摘要
变化是图像及信号处理方法中经常用到的信息，通常利用某种度量方法将其量化后加以利用。这些量度、量化图像和信号变化大小的方法称为变化度量。变化度量常用于信号变化检测方法、图像边缘检测方法、边缘型图像分割模型以及特征保持的图像平滑方法等多种处理方法中。
这些基于变化度量的方法以图像或信号的变化为主要利用信息，变化度量结果的准确与否直接影响了此类方法的性能。在那些高噪声、强随机的生物医学图像和信号处理中，现有的变化度量往往因受到噪声干扰而得到不甚准确的变化信息。这是导致基于变化度量的方法在处理信噪比较低的生物医学数据时性能下降的原因之一。
研究鲁棒的变化度量，利用其提高基于变化度量的图像和信号处理方法的抗噪声能力，尝试解决高噪声、强随机的生物医学图像和信号处理中因噪声干扰引发的问题，是本文的研究角度和基本思路。
另一方面，新的医学成像技术带来了新的数据形式。在处理这些新形式数据时，需要定义相应的变化度量。鲁棒地量度张量值和向量值数据的变化成为近年来图像处理技术发展中需要解决的新问题。
非平稳度量通过量度图像及信号的非平稳程度来反映和量化图像及信号中存在的变化，对噪声具有良好的免疫力，是一种鲁棒的变化度量。本文完善和拓展了非平稳度量方法，提出了几个基于非平稳度量的图像和信号处理方法，并将它们用于几种高噪声、强随机的生物医学图像和信号的处理中，有效减少了其中因噪声干扰而引发的多种不良现象的发生。具体研究内容如下：
对非平稳度量方法进行了较为全面的改善和拓展。提出了一般参数平稳概念，以此概念为基础，将原非平稳度量拓展为更具通用性的变化度量方法，并利用更为贴切的概念对此方法进行阐述和解释；归纳了非平稳度量算子的一般构造过程，研究了算子的多种典型输出形式，在理论上证明了二阶非平稳度量算子在抗噪声性能方面的优势，并探讨了算子的关键参数选择；给出了N维数据的非平稳度量方法，研究了向量值和张量值数据的非平稳度量，将非平稳度量方法拓展为能够量度多维、多数据类型、通用的、鲁棒的变化度量。
针对强随机信号的变化检测中易发生误检、漏检以及高噪声图像的边缘检测中易产生伪边缘的问题，分别提出了基于非平稳度量的信号变化检测方法和图像边缘检测方法，并将它们应用于随机性较强的脑电信号的变化检测以及噪声水平较高的心脏磁共振扩散加权图像的边缘检测中。实验结果表明，基于非平稳度量的检测方法能够获得较为准确的信号变化时刻和图像边缘位置，减少了变化点误检、漏检以及伪边缘现象的发生。
针对高噪声图像分割中易产生伪轮廓和边界泄漏的问题，提出了基于非平稳度量的几何活动轮廓(NSM-GAC)分割模型，并将其应用于颈动脉超声图像的分割中。该模型利用非平稳度量为边缘型几何活动轮廓模型提供边缘信息。高噪声合成图像以及仿真与真实的颈动脉超声图像的分割结果表明，NSM-GAC模型具有较好的抗噪声能力，能以较少的迭代次数、较短的运行时间达到更好的分割结果，减少了伪轮廓的产生，改善了边界泄漏现象。
着重研究了低信噪比图像平滑增强中难以兼顾噪声消除与特征保持的问题，提出了一种新的特征保持图像平滑方法——非平稳自适应滤波法(NAF)。总结了空域像素点同质邻域设计的约束条件，遵循这些约束设计了基于非平稳度量的同质成员规则，利用该规则确定每个像素点的自适应同质邻域，以该邻域内的均值代替当前点的灰度值，达到特征保持的图像平滑。将NAF方法应用于低信噪比的人体心脏磁共振扩散加权图像的二维和三维图像平滑处理中。实验结果表明，NAF方法更好地兼顾了噪声消除和边缘、细节特征保持，由平滑后的心脏扩散加权图像计算得到的心肌张量场在保持张量各向异性的同时获得了较好的正则化效果，由此追踪出的心肌纤维在长度和方向上获得了更好的局部一致性。
Intensity variation is often used in signal or image processing algorithms afterbeing quantified by a measurement method. The method of measuring andquantifying the intensity variation is called a change measure. Change measure iscommonly used in the methods for signal change detection, image edge detection,edge-based segmentation model, and feature-preserving smoothing, etc. They arecollectively referred as change measure-based methods.
