醫(yī)學(xué)影像處理試驗(yàn)室MedicalImageProcessinglab課件

1、Image EnhancementThe purpose of image enhancement methods is to process and acquired image for better contrast and visibility of features of interest for visual examination and subsequent computer-aided analysis and diagnosis.Different medical imaging modalities provide specific characteristic infor

2、mation about internal organs or biological tissues.Image contrast and visibility of the features of interest depend on the imaging modality and the anatomical regions.There is no unique general theory or method for processing all kinds of medical images for feature enhancement.Specific medical imagi

3、ng applications present different challenges in image processing for feature enhancement.Image Enhancement (cont.)Medical images from specific modalities need to be processed using a method that is suitable to enhance the features of interest.Chest X-ray radiographic imageRequired to improve the vis

4、ibility of hard bony structure.X-ray mammogramRequired to enhance visibility of microcalcification.A single image-enhancement method may not serve both of these applications.Image enhancement tasks and methods are very much application dependent.Image Enhancement (cont.)Image enhancement tasks are u

5、sually characterized in two categories:Spatial domain methodsManipulate image pixel values in the spatial domain based on the distribution statistics of the entire image or local regions.Histogram transformation, spatial filtering, region growing, morphological image processing and model-based image

6、 estimationFrequency domain methodsManipulate information in the frequency domain based on the frequency characteristics of the image.Frequency filtering, homomorphic filtering and wavelet processing methodsModel-based techniques are also used to extract specific features for pattern recognition and

7、 classification.Hough transform, matched filtering, neural networks, knowledge-based systemsSpatial Domain MethodsSpatial domain methods process an image with pixel-by pixel transformation based on the histogram statistics or neighbor.Faster than Fourier transformFrequency filtering methods may prov

8、ide better results in some applications if a priori information about the characteristic frequency components of the noise and features of interest is available.The spike-based degradation in MRI will be remove by Wiener filtering method.Spatial domain process willbe denoted by g(x,y)=Tf(x,y)where f

9、(x,y): input image g(x,y): processed image T: an operatormaskfilterkerneltemplatewindowsBackgroundSpatial domainThe aggregate of pixels composing an image.Operate directly on these pixelsTransformation Functions=T(r)where T is gray-level transformation functionProcessing technologies:Point processin

10、gEnhancement at any point in an image depends only on the gray level at that point.Mask processing or filteringBackground (cont.)Contrast stretchingthresholdingSome basic Gray Level Transformss = T(r)r: the gray level value before processs: the gray level value after processSome Basic Gray Level Tra

11、nsformsImage NegativesReversing the intensity levels of an imagePhotographic Negative s = L-1-rSuited for enhancing white or gray detail embedded in dark regions of an imageSome Basic Gray Level Transforms (cont.)Log TransformationsS = c log (1+r)Maps a narrow range of low gray-level values in the i

12、nput image into a wider range of output levels.Some Basic Gray Level Transforms (cont.)Power-Law Transformationss=crrs= c (r +e )rWhere c and r are positive constantsPower-law curves with fractional values of r map a narrow range of dark input values into a wider range of output values, with the opp

13、osite being true for higher values of input levels.Some Basic Gray Level Transforms (cont.)Some Basic Gray Level Transforms (cont.)Gamma CorrectionThe process used to correct this power-law response phenomenaSome Basic Gray Level Transforms (cont.)Example 3.1MR image of fractured human spinec=1, r=0

14、.4c=1, r=0.3c=1, r=0.6Some Basic Gray Level Transforms (cont.)Picewise-Linear Transformation FunctionSome Basic Gray Level Transforms (cont.)Contrast StretchingTo increase the dynamic range of the gray levels in the image being processed.Linear functionIf r1=s1 and r2=s2ThresholdingIf r1=r2, s1=0 an

15、d s2=L-1Control pointsPicewise-Linear Transformation FunctionGray-level SlicingHighlighting a specific range of gray levels in an image.Some Basic Gray Level Transforms (cont.)Some Basic Gray Level Transforms (cont.)Bit-plane SlicingHighlighting the contribution made to total image appearance by spe

