However n some cases, ths method can select the wrong ponts. For example, f one small chromosome touches a large chromosome by ts end, ths selecton method wll not work properly. Therefore, we have to use another crteron alongsde ths crteron n order to avod such errors. In order to avod ms-selecton, we can use both VAMD and SDTP n our fnal decson crteron. Therefore, n cases that SDPT cannot select the rght ponts, VAMD can help the algorthm avod ms-selecton. We defned a cost functon whch takes nto account both VAMD and SDTP and selects two ponts wth mnmum amount of cost functon as the crossponts. Cost() = Ds() λ θ (7) The parameter λ should be a postve number that can control the effect of θ n the cost functon. In order to mnmze ths functon, one needs to mnmze Ds() and maxmze θ. The value of λ can be determned by tral and error on a tranng set. Based on our smulaton λ=1000 produces satsfactory results. After applyng ths algorthm, we wll choose two ponts wth the two least values of Cost() as the cross-ponts and overlappng chromosome can be separated usng the lne between these two ponts. The result of ths step s shown n Fg.8. Fg. 7. Remanng pxels after applyng VAMD crteron Fg. 8. Separaton of chromosome clusters wth proposed method B. Sum of Dstances among Total Ponts (SDTP) Because of nose n chromosomes mages, after the aforementoned step, there may reman more than two ponts, so we should use another crteron to fnd the cross-ponts. Let us assume after the prevous step, M ponts have remaned. We denote these ponts wth B 1 to B M where M s the number of remanng ponts. The cross-ponts are usually located n the mddle of overlappng chromosomes (because overlappng chromosomes are formed by two or more chromosomes). For each remanng pxel, we fnd the sum of dstances between ths pxel and other remanng pxels and we expect ths sum IV. SEPARATION OF CHROMOSOME CLUSTERS WITH MORE THAN TWO CHROMOSOMES In the prevous sectons, we concentrated on chromosome clusters consstng of two chromosomes. In some cases, chromosome clusters may have more than two chromosomes. For bnary mages, t s dffcult to separate a chromosome cluster wth more than two sngle chromosomes n one step. However, we can easly separate ths type of chromosome clusters by a mult-step algorthm. In fact, f a chromosome cluster conssts of N sngle chromosomes, we can separate all sngle chromosomes n N-1 steps. We propose the followng algorthm for separaton of clusters wth more than two chromosomes:
TABLE I PROPOSED METHOD ACCURACY, COMMPARED TO METHODS IN THE LITERATURE Method Number of touchng or partally overlappng chromosoms Accuracy J (1989) [1] set 1 458 95% J (1989) [1] set 2 565 98% Lerner (1998) [4] 46 82% Grsan (2009) [9] 819 90% Proposed method 62 91.9% 1) Separate each chromosome cluster wth prevous methods. After separaton we wll have two new chromosomes. 2) For each new chromosome check whether t s a sngle chromosome or a chromosome cluster. 3) If both of the new chromosomes are sngle, the algorthm s fnshed. 4) If at least one of the new chromosome s a chromosome cluster, separate t usng the procedure n the second phase. 5) Contnue ths algorthm untl all new chromosomes are sngle. Fg. 9. method Examples of separaton of chromosome clusters usng proposed V. RESULTS By usng the proposed algorthm, we analyzed 25 mages contanng a total number of 1150 chromosomes. There are about 62 touchng or partally overlappng chromosomes n ths data set. We are nterested n assessment of the ablty of the proposed algorthm to successfully separate clusters nto ther composng chromosomes. We tested our algorthm on these 62 chromosome clusters and observed that ths algorthm separates 57 chromosome clusters correctly. So an accuracy rate about 91.9% s attaned. In Table I, we have reported the fracton of correct separatons of touchng and partally overlappng wth respect to ther total number. In ths table, we also have reported a comparson wth all smlar results reported n the lterature. Fg.9 presents results of separaton between sx touchng and partally overlappng chromosomes. As we can see, ths method provdes very effcent separaton of touchng and partally overlappng chromosomes. VI. CONCLUSION In ths paper, a geometrc-based approach s proposed for chromosome segmentaton. It uses three crtera for detecton of chromosome clusters. After that, t uses a novel geometrc method to fnd two cross-ponts on the boundary of clusters whch can be used for extracton of cut-lne. After the cutlne s found, we can decompose groups of chromosomes whch touch and overlap each other. Ths algorthm s able to decompose clusters of touchng or partally overlappng chromosomes that consst of more than two chromosomes. Another advantage of ths method s that t can easly apply to any type of mages, even bnary chromosome mages. In addton, due to use of geometrc features of chromosomes whch are ndependent of mage type, the proposed scheme does not need multspectral mages. In future, we wll focus on separaton of completely overlappng chromosomes. For ths purpose, frst we should dstngush between touchng chromosomes and overlappng chromosomes and apply the related algorthm to each class (separaton algorthm for touchng or partally overlappng chromosomes s dfferent from separaton algorthm for completely overlappng chromosomes). Separaton algorthm for completely overlappng chromosomes s based on fndng the cross secton between two overlappng chromosomes and usng t for separaton of chromosome clusters. ACKNOWLEDGMENTS The authors would lke to thank Prof. Hamd Aghajan for hs nvaluable help durng ths project. We would also thank Mr. Payam Delgosha, Mr. Amral Abdolrashd and Mr. Al Hashem for ther useful comments on our project. REFERENCES [1] L. J, "Intellgent splttng n the chromosome doman," Pattern Recognton, vol. 22, no. 5, pp. 519-532, 1989. [2] L. J, "Fully automatc chromosome segmentaton," Cytometry, vol. 17, pp. 196-208, 1994. [3] B. Lerner, "Toward a completely automatc neural-network-based human chromosome analyss," IEEE Trans. Syst., Man, Cybern. B, Cybern., vol. 28, no. 4, pp. 544-552, Aug. 1998. [4] B. Lerner, H. Guterman, and I. Dnsten, "A classfcaton-drven partally occluded object segmentaton (CPOOS) method wth applcaton to chromosome analyss," IEEE Trans. Sgnal Process., vol. 46, no. 10, pp. 2841-2847, Oct. 1998. [5] X. Shunren, X. Wedong, and S. Yutang, "Two ntellgent algorthms appled to automatc chromosome ncson," n Proc. IEEE Int. Conf. Acoust., Speech, Sgnal Process., 03. (ICASSP 03)., Apr., pp. 697-700.
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