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DARTMOUTH ENGS 167 - Image Analysis

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10/19/200611ENGG 167 MEDICAL IMAGINGLecture 11: Oct 16Image AnalysisReferences: Chapter 10, The Essential Physics of Medical Imaging, BushbergRadiation Detection and Measurement, Knoll, 2nded.Intermediate Physics for Medicine and Biology, Hobbie, 3rded.Principles of Computerized Tomographic Imaging, Kak and Slaney.(http://rvl4.ecn.purdue.edu/~malcolm/pct/pct-toc.html)2Image Analysis - Bushberg Chapter 101) Contrast2) Resolution3) Noise4) Contrast-Detail AnalysisRead Chapter 10 in BushbergOptional reading – Chapter 12 Hobbie text10/19/2006231) Grayscale contrast C = (I1–I2) / I1Ref: BushbergHuman vision can discern7 bits (0-127) levels of gray scaleImages stored can be stored at8 bit – 0-255 10 bit – 0-102412 bit – 0-409616 bit – 0-65,53532 bit – 0-4.2x10941) Contrast – x-ray versus MRIRef: BushbergX - ray subject contrast between transmission at two thicknesses Cs= (I1 –I2)/I1Given A = N0e-µ xand B = N0e-µ(x+z), leads to:Cs= 1- e-µ zNote contrast increases exponentially with either z or µ. MRI subject contrast between signal at two T2 valuesGiven A = k e-TE/T2’and B = k e -TE/T2’’, leads to:Cs= 1- e-ΤΕ/(T2’-T2’’)Note contrast is altered by either TE or T2 change.10/19/2006351) X-ray Contrast – µ and C both increase with decreasing keVRef: BushbergContrast always improves at lower x-ray photon energy,but in general, a moderate energy x-ray is used. Why? 61) MRI Contrast – dependence on echo timeRef: BushbergContrast obtained from temporal decay of RF signalGenerally longer echo times give best contrast but in practicethey are only kept moderately long. Why?10/19/2006471) X-ray film contrast – non-linear Ref: BushbergContrast is optimal at a given Optical Density (OD) near 0.7 mR exposure. Optimal conditions depend upon tissue transmission.Recall: maximal slope gives maximal contrast. (i.e. small changes in Exposure lead to large changes in OD).81) Rel. contrast = slope of response versus exposure Ref: Bushbergfilm has non-linear contrast Digital Imaging has linear or quasi-linear response10/19/2006591) Display Contrast - Digital systems can adjust contrast in softwareRef: BushbergApparent contrast can be increased by thresholds (upper and lower) and remapping image.Bx,y= m1(Ax,y-k1)Then values of Bx,yabove k2Bx,y=k2.10Windowing down improves contrast Grayscale reversal can improve apparent contrastRef: BushbergEx. 8-bit image whereI1=200 I2= 220C = |200-220|/200 = 0.1Inverted image:I1=255-200 = 55I2=255-220 = 35C = |55-35|/55 = 0.36Is this as good as it looks?10/19/20066112) Resolution 122) Spatial Resolution – point spread function (PSF) Ref: Bushberg∫∞∞−−−= '')','()','(),( dydxyyxxhyxfyxg∫∞∞−−−−−= '')','()','(),(0dydxyyxxhyyxxyxgoδ(Sect. 12.1 Hobbie chapt.)Convolution integral g(x,y) = imagef(x,y) = test objecth(x-x’,y-y’) = point spread function10/19/20067132) Spatial Resolution – relationship to imaging field Ref: Bushberg142) Measures of resolution – point, line, edge Ref: BushbergFor isotropic PSF system, a single LSF is sufficient to characterize the performance.For non-isotropic PSF, LSD must be measured at different angles.ESF used when large change in stimulus is needed to observe a change, and where a large amount of scattering is present.Fourier transform of the LSF is often used to calculate the MTF…10/19/20068152) Measures of resolution – Modulation Transfer Function (MTF) Ref: BushbergFourierTransformF(x) = ci162) MTF typically evaluated from line spread function (1-D)Ref: BushbergStandardResolutionTest charts10/19/2006917Modulation Transfer Function for film-screen systemsRef: Bushberg182) Modulation Transfer Function – total system response always has the lowest MTFRef: Bushberg10/19/20061019Modulation Transfer Function (MTF) in MammographyRef: Bushberg20Aliasing – low spatial frequency artifacts from under samplingRef: BushbergThe Nyquist Theorem dictates that in order to sample and record data accurately, frequencies components up to one-half the maximum sampling frequency must be obtained. Aliasing is what happens when we try to record and display frequencies higher than one-half the sampling rate. REF: http://www.ee.rochester.edu:8080/courses/EE102/kriss/lecture5.pdf10/19/200611213) Noise – what can be obtained experimentally from repeated samples from one detector?Ref: BushbergExperimental observables:meanStd. dev.Not dependent upon model223) Noise – estimation by statistical modelsRef: Knollp = probability for a single event, n = number of events sampledP(x) = probability of counting x events.10/19/200612233) Gaussian & Poisson models are very similar in most casesRef: BushbergPoisson statistics fit the physical principles better, butGaussian is easier to utilize, and matches well when σ=(mean)1/2.Both models have:= npσ2= xx243) Detector noise - Poisson counting statisticsRef: BushbergStandard deviationVarianceRelative noise(viewed by humans)Signal to Noise Ratio10/19/20061325Detector noise - including real detection efficiencyRef: BushbergQuantum detection efficiencyTheoretical signal to noiseReal SNR263) X-ray detector noise - including all sourcesRef: Bushberg10/19/200614273) Detective Quantum Efficiency – best measure of system efficiencyRef: BushbergNote: QDE = DQE(f=0) for ideal noise case.QDE = # photons detected# photons incidentnote NPS(f) = s2(f) 284) Noise affects Contrast Resolution – the ability to detect an object in the presence of noise Ref: BushbergRose’s criterion – CNR = 5 estimate required for humans to detect somethingContrast to noiseRatio is good indicatorof detectabilityC = (I1-I2)/I1Noise = σ/I1C/N = (I1-I2)/σ10/19/200615294) Contrast-Detail Analysis - qualitative analysis of system performanceRef: Bushberg304) Contrast-Detail Analysis - example phantom and dataRef: www.capintec.com10/19/200616314) Contrast-Detail Analysis - Which system is better, A or B ?Ref:


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