16、cific bits.Separating a digital image into its bit planes is useful for analyzing the relative importance played each bit of the image.Determining the adequacy of the number of bits used to quantize each pixel.Image compression.Some Basic Gray Level Transforms (cont.)An 8-bit fractal imageSome Basic

17、 Gray Level Transforms (cont.)The eight bit planes of the image in Fig. 3.13Histogramh(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 ProcessingMedical Images and HistogramsX-ray CT imageT2 weighted proton density im

18、ageHistogram Processing (cont.)Histogram EqualizationAssume that the transformation function T(r) satisfies the followsT(r) is a single-valued and monotonically increasing0=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(xiàn)下圖可用修改過的高斯高通濾波器來(lái)近似Example: 4.10In the original imageThe details inside the shelter

19、are obscured by the glare from the outside walls.Fig. (b) shows the result of processing by homomorphic filtering, with gL=0.5 and gH=2.0.A reduction of dynamic range in the brightness, together with an increase in contrast, brought out the details of objects inside the shelter.Wavelet TransformFour

20、ier Transform only provides frequency information. Fourier Transform does not provide any information about frequency localization. It does not provide information about when a specific frequency occurred in the signal.Short-Term Fourier TransformWindowed Fourier Transform can provide time-frequency

21、 localization limited by the window size.The entire signal is split into small windows and the Fourier Transform is individually computed over each windowed signal.The STFT provide some localization depending on the size of the window, it does not provide complete time-frequency localization.Wavelet

22、 Transform is a method for complete time-frequency localization for signal analysis and characterization.Wavelet TransformThe 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),

23、and the scaling function f(t).The wavelet transform decomposes 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.The multi-resolution approach (MRA) of the wavelet transform establishes a basi

24、c framework of the localization and representation of different frequencies at different scales.Wavelet TransformIn MRAScaling function is used to create a series of approximations of a function or image, each differing by a factor of a from its nearest neighboring approximations.Wavelets are then u

25、sed to encode the difference in information between adjacent approximating.Wavelet Transform.Wavelet Transform : Works 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 characterizationPr

26、ovides Orthonormal bases while STFT does not.Provides a multi-resolution signal analysis approach.Wavelet TransformUsing scales and shifts of a prototype wavelet, a linear expansion of a signal is obtained.Lower frequencies, where the bandwidth is narrow (corresponding to a longer basis function) ar

27、e sampled with a large time step.Higher frequencies corresponding to a short basis function are sampled with a smaller time step.Wavelet TransformA scaling function f(t) in time t can be defined asThe scaling and translation generates a family of functions using the following dilation equations (ref

28、inement equation)where hn is a set of filter (low-pass filter) coefficient.To induce a multi-resolution analysis of L2(R), where R is the space of all real numbers, it is required to have a nested chain of closed suspaces defined as(6.44)(6.45)(6.46)scaling parametertranslation parameterk決定fj,k(t)沿x

29、軸的位置，j決定fj,k(t)的寬度(沿x軸的寬度)透過此式可產(chǎn)生函數(shù)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(gòu)出來(lái)。以較低尺度函數(shù)所延展之子空間被逐層包含於以較高尺度函數(shù)所延展之子空間。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(shù)都是V1的一部分Wavelet TransformDefine a function y(t) as the “mother wavelet”The wavelet basis induces an orthogon

30、al decomposition of L2(R)y(t) can be expressed as a weighted sum of the shifted y(2t) aswhere gn is a set of filter (high-pass filter) coefficients.(6.47)(6.48)(6.49)Wj is a subspace spanned by y(2jt-k) Wavelet TransformThe wavelet-spanned subspace is such that it satisfies the relationSince the wav

31、elet functions span the orthogonal complement spaces, the orthogonality requires the scaling and wavelet filter coefficients to be related through the followingLet xn be an arbitrary square summable sequence representing a signal in the time domain such that(6.52)(6.51)(6.50)Wavelet TransformThe ser