In these methods, change measure plays such an important role that theirperformances are greatly affected by the measuring result of intensity variation. Inthe processing of biomedical images or signals, the existing change measures mayprovide inaccurate information on changes due to the high noise level or the strongrandomness, which leads to the degradation of the performance of the change-measure based methods.
In this context, our research perspective is to study a robust change measureand propose several processing methods based on it. These methods should berobust to noise, and could reduce undesirable phenomena which often present in theresults obtained by other change measure-based methods.
Moreover, prompted by new medical imaging techniques, many multi-valuedimage processing methods are proposed, which require corresponding changemeasures. How to robustly measure variations in tensor-valued data becomes a newproblem in image processing.
Non-Stationarity Measure (NSM) is a rubust change measure with a goodnoise-immunity ability. It can reflect and quantify changes in an image or a signalthrough measuring its degree of non-stationarity. In this work, the NSM method isimproved and extended, several image and signal processing approches based onthe NSM are proposed and applied to deal with various medical images with highnoise levels and signals showing strong randomness. Additionally, the extendedNSM can measure changes in the vector-and tensor-valued data. The specificresearch contents are as follows:
Firstly, the NSM is comprehensively improved and extended. The notion ofgeneral parameter stationarity is introduced. Based on the notion, the NSM iselaborated and explained using more appropriate notions and a general formulationof the NSM is given. Then, the construction process of the NSM operators isgeneralized. The outputs of the NSM operators in several typical cases are studied.The advantage of the NSM operator in terms of noise immunity is theoreticallyproved. And the selection of critical parameters is discussed. Finally, the NSM operator is extended to deal with N dimensional data and to measure changes in thevector-and tensor-valued data, thus becoming a general and robust changemesurement method.
Secondly, aiming at the problem of false alarms and misdetections in thechange detection of strong random signals and the problem of false edges in theedge detection of highly noisy signals, a NSM-based change detection method anda NSM-based edge detection method are respectively proposed and applied todetect changes in the heart rate signal and the EEG signal, and to detect edges inthe cardiac diffusion weighted (DW) images. Experimental results show that theNSM-based detection methods can provide more accurate positions of changepoints and edges, and can effectively reduce false detections which often present inthe results of other change measure-based methods.
Thirdly, aiming at the problem of false contours and leakages in thesegmentation of highly noisy images, a NSM-based geometric active contour(NSM-GAC) model is proposed and applied to segment the carotid ultrasoundimages. The model makes use of the NSM instead of the gradient magnitude toprovide edge information for driving the motion of the zero level set toward desiredlocations. The segmentation results of highly noisy synthetic images, simulated andreal carotid ultrasound images show that the NSM-GAC model can obtain betterresults with less iterations and computation time, and can reduce false contours andleakages.
Last and more important, focusing on the difficult compromise between thesmoothness of homogeneous regions and the preservation of desirable features inthe smoothing of low SNR images, a new feature-preserving smoothing approachNonstationarity adaptive filtering (NAF) is proposed. It estimates the intensity of apixel by averaging intensities in its adaptive homogeneous neighborhood. The latteris determined according to five constraints and the NSM map. The proposedapproach is applied to smooth the2-D and3-D cardiac DW images. Experimentalresults show that the proposed method can achieve a better compromise betweensmoothing homogeneous regions and preserving of desirable features such asboundaries, thus leading to homogeneously consistent tensor fields andconsequently more coherent fibers.
引文
[1] Basser P J, Pajevic S. Statistical artifacts in diffusion tensor MRI (DT-MRI)caused by background noise [J]. Magnetic Resonance in Medicine,2000,44(1):41-50.
[2] Jones D K, Basser P J."Squashing peanuts and smashing pumpkins": Hownoise distorts diffusion-weighted MR data [J]. Magnetic Resonance inMedicine,2004,52(5):979-93.
[3] Ding Z H, Gore J C, Anderson A W. Reduction of noise in diffusion tensorimages using anisotropic smoothing [J]. Magnetic Resonance in Medicine,2005,53(2):485-90.
[4] Chen B, Hsu E W. Noise removal in magnetic resonance diffusion tensorimaging [J]. Magnetic Resonance in Medicine,2005,54(2):393-401.
[5] Welk M, Weickert J, Becker F, et al. Median and related local filters fortensor-valued images [J]. Signal Processing,2007,87(2):291-308.
[6] Hamarnesh G, Hradsky J. Bilateral filtering of diffusion tensor magneticresonance images [J]. IEEE Transactions on Image Processing,2007,16(10):2463-75.
[7] Burgeth B, Pizarro L, Breuss M, et al. Adaptive Continuous-ScaleMorphology for Matrix Fields [J]. International Journal of Computer Vision,2011,92(2):146-61.
[8] Burgeth B, Didas S, Florack L, et al. A generic approach to diffusion filteringof matrix-fields [J]. Computing,2007,81(2-3):179-97.
[9] Demirci R. Similarity relation matrix-based color edge detection [J]. Aeu-International Journal of Electronics and Communications,2007,61(7):469-77.
[10] Wang Z Z, Vemuri B C. DTI segmentation using an information theoretictensor dissimilarity measure [J]. Ieee Transactions on Medical Imaging,2005,24(10):1267-77.
[11] Wang Z Z, Vemuri B C, Society I C. An affine invariant tensor dissimilaritymeasure and its applications to tensor-valued image segmentation;proceedings of the Proceedings of the2004Ieee Computer SocietyConference on Computer Vision and Pattern Recognition, Vol1, F,2004[C].
[12] Pennec X, Fillard P, Ayache N. A Riemannian framework for tensorcomputing [J]. International Journal of Computer Vision,2006,66(1):41-66.
[13] Arsigny V, Fillard P, Pennec X, et al. Log-euclidean metrics for fast andsimple calculus on diffusion tensors [J]. Magnetic Resonance in Medicine,2006,56(2):411-21.
[14] Yang P, Dumont G, Ansermino J M. Adaptive change detection in heart ratetrend monitoring in anesthetized children [J]. Ieee Transactions on BiomedicalEngineering,2006,53(11):2211-9.
[15] Chelani A B. Change detection using CUSUM and modified CUSUM methodin air pollutant concentrations at traffic site in Delhi [J]. StochasticEnvironmental Research and Risk Assessment,2011,25(6):827-34.
[16] Severo M, Gama J. Change detection with Kalman filter and CUSUM [M]Discovery Science, Proceedings.2006:243-54.
[17] Basseville M, Nikiforov I V. Detection of Abrupt Changes: Theory andApplication [M]. Upper Saddle River, NJ, USA: Prentice-Hall, Inc.,1993.
[18] Lavielle M. Using penalized contrasts for the change-point problem [J].Signal Processing,2005,85(8):1501-10.
[19] Lavielle M. Detection of multiple changes in a sequence of dependentvariables [J]. Stochastic Processes and Their Applications,1999,83(1):79-102.
[20] Ensign D L, Pande V S. Bayesian Detection of Intensity Changes in SingleMolecule and Molecular Dynamics Trajectories [J]. Journal of PhysicalChemistry B,2010,114(1):280-92.
[21] Laurent H, Doncarli C. Stationarity index for abrupt changes detection in thetime-frequency plane [J]. Ieee Signal Processing Letters,1998,5(2):43-5.
[22] Malegaonkar A, Ariyaeeinia A, Sivakumaran P, et al. Unsupervised speakerchange detection using Probabilistic pattern matching [J]. Ieee SignalProcessing Letters,2006,13(8):509-12.
[23] Ajmera J, Mccowan L, Bourlard H. Robust speaker change detection [J]. IeeeSignal Processing Letters,2004,11(8):649-51.
[24] Chen S, Gopalakrishnan P. Speaker, environment and channel changedetection and clustering via the Bayesian Information Criterion; proceedingsof the Proc DARPA Broadcast News Transcription and UnderstandingWorkshop, F,1998[C]. Virginia, USA.
[25] Huang C C, Wang J F, Wu D J. Automatic scene change detection forcomposed speech and music sound under low SNR noisy environment [J].Ieee Transactions on Speech and Audio Processing,2005,13(5):689-99.
[26] Cheng S S, Wang H M, Fu H C. BIC-Based Speaker Segmentation UsingDivide-and-Conquer Strategies With Application to Speaker Diarization [J].Ieee Transactions on Audio Speech and Language Processing,2010,18(1):141-57.
[27] Zhou B W, Hansen J H L. Efficient audio stream segmentation via thecombined T(2) statistic and Bayesian information criterion [J]. IeeeTransactions on Speech and Audio Processing,2005,13(4):467-74.
[28] Zhang C, Hansen J H L. Whisper-Island Detection Based on UnsupervisedSegmentation With Entropy-Based Speech Feature Processing [J]. IeeeTransactions on Audio Speech and Language Processing,2011,19(4):883-94.
[29] Malegaonkar A S, Ariyaeeinia A M, Sivakumaran P. Efficient speaker changedetection using adapted Gaussian mixture models [J]. Ieee Transactions onAudio Speech and Language Processing,2007,15(6):1859-69.
[30] Noble J A, Boukerroui D. Ultrasound image segmentation: A survey [J]. IeeeTransactions on Medical Imaging,2006,25(8):987-1010.
[31] Kuncheva L I. Change Detection in Streaming Multivariate Data UsingLikelihood Detectors [J]. Ieee Transactions on Knowledge and DataEngineering,2013,25(5):1175-80.
[32]王聪,孙晓颖.基于局部平稳的随机序列变化点检测及参数估计[J].吉林大学学报(工学版),2012, S1):396-400.
[33] Desobry F, Davy M, Doncarli C. An online Kernel change detection algorithm[J]. Ieee Transactions on Signal Processing,2005,53(8):2961-74.
[34] Liu S, Yamada M, Collier N, et al. Change-point detection in time-series databy relative density-ratio estimation; proceedings of the Joint IAPRInternational Workshops on Structural and Syntactic PatternRecognition,SSPR2012and Statistical Techniques in Pattern Recognition,SPR2012,November7,2012-November9,2012, Hiroshima, Japan, F,2012[C].Springer Verlag.
[35] La Rosa P S, Nehorai A, Eswaran H, et al. Detection of uterine MMGcontractions using a multiple change point-estimator and the K-means clusteralgorithm [J]. Ieee Transactions on Biomedical Engineering,2008,55(2):453-67.
[36] Rigaill G, Lebarbier E, Robin S. Exact posterior distributions and modelselection criteria for multiple change-point detection problems [J]. Statisticsand Computing,2012,22(4):917-29.
[37] Lebarbier E. Detecting multiple change-points in the mean of Gaussianprocess by model selection [J]. Signal Processing,2005,85(4):717-36.
[38] Huang R Q, Hansen J H L. Advances in unsupervised audio classification andsegmentation for the broadcast news and NGSW corpora [J]. IeeeTransactions on Audio Speech and Language Processing,2006,14(3):907-19.
[39] Tourneret J Y. Detection and estimation of abrupt changes contaminated bymultiplicative Gaussian noise [J]. Signal Processing,1998,68(3):259-70.
[40] Al-Assaf Y. Surface myoelectric signal analysis: Dynamic approaches forchange detection and classification [J]. Ieee Transactions on BiomedicalEngineering,2006,53(11):2248-56.
[41] Khalil M, Duchene J. Uterine EMC analysis: A dynamic approach for changedetection and classification [J]. Ieee Transactions on Biomedical Engineering,2000,47(6):748-56.
[42] Chendeb M, Khalil M, Duchene J. Methodology of wavelet packet selectionfor event detection [J]. Signal Processing,2006,86(12):3826-41.
[43] Nes P G. Fast multi-scale edge-detection in medical ultrasound signals [J].Signal Processing,2012,92(10):2394-408.
[44] Lin P C, Wang J C, Wang J F, et al. Unsupervised speaker change detectionusing SVM training misclassification rate [J]. Ieee Transactions on Computers,2007,56(9):1234-44.
[45] Kaplan A, Roschke J, Darkhovsky B, et al. Macrostructural EEGcharacterization based on nonparametric change point segmentation:application to sleep analysis [J]. Journal of Neuroscience Methods,2001,106(1):81-90.
[46] Delacourt P, Wellekens C J. DISTBIC: A speaker-based segmentation foraudio data indexing [J]. Speech Communication,2000,32(1-2):111-26.
[47] Gonzalez R C, Woods R E. Digital image processing,2nd ed.[M]. PrenticeHall,2002.
[48] Laligant O, Truchetet F. A Nonlinear Derivative Scheme Applied to EdgeDetection [J]. Ieee Transactions on Pattern Analysis and Machine Intelligence,2010,32(2):242-57.
[49] Kawaguchi T, Rizon M. Iris detection using intensity and edge information [J].Pattern Recognition,2003,36(2):549-62.
[50][50]Chen T. Derivative operator on smoothed images [M]. Image Processing:Algorithms and Systems Vi.2008.
[51] Barcelos C a Z, Boaventura M, Silva E C. A well-balanced flow equation fornoise removal and edge detection [J]. IEEE Transactions on Image Processing,2003,12(7):751-63.
[52] Xu X, Yang Z, Wang Y. A method based on rank-ordered filter to detect edgesin cellular image [J]. Pattern Recognition Letters,2009,30(6):634-40.
