1、1醫學影像處理實驗室醫學影像處理實驗室(Medical Image Processing Lab.)Chuan-Yu Chang Ph.D.Medical Image Processing Lab.)Chuan-Yu Chang Ph.D.Image EnhancementnThe purpose of image enhancement methods is to process and acquired image for better contrast and visibility of features of interest for visual examination and su
2、bsequent computer-aided analysis and diagnosis.qDifferent medical imaging modalities provide specific characteristic information about internal organs or biological tissues.nImage contrast and visibility of the features of interest depend on the imaging modality and the anatomical regions.nThere is
3、no unique general theory or method for processing all kinds of medical images for feature enhancement.qSpecific medical imaging applications present different challenges in image processing for feature enhancement.2醫學影像處理實驗室醫學影像處理實驗室(Medical Image Processing Lab.)Chuan-Yu Chang Ph.D.Medical Image Pr
4、ocessing Lab.)Chuan-Yu Chang Ph.D.Image Enhancement(cont.)nMedical images from specific modalities need to be processed using a method that is suitable to enhance the features of interest.qChest X-ray radiographic imagenRequired to improve the visibility of hard bony structure.qX-ray mammogramnRequi
5、red to enhance visibility of microcalcification.nA single image-enhancement method may not serve both of these applications.nImage enhancement tasks and methods are very much application dependent.3醫學影像處理實驗室醫學影像處理實驗室(Medical Image Processing Lab.)Chuan-Yu Chang Ph.D.Medical Image Processing Lab.)Chu
6、an-Yu Chang Ph.D.Image Enhancement(cont.)nImage enhancement tasks are usually characterized in two categories:qSpatial domain methodsnManipulate image pixel values in the spatial domain based on the distribution statistics of the entire image or local regions.nHistogram transformation,spatial filter
7、ing,region growing,morphological image processing and model-based image estimationqFrequency domain methodsnManipulate information in the frequency domain based on the frequency characteristics of the image.nFrequency filtering,homomorphic filtering and wavelet processing methodsqModel-based techniq
8、ues are also used to extract specific features for pattern recognition and classification.nHough transform,matched filtering,neural networks,knowledge-based systems4醫學影像處理實驗室醫學影像處理實驗室(Medical Image Processing Lab.)Chuan-Yu Chang Ph.D.Medical Image Processing Lab.)Chuan-Yu Chang Ph.D.Spatial Domain M
9、ethodsnSpatial domain methods process an image with pixel-by pixel transformation based on the histogram statistics or neighbor.qFaster than Fourier transformqFrequency filtering methods may provide better results in some applications if a priori information about the characteristic frequency compon
10、ents of the noise and features of interest is available.nThe spike-based degradation in MRI will be remove by Wiener filtering method.5醫學影像處理實驗室醫學影像處理實驗室(Medical Image Processing Lab.)Chuan-Yu Chang Ph.D.Medical Image Processing Lab.)Chuan-Yu Chang Ph.D.Spatial domain process willbe denoted by g(x,y
11、)=Tf(x,y)where f(x,y):input image g(x,y):processed image T:an operatormaskfilterkerneltemplatewindowsBackgroundnSpatial domainqThe aggregate of pixels composing an image.qOperate directly on these pixels6醫學影像處理實驗室醫學影像處理實驗室(Medical Image Processing Lab.)Chuan-Yu Chang Ph.D.Medical Image Processing La
12、b.)Chuan-Yu Chang Ph.D.nTransformation Functionqs=T(r)qwhere T is gray-level transformation functionnProcessing technologies:qPoint processingnEnhancement at any point in an image depends only on the gray level at that point.qMask processing or filteringBackground(cont.)Contrast stretchingthresholdi
13、ng7醫學影像處理實驗室醫學影像處理實驗室(Medical Image Processing Lab.)Chuan-Yu Chang Ph.D.Medical Image Processing Lab.)Chuan-Yu Chang Ph.D.nSome basic Gray Level Transformsqs=T(r)qr:the gray level value before processqs:the gray level value after processSome Basic Gray Level Transforms8醫學影像處理實驗室醫學影像處理實驗室(Medical Ima
