医学图像处理绪论new课件

医学图像处理和分析第一章 绪论1. 医学图像处理和分析的意义和由来2. 医学图像处理与分析的研究内容、研究方法3. 医学图像的成像系统和成像原理 CT (Computerized Tomography) 研究内容 图像增强，滤波图像配准、图像分割、图像显示、图像辅助治疗 图像引导手术、医学虚拟环境 CT 成像基本原理d in oute I I ∆-=μd ∆为X 射线在生物体内传播距离μ为衰减系数。

穿过一组不同物质时)(2211i i d d d in out e I I ∆+∆+∆-=μμμCT原理示意图常用影像技术优缺点结构成像：X、CT、MRI、Ultrasound功能成像: f MRI、PET、SPECT1895年X射线机1969年英国工程师Hoopsfield设计成功第一台断层摄影装置CT 1972年应用于临床，获得第一幅脑肿瘤图像。

1979年Hoopsfield获诺贝尔奖螺旋CT 1987年出现于专利文献特点：数据无任何时间和空间间隔CT 连续两次扫描有一段间隔，螺旋CT没有，且空间分辨率更高。

MRI1946年Bloch and Purcell发现核磁共振NMR现象1952年获诺贝尔奖1973年第一幅核磁共振图像，纽约州立大学，两个充水式管1980年第一幅人体核磁共振图像。

