1 Correction of Artifacts in MR Image Analysis

1 Correction of Artifacts in MR Image Analysis Jayaram K. Udupa Medical Image Processing Group Department of Radiology University of Pennsylvania Philadelphia, PA http: //www. mipg. upenn. edu/ Udupa

2 CAVA: Computer-Aided Visualization and Analysis The science underlying computerized methods of image processing, analysis, and visualization to facilitate new therapeutic strategies, basic clinical research, education, and training.

3 CAD vs CAVA CAD: Computer-Aided Diagnosis The science underlying computerized methods for the diagnosis of diseases via images

4 Purpose of CAVA In: Multiple multimodality multidimensional images of an object system. Out: Qualitative/quantitative information about objects in the object system. Object system – a collection of rigid, deformable, static, or dynamic, physical or conceptual objects.

6 CAVA Operations Img Processing: for enhancing information about and defining object system. Visualization: for viewing and comprehending object system. Manipulation: for altering object system (virtual surgery). Analysis: for quantifying information about object system.

7 Terminology voxels: Cuboidal elements into which body region is digitized by the imaging device. Scene: Multidimensional (2 D, 3 D, 4 D, …) image of the body region; S = (C, f ) Scene domain: Rectangular array of voxels on which the scene is defined; C. Scene intensity: Values assigned to voxels; f (c).

8 The CAVA Process Object System Scan Scenes Img process Manipulate Structure System Analyze Quantitative Information Visualize Renditions

9 g a g : body coordinate system a abc: scanner coordinate system b w u xyz: scene coordinate system uvw: structure coordinate system rst: display coordinate system voxel z c v t s a r y x pixel structure scene domain

10 CAVA Operations Img processing: Visualization Manipulation Analysis Volume of interest Filtering Interpolation Registration Segmentation

Scale in CAVA Scale represents level of detail of object information in scenes. Scale is needed to handle variable object size in different parts of the scene. Global scale: Process the scene at each of various fixed scales and then combine the results – scale space approach. Local scale: At each voxel, define largest homogeneous region, and treat these as fundamental units in the scene. 11

Global Scale Not clear how to combine results from multiple scales. 12

13 Local Scale At any voxel v in a scene, b-scale: largest homogeneous ball centered at v. t-scale: largest homogeneous ellipsoid centered at v. g-scale: largest connected homogeneous region containing v.

14 Local Scale brain PD slice ball scale tensor scale generalized scale b-, t-, and g-scales can be employed for controlling CAVA operation parameters locally adaptively.

15 Filtering Scene Purpose: Scene To suppress unwanted (non-object) information. To enhance wanted (object) information. Suppressive: Mainly for suppressing random noise. Enhancive: For enhancing edges, regions. For correcting background variation. For intensity scale standardization.

16 Suppressive Filtering – Gaussian, Median Gaussian: f. F(v) is a Gaussian weighted average of f(v) in a neighborhood of v. This neighborhood may be a b-, t-, or g-scale region of v. Median: f. F(v) is the median of the intensities f(u) in a neighborhood of v. This neighborhood may be a b-, t-, or g-scale region of v.

Suppressive Filtering - Diffusion Intensity at v diffuses to neighboring voxels iteratively, except at boundary interfaces, where diffusion is reduced considerably or halted. This modification of diffusion is controlled by the size, shape, and orientation of scale region. 17

18 Suppressive Filtering - Diffusion Conductance t(c, d) controlling flow Vt from voxel c to voxel d at the t-th iteration is: s: large in the deep interior of large scale regions, large along boundaries, small near boundaries in orthogonal direction.

19 Suppressive Filtering - Diffusion The iterative process is defined as follows: A - constant (depends on adjacency) D(c, d) - unit vector from c to d. Nc - neighborhood of c.