14、ge Processing Lab.)Chuan-Yu Chang Ph.D.Medical Image Processing Lab.)Chuan-Yu Chang Ph.D.nImage NegativesqReversing the intensity levels of an imageqPhotographic Negativeq s=L-1-rqSuited for enhancing white or gray detail embedded in dark regions of an imageSome Basic Gray Level Transforms(cont.)9醫學
15、影像處理實驗室醫學影像處理實驗室(Medical Image Processing Lab.)Chuan-Yu Chang Ph.D.Medical Image Processing Lab.)Chuan-Yu Chang Ph.D.nLog TransformationsqS=c log(1+r)qMaps a narrow range of low gray-level values in the input image into a wider range of output levels.Some Basic Gray Level Transforms(cont.)10醫學影像處理實驗
16、室醫學影像處理實驗室(Medical Image Processing Lab.)Chuan-Yu Chang Ph.D.Medical Image Processing Lab.)Chuan-Yu Chang Ph.D.nPower-Law Transformationsqs=crrqs=c(r+e)rqWhere c and r are positive constantsqPower-law curves with fractional values of r map a narrow range of dark input values into a wider range of ou
17、tput values,with the opposite being true for higher values of input levels.Some Basic Gray Level Transforms(cont.)11醫學影像處理實驗室醫學影像處理實驗室(Medical Image Processing Lab.)Chuan-Yu Chang Ph.D.Medical Image Processing Lab.)Chuan-Yu Chang Ph.D.Some Basic Gray Level Transforms(cont.)nGamma CorrectionqThe proc
18、ess used to correct this power-law response phenomena12醫學影像處理實驗室醫學影像處理實驗室(Medical Image Processing Lab.)Chuan-Yu Chang Ph.D.Medical Image Processing Lab.)Chuan-Yu Chang Ph.D.Some Basic Gray Level Transforms(cont.)nExample 3.1qMR image of fractured human spinec=1,r=0.4c=1,r=0.3c=1,r=0.613醫學影像處理實驗室醫學影
19、像處理實驗室(Medical Image Processing Lab.)Chuan-Yu Chang Ph.D.Medical Image Processing Lab.)Chuan-Yu Chang Ph.D.Some Basic Gray Level Transforms(cont.)14醫學影像處理實驗室醫學影像處理實驗室(Medical Image Processing Lab.)Chuan-Yu Chang Ph.D.Medical Image Processing Lab.)Chuan-Yu Chang Ph.D.Picewise-Linear Transformation Fu
20、nctionSome Basic Gray Level Transforms(cont.)nContrast StretchingqTo increase the dynamic range of the gray levels in the image being processed.qLinear functionnIf r1=s1 and r2=s2qThresholdingnIf r1=r2,s1=0 and s2=L-1Control points15醫學影像處理實驗室醫學影像處理實驗室(Medical Image Processing Lab.)Chuan-Yu Chang Ph.
21、D.Medical Image Processing Lab.)Chuan-Yu Chang Ph.D.Picewise-Linear Transformation FunctionnGray-level SlicingnHighlighting a specific range of gray levels in an image.Some Basic Gray Level Transforms(cont.)16醫學影像處理實驗室醫學影像處理實驗室(Medical Image Processing Lab.)Chuan-Yu Chang Ph.D.Medical Image Processi
22、ng Lab.)Chuan-Yu Chang Ph.D.Some Basic Gray Level Transforms(cont.)nBit-plane SlicingqHighlighting the contribution made to total image appearance by specific bits.qSeparating a digital image into its bit planes is useful for analyzing the relative importance played each bit of the image.nDeterminin
23、g the adequacy of the number of bits used to quantize each pixel.nImage compression.17醫學影像處理實驗室醫學影像處理實驗室(Medical Image Processing Lab.)Chuan-Yu Chang Ph.D.Medical Image Processing Lab.)Chuan-Yu Chang Ph.D.Some Basic Gray Level Transforms(cont.)nAn 8-bit fractal image18醫學影像處理實驗室醫學影像處理實驗室(Medical Imag
24、e Processing Lab.)Chuan-Yu Chang Ph.D.Medical Image Processing Lab.)Chuan-Yu Chang Ph.D.Some Basic Gray Level Transforms(cont.)nThe eight bit planes of the image in Fig.3.1319醫學影像處理實驗室醫學影像處理實驗室(Medical Image Processing Lab.)Chuan-Yu Chang Ph.D.Medical Image Processing Lab.)Chuan-Yu Chang Ph.D.Histog
25、ramh(rk)=nkrk is the k-th gray-levelnk is the number of pixels in the image having gray-level k Normalized Histogramp(rk)=nk/nHistogram Processing20醫學影像處理實驗室醫學影像處理實驗室(Medical Image Processing Lab.)Chuan-Yu Chang Ph.D.Medical Image Processing Lab.)Chuan-Yu Chang Ph.D.Medical Images and Histograms X-r
26、ay CT imageT2 weighted proton density image21醫學影像處理實驗室醫學影像處理實驗室(Medical Image Processing Lab.)Chuan-Yu Chang Ph.D.Medical Image Processing Lab.)Chuan-Yu Chang Ph.D.Histogram Processing(cont.)nHistogram Equalization10)(rrTsAssume that the transformation function T(r)satisfies the follows(a)T(r)is a s
27、ingle-valued and monotonically increasing(b)0=T(r)=1 for 0=r 1rL1,rL1則濾波器將減少照度，並放大反射所做的貢獻下圖可用修改過的高斯高通濾波器來近似114醫學影像處理實驗室醫學影像處理實驗室(Medical Image Processing Lab.)Chuan-Yu Chang Ph.D.Medical Image Processing Lab.)Chuan-Yu Chang Ph.D.Example:4.10nIn the original imageqThe details inside the shelter are o
28、bscured by the glare from the outside walls.qFig.(b)shows the result of processing by homomorphic filtering,with gL=0.5 and gH=2.0.qA reduction of dynamic range in the brightness,together with an increase in contrast,brought out the details of objects inside the shelter.115醫學影像處理實驗室醫學影像處理實驗室(Medical
29、 Image Processing Lab.)Chuan-Yu Chang Ph.D.Medical Image Processing Lab.)Chuan-Yu Chang Ph.D.Wavelet TransformnFourier Transform only provides frequency information.nFourier Transform does not provide any information about frequency localization.nIt does not provide information about when a specific
30、 frequency occurred in the signal.nShort-Term Fourier TransformnWindowed Fourier Transform can provide time-frequency localization limited by the window size.nThe entire signal is split into small windows and the Fourier Transform is individually computed over each windowed signal.nThe STFT provide
31、some localization depending on the size of the window,it does not provide complete time-frequency localization.nWavelet Transform is a method for complete time-frequency localization for signal analysis and characterization.116醫學影像處理實驗室醫學影像處理實驗室(Medical Image Processing Lab.)Chuan-Yu Chang Ph.D.Medi
32、cal Image Processing Lab.)Chuan-Yu Chang Ph.D.Wavelet TransformnThe wavelet transform provides a series expansion of a signal using a set of orthonormal basis function that are generated by scaling and translation of the mother wavelet y(t),and the scaling function(t).nThe wavelet transform decompos
33、es the signal as a linear combination of weighted basis functions to provide frequency localization with respect to the sampling parameter such as time or space.nThe multi-resolution approach(MRA)of the wavelet transform establishes a basic framework of the localization and representation of differe
34、nt frequencies at different scales.117醫學影像處理實驗室醫學影像處理實驗室(Medical Image Processing Lab.)Chuan-Yu Chang Ph.D.Medical Image Processing Lab.)Chuan-Yu Chang Ph.D.Wavelet TransformnIn MRAqScaling function is used to create a series of approximations of a function or image,each differing by a factor of a f
35、rom its nearest neighboring approximations.qWavelets are then used to encode the difference in information between adjacent approximating.118醫學影像處理實驗室醫學影像處理實驗室(Medical Image Processing Lab.)Chuan-Yu Chang Ph.D.Medical Image Processing Lab.)Chuan-Yu Chang Ph.D.Wavelet Transform.nWavelet Transform:nWo
36、rks like a microscope focusing on finer time resolution as the scale becomes small to see how the impulse gets better localized at higher frequency permitting a local characterizationnProvides Orthonormal bases while STFT does not.nProvides a multi-resolution signal analysis approach.119醫學影像處理實驗室醫學影
37、像處理實驗室(Medical Image Processing Lab.)Chuan-Yu Chang Ph.D.Medical Image Processing Lab.)Chuan-Yu Chang Ph.D.Wavelet TransformnUsing scales and shifts of a prototype wavelet,a linear expansion of a signal is obtained.nLower frequencies,where the bandwidth is narrow(corresponding to a longer basis func
38、tion)are sampled with a large time step.nHigher frequencies corresponding to a short basis function are sampled with a smaller time step.120醫學影像處理實驗室醫學影像處理實驗室(Medical Image Processing Lab.)Chuan-Yu Chang Ph.D.Medical Image Processing Lab.)Chuan-Yu Chang Ph.D.Wavelet TransformnA scaling function(t)in