[53] Direkoglu C, Nixon M S. Moving-edge detection via heat flow analogy [J].Pattern Recognition Letters,2011,32(2):270-9.
[54] Canny J. A Computational Approach to Edge Detection [J]. Ieee Transactionson Pattern Analysis and Machine Intelligence,1986,8(6):679-98.
[55] Bao P, Zhang L, Wu X L. Canny edge detection enhancement by scalemultiplication [J]. Ieee Transactions on Pattern Analysis and MachineIntelligence,2005,27(9):1485-U1.
[56] Shui P-L, Zhang W-C. Noise-robust edge detector combining isotropic andanisotropic Gaussian kernels [J]. Pattern Recognition,2012,45(2):806-20.
[57] Lopez-Molina C, De Baets B, Bustince H. Generating fuzzy edge images fromgradient magnitudes [J]. Computer Vision and Image Understanding,2011,115(11):1571-80.
[58] Mallat S, Zhong S. Characterization of signals from multiscale edges [J]. IeeeTransactions on Pattern Analysis and Machine Intelligence,1992,14(7):710-32.
[59] Mallat S. A wavelet tour of signal processing: the sparse way,3rd ed.[M].Academic Press,2009.
[60] Morrone M C, Ross J, Burr D C, et al. MACH BANDS ARE PHASEDEPENDENT [J]. Nature,1986,324(6094):250-3.
[61] Morrone M C, Owens R A. Feature detection from local energy [J]. PatternRecognition Letters,1987,6(5):303-13.
[62] Kovesi P. Phase congruency: A low-level image invariant [J]. PsychologicalResearch-Psychologische Forschung,2000,64(2):136-48.
[63] Ke W, Pengfeng X, Xuezhi F, et al. Image feature detection from phasecongruency based on two-dimensional Hilbert transform [J]. PatternRecognition Letters,2011,32(15):2015-24.
[64]王珂,肖鹏峰.基于二维希尔伯特变换的相位一致模型图像特征检测方法[J].测绘学报,2010,06):605-10+17.
[65]王珂,肖鹏峰,冯学智, et al.基于改进二维离散希尔伯特变换的图像边缘检测方法[J].测绘学报,2012,03):421-7+33.
[66]张建新,欧宗瑛.基于Log-Gabor小波相位一致的掌纹线特征提取[J].光电子激光,2008,05):704-7.
[67] Struc V, Pavesic N. Phase congruency features for palm-print verification [J].Iet Signal Processing,2009,3(4):258-68.
[68] Zhang L, Zhang L, Zhang D, et al. Phase congruency induced local featuresfor finger-knuckle-print recognition [J]. Pattern Recognition,2012,45(7):2522-31.
[69] Park D J, Nam K M, Park R H. Multiresolution edge detection techniques [J].Pattern Recognition,1995,28(2):211-29.
[70] Chao S-M, Tsai D-M. An improved anisotropic diffusion model for detail-andedge-preserving smoothing [J]. Pattern Recognition Letters,2010,31(13):2012-23.
[71] Kim D S, Lee W H, Kweon I S. Automatic edge detection using3x3idealbinary pixel patterns and fuzzy-based edge thresholding [J]. PatternRecognition Letters,2004,25(1):101-6.
[72] Konishi S, Yuille A L, Coughlan J M, et al. Statistical edge detection:Learning and evaluating edge cues [J]. Ieee Transactions on Pattern Analysisand Machine Intelligence,2003,25(1):57-74.
[73] Konishi S, Yuille A, Coughlan J. A statistical approach to multi-scale edgedetection [J]. Image and Vision Computing,2003,21(1):37-48.
[74] Deledalle C-A, Denis L, Tupin F. How to Compare Noisy Patches? PatchSimilarity Beyond Gaussian Noise [J]. Int J Comput Vis,2012,99(86–102.
[75] Sun G, Liu Q, Liu Q, et al. A novel approach for edge detection based on thetheory of universal gravity [J]. Pattern Recognition,2007,40(10):2766-75.
[76] Lopez-Molina C, Bustince H, Fernandez J, et al. A gravitational approach toedge detection based on triangular norms [J]. Pattern Recognition,2010,43(11):3730-41.
[77] Bouda B, Masmoudi L, Aboutajdine D. CVVEFM: Cubical voxels and virtualelectric field model for edge detection in color images [J]. Signal Processing,2008,88(4):905-15.
[78] Li C M, Xu C Y, Gui C F, et al. Distance Regularized Level Set Evolution andIts Application to Image Segmentation [J]. IEEE Transactions on ImageProcessing,2010,19(12):3243-54.