20 Suppressive Filtering - Diffusion: Examples original b-diffusion regular-diffusion g-diffusion

21 Suppressive Filtering - Diffusion: Examples original ROI regular diffusion b-diffusion t-diffusion

22 FOC curve (200 iterations) g. B D # iterations b. D NCD

23 Enhancive Filtering Enhancing edges: Edge detection. Enhancing regions: Histogram equalization. Intensity scale standardization: For MRI – to make sure that intensity values have the same tissue specific meaning. Inhomogeneity correction: For correcting background intensity variation.

24 Enhancive Filtering: Intensity Standardization Problem: • MRI intensities do not have a fixed meaning, even for the same protocol, body region, patient, scanner. • Poses problems for image operations (segmentation). • Simple linear scaling does not help.

25 Enhancive Filtering: Intensity Standardization Before standardization After standardization Histograms of WM regions in 10 PD-weighted MRI scenes: Shown separately (left); and combined into one distribution (right).

26 Enhancive Filtering: Intensity Standardization Approach consists of: Training Transformation Training: (1) Identify tissue specific landmarks LM 1, …. , LMn on each of a set of images. (2) Choose a standard scale, say [0, 4000]. (3) Map LM 1, …. , LMn from each input image on to standard scale. (4) Find average location each landmark. on standard scale for

27 Enhancive Filtering: Intensity Standardization image scale standard scale ·····

28 Enhancive Filtering: Intensity Standardization Transformation: std scale (1) Identify landmarks in image scale. (2) Map them to standard scale and determine transformation. (3) Map all intensities in image scale as per this transformation to standard scale. input image scale

29 Enhancive Filtering: Intensity Standardization Choosing landmarks on intensity scale: (1) On image histogram – median, mode, quartiles, (2) deciles, … (2) Using local scales – largest b-scale or g-scale (3) Interactively – paint regions corresponding to different tissues where mean intensities are used as LMi.

30 Enhancive Filtering: Intensity Standardization Before standardization After standardization Histograms of WM regions in 10 PD-weighted MRI scenes: Shown separately (left); and combined into one distribution (right).

31 Enhancive Filtering: Intensity Standardization Before After Data set 1 Data set 2 Data set 3 PD-weighted brain MRI scenes of three subjects

Enhancive Filtering: Intensity Standardization 32 Original PD scenes with WM highlighted for fixed intensity range Standardized PD scenes with WM highlighted for fixed intensity range MTR scenes with WM highlighted for fixed intensity range

33 Enhancive Filtering: Intensity Standardization Before After

34 Enhancive Filtering: Intensity Standardization Data from Different Hospitals Before After

36 Enhancive Filtering: Intensity Standardization (1) 20 Patient scene data sets (2) Segment WM, GM, CSF (3) Determine % CV of mean intensity in tissue (4) regions across patients. Scanner dependent inter-patient variations are considerably reduced after standardization.

Enhancive Filtering: Intensity Non Uniformity Correction Problem: • Imperfections in the RF field cause background variations in MR images. • Poses challenges in image segmentation and analysis. Original N 3 (Sled et al. ) SBC 37

38 Enhancive Filtering: Intensity Non Uniformity Correction Goal: To develop a general method for correcting the variations that fulfills: (R 1) no need for user help per scene (R 2) no need for accurate prior segmentation (R 3) no need for prior knowledge of tissue intensity distribution A standardization Based Correction (SBC) method is described.

39 Non Uniformity Correction – SBC Method Step 0: Set Cc = C, the given scene. Step 1: Standardize Cc to the standard intensity gray scale for the particular imaging protocol and body region under consideration and output scene Cs ; Step 2: determine tissue regions CB 1, CB 2, . . . , CBm by using fixed threshold intervals on Cs ; Step 3: if CBi determined in the previous iteration are insignificantly (<0. 1%) different from the current CBi, stop; Step 4: else, estimate background variation in Cs as a scene Cbe, compute corrected scene Cc, and go to Step 1;

40 Non Uniformity Correction – SBC Method Oi Oj x Illustration of discontinuity between inhomogeneity maps (continuous lines) estimated independently from different tissue regions Oi and Oj. We need a single combined inhomogeneity map.