32、ies 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(shù)where Xk is the transform of xnAll basis function must satisfy the orthonormality conditionwith(6.53)(6.54)Wavelet TransformThe series expansion is considered to be complete if ev

33、ery signal from l2(Z) can be expressed using the expression in Eq.(6.35)Using a set of bio-orthogonal basis function, the series expansion of the signal xn can be expressed aswhereand(6.55)訊號(hào)xn可由一組bi-orthogonal basisfunctions 所組成。Wavelet TransformUsing a quadrature-mirror filter theory, the orthonor

34、mal bases jk(n) can be expressed as low-pass and high-pass filters for decomposition and reconstruction of a signal.It can be shown that a discrete signal xn can be decomposed into Xk aswhereandLow-pass filterHigh-pass filter(6.56)h0和h1用來(lái)分解訊號(hào)g0和g1用來(lái)重建訊號(hào)is a filter most commonly used toimplement a fi

35、lter bank that splitsan input signal into two bands.Wavelet TransformA perfect reconstruction of the signal can be obtained if the orthonomal bases are used in decomposition and reconstruction stages asThe scaling function provides low-pass filter coefficients and the wavelet function provides the h

36、igh-pass filter coefficients.(6.57)Scaling function(low-pass filter)Wavelet function(high-pass function)Wavelet TransformA multi-resolution signal representation can be constructed based on the differences of information available at two successive resolutions 2j and 2j-1.Decomposing a signal using

37、the wavelet transformThe signal is filtered using the scaling function (low-pass filter)Sub-sampling the filtered signal (scale information)Filtering the signal with the wavelet (high-pass filter) and subsampling by a factor of two. (detail signal)The difference of information between resolution 2j

38、and 2j-1 is called “detail” signal at resolution 2j .Wavelet TransformFigure 6.19. (a) A multi-resolution signal decomposition using Wavelet transform and (b) the reconstruction of the signal from Wavelet transform coefficients. xnX(1)2k+1(a)(b)X(1)2kX(2)2k+1X(2)2kX(3)2k+1X(3)2kX(3)2k+1X(3)2kX(2)2k+

39、1X(1)2k+1DecompositionReconstructionScale informationDetail signalWavelet TransformThe signal decomposition at the jth stage can thus be generalized asTo decompose an image, the above method for 1D signals is applied first along the rows of the image, and then along the columns.The image at resoluti

40、on 2j+1, represented by Aj+1, is first low-pass and high-pass filtered along the rows.The result of each filtering process is subsampled.Next the subsampled results are low-pass and high-pass filtered along each column.The results of these filtering processes are again subsampled.(6.58)Wavelet Trans

41、formFigure 6.20. Multiresolution decomposition of an image using the Wavelet transform.2H12H02H12H02H12H0HorizontalSubsamplingVerticalSubsampling2H12H02H12H022H122H02H12H02H12H022H122H02H12H02H12H022H122H0HorizontalSubsamplingVerticalSubsamplingLow-Low AjHigh-High Dj3High-Low Dj2Low-High Dj1Wavelet

42、TransformThis scheme can be iteratively applied to an image to further decompose the signal into narrower frequency bands.Each frequency band can be further decomposed into four narrower bands.Each level of decomposition reduces the resolution by a factor of two, the length of the filter limits the

43、number of levels of decomposition.Daubechies (1992) proposed the least asymmetric waveletsComputed for different support widths as larger support widths provide more regular wavelets.See Figure 6.21 and Table 6.1Wavelet and Scaling FunctionsWavelet TransformTable 6.1 Coefficients for the Corresponding Low-pass and High-Pass Filter for the Least Asymmetric WaveletNHigh-PassLow-Pass0-0.1071489014180.0455703458961-0.0419109651250.01782470144220.703739068656-0.14031762417931.136658243408- 0.42123453420440.4212345342041/p>