[79] Zhang W, Liu F, Jiao L, et al. SAR Image Despeckling Using Edge Detectionand Feature Clustering in Bandelet Domain [J]. Ieee Geoscience and RemoteSensing Letters,2010,7(1):131-5.
[80] Shacham O, Haik O, Yitzhaky Y. Blind restoration of atmosphericallydegraded images by automatic best step-edge detection [J]. PatternRecognition Letters,2007,28(15):2094-103.
[81]王向阳,陈景伟,于永健.一种基于彩色边缘综合特征的图像检索算法[J].模式识别与人工智能,2010,02):216-21.
[82]乔闹生,邹北骥,邓磊, et al.一种基于图像融合的含噪图像边缘检测方法[J].光电子激光,2012,11):2215-20.
[83]魏颖,武林,贾同, et al.梯度熵改进边缘检测的自适应阈值曲面分割算法[J].东北大学学报(自然科学版),2011,06):781-5.
[84]钮圣虓,王盛,杨晶晶, et al.完全基于边缘信息的快速图像分割算法[J].计算机辅助设计与图形学学报,2012,11):1410-9.
[85] Caselles V, Catte F, Coll T, et al. A Geometric Model For Active Contours InImage-Processing [J]. Numerische Mathematik,1993,66(1):1-31.
[86] Malladi R, Sethian J A, Vemuri B C. Shape Modeling With Front Propagation-A Level Set Approach [J]. Ieee Transactions on Pattern Analysis andMachine Intelligence,1995,17(2):158-75.
[87]何宁,张朋.基于边缘和区域信息相结合的变分水平集图像分割方法[J].电子学报,2009,10):2215-9.
[88]薛维琴,周志勇,张涛, et al.灰度不均的弱边缘血管影像的水平集分割方法[J].软件学报,2012,09):2489-99.
[89] Tian Y, Duan F Q, Zhou M Q, et al. Active contour model combining regionand edge information [J]. Machine Vision and Applications,2013,24(1):47-61.
[90] Zhang H Z, Morrow P, Mcclean S, et al. Coupling edge and region-basedinformation for boundary finding in biomedical imagery [J]. PatternRecognition,2012,45(2):672-84.
[91] J hne B. Digital Image Processing: Concepts, Algorthms, and ScientificApplications, fourth ed.[M]. Berlin: Springer,1997.
[92] Saintmarc P, Chen J S, Medioni G. ADAPTIVE SMOOTHING-A GENERALTOOL FOR EARLY VISION [J]. Ieee Transactions on Pattern Analysis andMachine Intelligence,1991,13(6):514-29.
[93] Tomasi C, Manduchi R. Bilateral filtering for gray and color images;proceedings of the Computer Vision,1998Sixth International Conference on,F4-7Jan1998,1998[C].
[94] Grazzini J, Soille P. Edge-preserving smoothing using a similarity measure inadaptive geodesic neighbourhoods [J]. Pattern Recognition,2009,42(10):2306-16.
[95] Perona P, Malik J. SCALE-SPACE AND EDGE-DETECTION USINGANISOTROPIC DIFFUSION [J]. Ieee Transactions on Pattern Analysis andMachine Intelligence,1990,12(7):629-39.
[96] Weickert J. Anisotropic Diffusion in Image Processing [M]. B.G. Teubner:Stuttgart,1998.
[97] Elad M. On the origin of the bilateral filter and ways to improve it [J]. IEEETransactions on Image Processing,2002,11(10):1141-51.
[98] Paris S, Kornprobst P, Tumblin J, et al. Bilateral Filtering: Theory andApplications [J]. Foundations and Trends in Computer Graphics and Vision,2008,4(1):1-73.
[99] Lerallut R, Decenciere E, Meyer F. Image filtering using morphologicalamoebas [J]. Image and Vision Computing,2007,25(4):395-404.
[100]郭超峰,曹奎.一种新的边缘保持自适应平滑算法[J].河南大学学报(自然科学版),2007,05):518-22.
[101]王兴旺,易辉伟,朱建军, et al.基于有选择保边缘平滑法的SAR干涉图像滤波算法[J].工程勘察,2008,11):50-3+8.
[102] Lukac R, Plataniotis K N. Vector edge operators for cDNA microarray spotlocalization [J]. Computerized Medical Imaging and Graphics,2007,31(7):510-22.
[103] Coulon O, Alexander D C, Arridge S. Diffusion tensor magnetic resonanceimage regularization [J]. Medical Image Analysis,2004,8(1):47-67.