41 Non Uniformity Correction – SBC Method 1. Find a weight factor λ to minimize 2. Combine the two inhomogeneity maps 1 and 2 to obtain a new discrete inhomogeneity map d(c): C [0, ) such that for any c C, 3. Determine a 2 nd degree polynomial that constitutes a LSE fit to d. The above steps merge O 1 and O 2 and are then repeated until we have only one region and a single unified inhomogeneity map.

42 Non Uniformity Correction – SBC Method GM WM Iteration 1 3 5 10 20

43 Non Uniformity Correction – SBC Method WM GM Iteration 1 3 5 10 20 WM and GM modes are improved with correction.

44 Non Uniformity Correction – SBC Method GM Original N 3 (Sled et al. ) WM SBC WM and GM modes are improved with correction.

45 Non Uniformity Correction – SBC Method WM GM Original N 3 (Sled et al. ) SBC WM and GM modes are improved with correction.

46 Non Uniformity Correction – SBC Method WM GM Original N 3 (Sled et al. ) SBC WM and GM modes are improved with correction.

47 Non Uniformity Correction – SBC Method

48 Non Uniformity Correction – SBC Method The % cv values for the SBC method are smaller than that for the N 3 method, which has been found to be statistically significant under a paired t-test for each protocol at a level of p < 0. 001.

49 Non Uniformity Correction – Interplay Between Standardization and Correction • What order to apply correction and standardization? Cor Std Cor or Cor Std. . . or Std Cor… • Does correction affect standardness or vice versa? • How does noise filtering affect correction/ standardization and vice versa? Cor Std Flt Cor or ….

Non Uniformity Correction – Interplay Between Standardization and Correction MTR g-scale corrected MTR scenes g. B-scale corrected MTR scenes Correction introduces non-standardness and enhances noise. Best sequence is Std Cor Std Fltr or Cor Std Fltr. Prior to segmentation, perform Corr Std Fltr on all MR images. 50

51 Conclusions (1) Three main types of artifacts (3 n’s): noise, non standardness, non uniformity. (2) Essential to correct for these for effective MR (3) image analysis. (3) Local (b-, t-, g-)scale based strategies are effective (4) in overcoming all these artifacts. (4) Correction can introduce non standardness and (5) enhance noise. (6) (5) The best order of operation: Cor, Std, Fltr.

52 Key References Background, Classification of Methods 1) Udupa, “Three-Dimensional J. K. : Image Processing, Analysis, Visualization: and Methods Techniques, ” and Categorical Course in Diagnostic Radiology Physics: Multidimensional Image Processing, Analysis and Display. Editors: S. G. Armato III and M. S. Brown, Radiological Society of North America, Inc. Oak Brook, Illinois, pp. 9 -26, 2005. 2) Udupa, Florida, 2000. Scale Cybernetics, 55: 367 -375, 1987. 4) Wang, Machine Intelligence, 20(10): 1040 -1055, 1998. 5) Burt, 1981. 6) Burt, Communications, 31(4): 532 -540, 1983. 7) Witkin, Intelligence , pp. 1019 -1022, 1983. 8) Lindeberg, Proceedings of Fundamental Structural Properties in Image and Pattern Analysis, 130: 9 -23, 1999.

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44) Montillo, A. , J. K. Udupa, L. Axel and D. N. Metaxas: “ Integrated Approach for the Removal of Intensity Inhomogeneity and Thermal Noise in SPAMM-MRI Using Scale-Based Fuzzy Connectedness and Multiple Nonlinear Adaptive Filters, ” in Proceedings of SPIE: Medical Imaging, 5032: 1025 -1036, 2003. 45) Intensity Standardization 45) Nyul, L. G. and J. K. Udupa: “On Standardizing the MR Image Intensity Scale, ” Magnetic Resonance in Medicine, 42: 1072 -1081, 1999. 46) Nyul, L. G. , J. K. