Micro Image Overlapped Cell Recognition Based On Singular Value Decomposition

The effect of the computer-medical image becomes more and more remarkable in the field of clinic diagnosis and therapy, and the automatic analyse of microimage is one of the most important subject of research in the disposal and analyse of medical image. For the favorable character of the singular values eigenvector,the author takes advantage of the method of two-dimension adaptive thresholding segmentation algorithm to make the overlapped cells and their background detached, then divide the overlapped cells into sole ones by Boundary-Stripped algorithm (intact ones and not intact ones). At last , the author takes advantage of the character that describes image matrix exclusively of singular values eigenvector(SV)and the characters of stability ,transpose invariance ,displacement invariance and some others.Using favorable qualities of utilize singular values eigenvector,the author utility the degree of membership of image to identify image. 1 ,Two-dimension adaptive thresholding segmentation algorithm Threshold value method is an important technology in image segmentation, traditional threshold value segmentation method utility one-dimension greyhound histogram.It separate impossibly the cells needed. In view of such an instance,the author introduce an two-dimension greyhound segmentation algorithm,one of the two-dimension is the pixel's gray value and the other is its neighboring average gray value.Because of utiliting sufficiently image pixel and its nerghboring average gray value,the author separated commendably overlapped cells.Define discrete degree matrix as SB=∑=10()kp Ck[( μk-μT)( μk-μT) T ] (8) Define trace of discrete degree matrix as measure of discrete degree tr(SB)=P0[( μ0,i-μT,i)2+( μ0,j-μT,j)2]+ P1[( μ1,i-μT,i)2+( μ1,j-μT,j)2] (9) When trace of discrete degree matrix acquire maximum value,its corresponding segmentation threshold value is the optimized value(S,T) : tr(SB(S,T)) = 0≤m s ,ta≤xL?1{ tr(SB)(s,t)} (10) 2,Boundary-Stripped algorithm of overlapped cells This is an kind of effective segmentation method, the boundary of clustering cells is stripped layer by layer in this arithmetic.During stripping, judgement is made to determine whether the splitting has happened,and then the actual separation is taken in the original cell image.Thismethod avoid request of joint concavity of clustering cells in most of the existed separating algorithms,or request of exist part least gray value at points where the cells touch. The idea of boundary-Stripped algorithm of overlapped cells is as follows: First of all,the boundary of clustering cells is stripped in the first time. During stripping ,judgement is made to determine whether the splitting has happened.If splitting has happened,and then we should search partial point separated,moreover,we should search line separated, finally,we achieve separateness of cells. This process of stripping is repeated continuously until area of single cell is less than threshold enacted. 3 ,Overlapped cell recognition and quantitative analysis for the micro image First,the author start from algebraic theory and fuzzy mathematics,the degree of any vectorsubspace accepting any vector is discussed in this chapter,which is defined as the degree of membership of vector.It is proved to have some properties of algebraic invariance and then it is applied to image recognition for constructing the degree of membership of image.Then, the author takes advantage of singular values eigenvector to identify image. Definition 2: If we have known the image matrix of ? iis {A (ji )}Nij =1 ,the matrix of unknown image is C, the corresponding eigenvector are {X j }Nij =1 andY,so define the degree of unknown image that vests in ? iis: f? i(Y)=1||YλX||α1mij1ijij+∑=-()() in short is image adscription, α≥1,{Xj}Nij=1 is the orthonormal basis of the image of kind ? i. We make the dividen cells as a matrix , thendo singular value decomposition to it ,calculate singular value to be one-dimension characteristic vector,use it to replace the image of the cells that have been dividen. Lemma(SVD): Ordering A m×nis real number matrix(m≥n),and rank(A)=k,therefore,being two orthogonal matrix U m×m and V n×n,diagonal matrix D m×n ,as follows : A=UDVT (1) If matrix A represent a cell image ,then formula (2) is orthogonal solution for the cell image, structure a n-dimension line vector: X n ×1=D n×ne=( δ1,…, δk,0,…,0)T (3) X n ×1 is the singular values eigenvector of A The steps of image recognization as follows: (1) calculating the singular values eigenvector of all kinds of image matrix image sample excised,checking-up the same kind of singular values eigenvector is linked with linearity or not ,if it is , change the samples until the same kind the singular values eigenvector is linked with each other in linearity. Make all the extract the singular values eigenvector orthogonalize,then it becomes the orthonormal basis of each kind of image . (2) Calculating the singular values eigenvector of the image matrix of real samples. (3) Calculating the degree of membership of red and white cells with the singular values eigenvector of the image matrix of real samples separately,then obtain the thresholding of red and white cells . (4) Calculating the the singular values eigenvector of the image matrix that is waiting for measuring. (5) Calculating the degree of membership of the image that is waiting for measuring , which comparing with each kind of image .(6) Ordering f? i(X)= max1≤j≤m(f? i(X)),1≤i≤m.if f? i(X)≥thresholding setted, judge the image that is waiting for measuring is i kind,if f? i(X)