[104] Scharcanski J, Venetsanopoulos A N. Edge detection of color images usingdirectional operators [J]. Ieee Transactions on Circuits and Systems for VideoTechnology,1997,7(2):397-401.
[105] Theoharatos C, Economou G, Fotopoulos S. Color edge detection using theminimal spanning tree [J]. Pattern Recognition,2005,38(4):603-6.
[106] Trahanias P E, Venetsanopoulos A N. Color edge detection using vector orderstatistics [J]. IEEE Transactions on Image Processing,1993,2(2):259-64.
[107] Trahanias P E, Venetsanopoulos A N. Vector order statistics operators as coloredge detectors [J]. Ieee Transactions on Systems Man and Cybernetics Part B-Cybernetics,1996,26(1):135-43.
[108] Kuo C T, Cheng S C. Fusion of color edge detection and color quantizationfor color image watermarking using principal axes analysis [J]. PatternRecognition,2007,40(12):3691-704.
[109] Rousson M, Lenglet C, Deriche R. Level set and region based surfacepropagation for diffusion tensor MRI segmentation [M]. Computer Vision andMathematical Methods in Medical and Biomedical Image Analysis.2004:123-34.
[110] Wang Z Z, Vemuri B C. Tensor field segmentation using region based activecontour model [M]. Computer Vision-Eccv2004, Pt4.2004:304-15.
[111] Wiegell M R, Tuch D S, Larsson H B W, et al. Automatic segmentation ofthalamic nuclei from diffusion tensor magnetic resonance imaging [J].Neuroimage,2003,19(2):391-401.
[112] Lenglet C, Rousson M, Deriche R, et al. Statistics on the manifold ofmultivariate normal distributions: Theory and application to Diffusion TensorMRI processing [J]. Journal of Mathematical Imaging and Vision,2006,25(3):423-44.
[113] Lenglet C, Rousson M. DTI segmentation by statistical surface evolution [J].Ieee Transactions on Medical Imaging,2006,25(6):685-700.
[114] Guo W H, Chen Y M, Zeng Q G. A geometric flow-based approach fordiffusion tensor image segmentation [J]. Philosophical Transactions of theRoyal Society a-Mathematical Physical and Engineering Sciences,2008,366(1874):2279-92.
[115] Malcolm J, Rathi Y, Tannenbaum A, et al. A graph cut approach to imagesegmentation in tensor space; proceedings of the2007Ieee Conference onComputer Vision and Pattern Recognition, Vols1-8, F,2007[C].
[116] Castano-Moraga C A, Lenglet C, Deriche R, et al. A Riemannian approach toanisotropic filtering of tensor fields [J]. Signal Processing,2007,87(2):263-76.
[117] Batchelor P G, Moakher M, Atkinson D, et al. A rigorous framework fordiffusion tensor calculus [J]. Magnetic Resonance in Medicine,2005,53(1):221-5.
[118] Liu W Y. Detection de Rupture par Mesure de Non Stationnarite Locale:Application a la Segmentation de Signaux Multidimensionnels [D]; InstitutNational des Sciences Appliquées (INSA),1994.
[119] Pal N R, Pal S K. A review on image segmentation techniques [J]. PatternRecognition,1993,26(9):1277-94.
[120] Liu W Y, Magnin I E, Gimenez G. Un nouvel opérateur pour la détection derupture dans des signaux bruités [J]. Traitement du Signal,1995,12(3):226-36.
[121] Liu W Y, Magnin I E, Gimenez G. A new approach for the segmentation ofstochastic processes [M]. Int Conf on Signal Processing'93. Beijing, P.R.China.1993:584–7.
[122] Liu W Y, Dautraix-Ricard I, Magnin I E, et al. A statistic based preprocessingtechnique for ultrasonic stereoechography [M]. Int Conf on Signal Processing'93. Beijing, P.R. China.1993:916–9.
[123] Liu W Y, Magnin I E, Gimenez G. A statistic based approach for segmentation
[M]. Conf Proc IEEE Eng Med Biol Soc. Paris, France.1992:1924–5.
[124] Vincent Arsigny P F, Xavier Pennec,Nicholas Ayache,5584[R]: Unité derecherche INRIA Sophia Antipolis,2005.
[125]于维汉.心肌病学[M].科学出版社,2006.
[126] Chan T F, Vese L A. Active contours without edges [J]. IEEE Transactions onImage Processing,2001,10(2):266-77.
[127] Yu Y J, Acton S T. Speckle reducing anisotropic diffusion [J]. IEEETransactions on Image Processing,2002,11(11):1260-70.