1991年Ernst获诺贝尔化学奖在NMR中引入了Fourier变换超声成像光纤内窥镜成像。

MRA磁共振血管造影技术MagneticResonance Angiography正电子放射断层成像 PET (Position Emission Tomography) 单光子放射断层成像 SPECT (Single Photon Emission Computed Tomography)DSA 数字减影血管造影术 Digital Subtraction Angiography 参考书籍医学影像处理和分析, 田捷等编著, 电子工业出版社, 2003. 3D Imaging Medicine, J.K. Udupa, G .T. He4rman, CRC Press, 2000.第二章 图像的预处理1．直方图NN p ii =1,,1,0-=k i 110=∑-=k i ipN Nk i i=∑-=1直方图变换，拉伸和压缩)(r T s = )1,0(-∈L r线性变换⎪⎩⎪⎨⎧-+-+-+=322121121111)()()(tr r t r r t r t r r t r rt s 102211-≤<≤<≤≤L r r r r r r r321,,t t t 是变换系数直方图均衡化10<≤r(a) 在10<≤r ,)(r T 为单调增加 (b)例．假定一幅6464⨯．８个灰度级．分布如下．44.025.019.0)()()()(19.0)()()(1011100000=+=+=======∑∑==r p r p r p r T s r p r pr r T s r r j j r r j j2s =0.653s =0.81 4s =0.845s =0.956s =0.987s =1.00重新定义710≈s 731≈s 752≈s 763≈s 14≈s0s 790 1s 1023 2s 850 3s 985 4s 448总体 显示直方图统计，直方图均衡化，直方图分割滤波中值滤波高斯滤波参考文献：1.J. G. Liu, Y. Z. Liu, and G. Y. Wang, “Fast discrete W transforms via computat ionof moments”, IEEE Transactions on Signal Processing, vol. 53, no.2, pp.654-659, 2005.2.J. G. Liu, Y. Z. Liu, and G. Y. Wang, “Fast DCT-I, DCT-III, and DCT-IV viamoments”,EURASIP Applied Signal Processing, no.12, pp.1902-1909, 2005. 3.J. G. Liu, F. H. Y. Chan, F. K. Lam, H. F. Li, and George S. K. Fung,“Moment-based fast discrete Hartley transform”, Signal Processing, vol. 83, no. 8, pp. 1749-1757, 2003.4.J. G. Liu, F. H. Y. Chan, F. K. Lam, and H. F. Li, “Moment-based fast discretesine transforms”, IEEE Signal Processing Letters, vol. 7, no. 8, pp. 227-229, 2000.5.J. G. Liu, F. H. Y. Chan, F. K. Lam, and H. F. Li, “A novel approach to fastcalculation of moments of 3D gray level images”, Parallel Computing, vol. 26, no.6, pp. 805-815, 2000.6.J. G .Liu, H. F. Li, F. H. Y. Chan, and F. K. Lam, “A novel approach to fastdiscrete Fourier transform”, Journal of Parallel and Distributed computing, vol.54, pp. 48-58, 1998.7.J. G. Liu, H. F. Li, F. H. Y. Chan, and F. K. Lam, “Fast discrete cosine transformvia com putation of moments”, Journal of VLSI Signal Processing, vol. 19, no. 2, pp. 257-268, 1998.8.. F. H. Y. Chan, F. K. Lam, H. F. Li, and J. G. Liu, “An all adder systolic structurefor fast computation of moments”, Journal of VLSI Signal Processing, vol.12, no.2, pp. 159-175, 1996.矩和不变矩Since moment invariants were proposed by Hu in 1962, moment invariants, by virtue of invariance properties under translation, scaling and rotation, have played an important role in image analysis and pattern recognition. However, computing moment invariants directly is relatively expensive because of the large number of multiplications it requires and this weakness limits its extensive real-time applications. So fast computation of moment invariants has received considerable attention and many efforts have been made to solve it.Let f(x,y) be the image intensity function. The (p+q) order moments are defined aspq p q m x y f(x,y)dxdy =-∞+∞-∞+∞⎰⎰where p, q ∈{,,,...}012. Their discrete forms arem i j f pq p q i j j ni n===∑∑ 11where n n ⨯ is the image size and the size of a pixel is taken as the unit, f i j =f(i, j)The central moments of f(x, y) are defined asνpq p q x x y y f x y dxdy =---∞+∞-∞+∞⎰⎰()()(,) where x m m y m m ==10001000/,/ , with their discrete forms asνpq j ni n p q i i m m j m m f =--==∑∑(/)(/)1000110100 jThe central moment of order up to 3 are ,23 22 22 023 0 01202030301020201220112121102020102021*********2203030101011110000m y m y m m y m m x m y m x m m x m m y m x m y m m x m x m m y m m +-=-=+--=-=+--==+-==-==ννννννννννIn order to obtain moment invariants, transformation of the above moments is necessary,μνpq pq p q m =++/()/0012p, q={0, 1, 2, 3, ......