39、 time t can be defined asnThe scaling and translation generates a family of functions using the following dilation equations(refinement equation)where hn is a set of filter(low-pass filter)coefficient.nTo induce a multi-resolution analysis of L2(R),where R is the space of all real numbers,it is requ
40、ired to have a nested chain of closed suspaces defined as)2(2)(2/,kttjjkj)2(2)(nthtZnn22101LVVVV(6.44)(6.45)(6.46)scaling parametertranslation parameterk決定j,k(t)沿x軸的位置，j決定j,k(t)的寬度(沿x軸的寬度)透過此式可產生函數家族；任何子空間的展開函式，可由它們自己解析度加倍的複製版本建構出來。以較低尺度函數所延展之子空間被逐層包含於以較高尺度函數所延展之子空間。121醫學影像處理實驗室醫學影像處理實驗室(Medical Ima
41、ge Processing Lab.)Chuan-Yu Chang Ph.D.Medical Image Processing Lab.)Chuan-Yu Chang Ph.D.Wavelet Transform以較低尺度之scaling function所延展之子空間被逐層包含於以較高scaling function所延展之子空間所有V0的展開函數都是V1的一部分122醫學影像處理實驗室醫學影像處理實驗室(Medical Image Processing Lab.)Chuan-Yu Chang Ph.D.Medical Image Processing Lab.)Chuan-Yu Chang
42、 Ph.D.Wavelet TransformnDefine a function y(t)as the“mother wavelet”nThe wavelet basis induces an orthogonal decomposition of L2(R)ny(t)can be expressed as a weighted sum of the shifted y(2t)aswhere gn is a set of filter(high-pass filter)coefficients.)2(2)(2/,kttjjkjyy22101LWWWW)2(2)(ntgtnnyy(6.47)(
43、6.48)(6.49)Wj is a subspace spanned by y(2jt-k)123醫學影像處理實驗室醫學影像處理實驗室(Medical Image Processing Lab.)Chuan-Yu Chang Ph.D.Medical Image Processing Lab.)Chuan-Yu Chang Ph.D.Wavelet TransformnThe wavelet-spanned subspace is such that it satisfies the relationnSince the wavelet functions span the orthogon
44、al complement spaces,the orthogonality requires the scaling and wavelet filter coefficients to be related through the followingnLet xn be an arbitrary square summable sequence representing a signal in the time domain such thatmmmWVV1nnnhg1)1()(2Zlnx(6.52)(6.51)(6.50)124醫學影像處理實驗室醫學影像處理實驗室(Medical Ima
45、ge Processing Lab.)Chuan-Yu Chang Ph.D.Medical Image Processing Lab.)Chuan-Yu Chang Ph.D.Wavelet TransformnThe series expression of a discrete signal xn using a set of orthonomal basis function jknis given bywhere Xk=Sj*k(l)xl為展開函數where Xk is the transform of xnnAll basis function must satisfy the o
46、rthonormality conditionwithZkkkZkknkXnlxlnx)(),(jjjlklkknnlk10 1)(),(jj22|Xx(6.53)(6.54)125醫學影像處理實驗室醫學影像處理實驗室(Medical Image Processing Lab.)Chuan-Yu Chang Ph.D.Medical Image Processing Lab.)Chuan-Yu Chang Ph.D.Wavelet TransformnThe series expansion is considered to be complete if every signal from l
47、2(Z)can be expressed using the expression in Eq.(6.35)nUsing a set of bio-orthogonal basis function,the series expansion of the signal xn can be expressed aswhereandZkkZkkkZkkZkkknkXnlxlnkXnlxlnx)(),()(),(jjjjjj)(),()(),(lxlkXandlxlkXkkjjlklkknnlk10 1,jj(6.55)訊號xn可由一組bi-orthogonal basisfunctions 所組成
48、。126醫學影像處理實驗室醫學影像處理實驗室(Medical Image Processing Lab.)Chuan-Yu Chang Ph.D.Medical Image Processing Lab.)Chuan-Yu Chang Ph.D.Wavelet TransformnUsing a quadrature-mirror filter theory,the orthonormal bases jk(n)can be expressed as low-pass and high-pass filters for decomposition and reconstruction of a
49、 signal.nIt can be shown that a discrete signal xn can be decomposed into Xk aswhereandZkkZkkknkXnlxlnx)(),(jjj22221112002kngnkhnkngnkhnkkjj,2 12,2210lxlkhkXlxlkhkXLow-pass filterHigh-pass filter(6.56)h0和h1用來分解訊號g0和g1用來重建訊號is a filter most commonly used toimplement a filter bank that splitsan input
50、signal into two bands.127醫學影像處理實驗室醫學影像處理實驗室(Medical Image Processing Lab.)Chuan-Yu Chang Ph.D.Medical Image Processing Lab.)Chuan-Yu Chang Ph.D.Wavelet TransformnA perfect reconstruction of the signal can be obtained if the orthonomal bases are used in decomposition and reconstruction stages asnThe