[128] Bamber J C, Dickinsont R J. Ultrasonic B-scanning: a computer simulation [J].Phys Med Biol,1980,25(3):463-79.
[129] Assaf Y, Pasternak O. Diffusion tensor imaging (DTI)-based white mattermapping in brain research: A review [J]. Journal of Molecular Neuroscience,2008,34(1):51-61.
[130] Alexander A L, Lee J E, Lazar M, et al. Diffusion tensor imaging of the brain[J]. Neurotherapeutics,2007,4(3):316-29.
[131] Xu Q, Anderson A W, Gore J C, et al. Unified Bundling and Registration ofBrain White Matter Fibers [J]. Ieee Transactions on Medical Imaging,2009,28(9):1399-411.
[132] Wu M T, Tseng W Y I, Su M Y M, et al. Diffusion tensor magnetic resonanceimaging mapping the fiber architecture remodeling in human myocardiumafter infarction-Correlation with viability and wall motion [J]. Circulation,2006,114(10):1036-45.
[133] Wu M T, Su M Y M, Huang Y L, et al. Sequential Changes of MyocardialMicrostructure in Patients Postmyocardial Infarction by Diffusion-TensorCardiac MR Correlation With Left Ventricular Structure and Function [J].Circulation-Cardiovascular Imaging,2009,2(1):32-40.
[134] Frindel C, Robini M, Croisille P, et al. Comparison of regularization methodsfor human cardiac diffusion tensor MRI [J]. Medical Image Analysis,2009,13(3):405-18.
[135] Notohamiprodjo M, Glaser C, Herrmann K A, et al. Diffusion tensor imagingof the kidney with parallel imaging: Initial clinical experience [J].Investigative Radiology,2008,43(10):677-85.
[136] Raya J G, Horng A, Dietrich O, et al. Articular Cartilage: In Vivo Diffusion-Tensor Imaging [J]. Radiology,2012,262(2):550-9.
[137] Eyal E, Shapiro-Feinberg M, Furman-Haran E, et al. Parametric DiffusionTensor Imaging of the Breast [J]. Investigative Radiology,2012,47(5):284-91.
[138] Wang Z Z, Vemuri B C, Chen Y M, et al. A constrained variational principlefor direct estimation and smoothing of the diffusion tensor field from complexDWI [J]. Ieee Transactions on Medical Imaging,2004,23(8):930-9.
[139] Parker G J M, Schnabel J A, Symms M R, et al. Nonlinear smoothing forreduction of systematic and random errors in diffusion tensor imaging [J].Journal of Magnetic Resonance Imaging,2000,11(6):702-10.
[140] Weickert J. Coherence-enhancing diffusion filtering [J]. International Journalof Computer Vision,1999,31(2-3):111-27.
[141] Moraschi M, Hagberg G E, Di Paola M, et al. Smoothing That Does Not Blur:Effects of the Anisotropic Approach for Evaluating Diffusion Tensor ImagingData in the Clinic [J]. Journal of Magnetic Resonance Imaging,2010,31(3):690-7.
[142] Xu Q, Anderson A W, Gore J C, et al. Efficient anisotropic filtering ofdiffusion tensor images [J]. Magnetic Resonance Imaging,2010,28(2):200-11.
[143] Vemuri B C, Chen Y, Rao M, et al. Fiber tract mapping from diffusion tensorMRI; proceedings of the Ieee Workshop on Variational and Level Set Methodsin Computer Vision, Proceedings, F,2001[C].
[144] Tabelow K, Polzehl J, Spokoiny V, et al. Diffusion tensor imaging: Structuraladaptive smoothing [J]. Neuroimage,2008,39(4):1763-73.
[145] Wang Z, Bovik A C, Sheikh H R, et al. Image quality assessment: From errorvisibility to structural similarity [J]. IEEE Transactions on Image Processing,2004,13(4):600-12.
[146] Kingsley P B. Introduction to diffusion tensor imaging mathematics: Part II.Anisotropy, diffusion-weighting factors, and gradient encoding schemes [J].Concepts in Magnetic Resonance Part A,2006,28A(2):123-54.
[147] Basser P J, Pierpaoli C. Microstructural and physiological features of tissueselucidated by quantitative-diffusion-tensor MRI [J]. Journal of MagneticResonance Series B,1996,111(3):209-19.
[148] P. Fillard N T, T.-C. Souplet, T. Mansi. MedINRIA Version1.8.0[M].http://www-sop.inria.fr/asclepios/software/MedINRIA/: INRIA-AsclepiosResearch Team,2007.