The Method Of Least Squares For Medical Image Registration

The idenfication and analyse of iatrical pictures are very importand means of knowing people's health, they also play great roles on diagnosing and curing of diseases.Imagings of patients are often required by various of modes when came to the clinic. To do quantitative analysis of several different images,first we need to solve the problem of the registratons of the pictures, that's the so called image registration .This article will focus on the registration of human brains' images.After the original dealing and partition, we registrate the images with the method of least squares .The method of least squares in iatrology:1.Foreclosing the registated images so that the further partition and registration can move more smoothly.Use the method of histogram equalization. 2.Partition the fringes of the images,do a general registration,minish the later calculating amount in least squares iteration. To decrease the mistakes caused by the partition,also with the concern of the calculating amount, we take the method of 2D histogram dividing value segmentation. 3.the method of least squares:(1)Suppose that there were gray scale functionsg₁(x₁,y₁) = g₂(x₂,y₂) on both sides of the solid images, with the concern of the random noise's effections,we have...Generally speaking,letv(x,y) = g₁(x,y) - h(g₂(T{x,y)))and our aim is to find the minimal V so as to(l)can be conversed with:gi(x,y) = h0 + hig2(a0 + axx + a2y,b0 + hx + b2y) + n2{x,y) (2) (2) ho,hi,ao,ai,02,60,61,&2 can be expand with formula Taylor. v(x, y) = Aho + gAhi + gxAa0 + gxxAax + gxyAa2there+gyAb0 + gyxAbi + gyyAb2 - Ag{x,y) = gi(x,y) - {h0 + hig2{ao + aix + a2y,b0 + 61a; + 62y)), (4)9* = 9i(I, J) = \W + 1, J) 9(1 - 1, J)] (5) \ + l)-g(I,J-l)\ (6)/ = ao + 01X0 + a2y, J — b0 + b\x + b2yand for (4),ho,h\,ao,ai,a2,bo,bi,b2 are all transpositional parameter thatcomputed from the last iteration.letc(x, y)is the corresponding transpositional parameters'amend vectors' coefficient vectors of the pixel (a;, y) in the window of aim. so in the point (a;, y),the equation isv(x,y) = cT(x,y)x - Ag(x,y)our aim is computer X, so as to ï¿¡ v2{%,y) -* min? ans thefunction of {Aho,Ahi,Aau,Aai2,Aa2i,Abu,Abi2,Ab2i,} so we can compute it with& ZQv2(x,y) -^k----=0videlicet 2 2v(x,y)c(x,y) = ^ 2c{x,y)\cT{x,y)x-Ag{x,y)\ = 0 en x,yen c(x,y)cT(x,y)X = ^ Ap(a-, j/)c(a;, y) (7)z,y€fisuppose that E e(a;, y)cT(x,y) is reversible, so there is y) (8)x,j/€fi x.ygfithe sum of formula is computered with all the pels (x, y) in the aimd window. (3)compute ho,hi,oq,oi,0,2, bo, b\, 62, 6 + &lr} A6?(4)if the correlative coefficient is smaller than the correlative coefficient last time ,we can take it as an end to the iteration. (Also it can be infered by judging if the variable was smaller than the dividing value estimated beforehand.) We in know if the further iteration is needed by the judging of the dividing value .When the iteration is finished, a[\ ,a\l2 ,a^ ,b[\ ,b['2 ,&21 1^0 -M would be the required variable.(5)the points that make iteration convergent or stop is the true conjugate points unnecessarily,in this article we choose multi-points to improve the accuracy of arithmetic. (6)compute the prime position of registration.x,y€Cl a:,J/efiVt =Vs =...