} Seven functions of the second- and the third-order moments were first derived in 1961. These functions are known as Hu's moment invariants as follows,])()(3)[)(3( ])(3)()[()3())((4+ ])()()[(])()(3)[)(3(+ ])(3))[()(3()()()3()3(4)(221032301221033012203212123012300321721031230112032121230022062210323012210303212032121230123030125203212301242032121230321120220202201μμμμμμμμμμμμμμμμφμμμμμμμμμμμφμμμμμμμμμμμμμμμμφμμμμφμμμμφμμμφμμφ+-++-++-++-=+++-+-=+-++-+-++-=+++=-+-=++=+=They are invariant to image translation, rotation and scaling invariants and are expressed in terms of the ordinary moments m pq . In a direct computation of m pq , n 2 additions and n 2(p+q) multiplications are required. Obviously, for large values of n, the process will take a long time.Computation complexity O(n 2) .3. SYSTOLIC ARRAY FOR COMPUTING MOMENT INV ARIANTS We introduce the array generated the ordinary moments briefly here [2, 3].The p-network shown in Fig. 1 represents a map of transforming the vector (1, x, x 2, ...... x p-1, x p) into (1, (1+x), (1+x)2, ...... (1+x)p-1, (1+x)p). It is denoted by F p , i. e.F p (1, x, x 2, ...... x p-1, x p)=(1, (1+x), (1+x)2, ...... (1+x)p-1, (1+x)p)The equations below follow immediately.F p (1, 1, 1, ...... 1, 1)=(1, 2, 4, ......2p-1, 2p)F p (a, a, a, ...... a, a)=(a, 2a, 4a, ......2p-1a, 2pa)The equations below can then be verified by inputting data into the p-network.F p (a, ax, ax 2, ...... ax p-1, ax p)=(a, a(1+x), a(1+x)2, ...... a(1+x)p-1, a(1+x)p) F p (a+b, a+b, a+b, ...... a+b, a+b)=F p (a, a, a, ...... a, a)+F p (b, b, b, ...... b, b)F p2(1, x, x2, ...... x p-1, x p)=F p(F p(1, x, x2, ...... x p-1, x p))=F p(1, (1+x), (1+x)2, ...... (1+x)p-1, (1+x)p)=(1,(2+x), (2+x)2, ...... (2+x)p-1, (2+x)p)Fig. 1.The p-network.and in general,F p n-1(1, x, x2, ...... x p-1, x p)=F p(......F p(1, x, x2, ...... x p-1, x p)......)=(1, (n-1+x), (n-1+x)2, ...... (n-1+x)p-1, (n-1+x)p)By substitution,F p n-1(1, 1, 1, ......, 1, 1)=F p(......F p(1, 1, 1, ......, 1, 1)......)=(1, n, n2, ......, n p-1, n p)andF p n-1(a, a, a, ......, a, a)=(a, na, n2a, ......, n p-1a, n p a)Let a i=(a i, a i, a i,...... a i), i=1, 2, 3, ......, n, and a i is a (p+1)-dimensional vector, thenF p (F p (a n )+a n-1)=F p (F p (a n ))+F p (a n-1)=F p 2(a n )+F p (a n-1)Generally,F p (F p ......(F p (F p (F p (a n )+a n-1)+a n-2)+......a 2)+a 1=F p n-1(a n )+F p n-2(a n-1)+F p n-3(a n-1)+......+F p 2(a 3)+F p (a 2)+a 1=(, , ...... , , , 1112111i a ia i a i a a p ni i p ni in i i n i in i i∑∑∑∑∑=-====)The equation above can be proved by mathematical induction. These components of the resultant vector are known as 1-D moments. To compute these 1-D moments, F p is used (n-1) times in the iteration procedure except for the (n-1) additions of (p+1)-dimensional vectors.The ordinary moments of a discrete 2-D image, m pq (p, q = 0, 1, 2, .......), can be calculated by the following equation.m i j f jif pq pj n i n qij qj npi nij ======∑∑∑∑1111Let kj ki nij g if ==∑1( k=0, 1, 2, 3, ......, p, ......, )such that pq qpj j nm jg ==∑1It shows the computation of 2-D ordinary moments could be analyzed into two computation of 1-D moments .Without loss of generality, p ≥q is assumed. The systolic array for computing moments is shown in Fig. 2 [2, 3]. The systolic array consist of (n-1) p-network with someadders and proper feedbacks. In Fig. 2, data are pipelined from left to right at the speed of one cell per clock tick. At the same time, the correspondent input latches (denoted by squares in Fig.1) or adder-latches (denoted by circles) moved to their respective outputs. To retime the network, additional latches must be inserted between some nodes of the network. For simplicity, these latches are not explicitly drawn in Figure 2 but are represented by numbers enclosed in square brackets that are beside vertical and skew line.Fig. 2. The systolic array for computing the 2-D ordinary moments.By analyzing the schedule, the processing time for deriving all m r,s ( r=0, 1, 2, ......, p; s=0, 1, 2, ......q. ) is given byT=[(p+1)+(n-2)(p+1)]+1+[(q+1)+(n-1)(q+1)] =(p+q+2)nThe term [(p+1)+(n-2)(p+1)] is for calculating g 0,n , followed by a clock cycle to pass through the bridge cell, and the term [(q+1)+(n-1)(q+1)] is used in the second phase. Finally p cycles are needed to collect all the results. Altogether the number of additions performed is given by [(p+1)(p+2)(n-1)n/2+(q+1)(q+2)(n-1)(p+1)/2].在基于矩的算法中，要计算一种常系数的线性矩组合，算法中存余的浮点乘法就是常系数与矩的相乘，我们准备采用移位、累加方法将全部浮点乘法转化为定点整数加法。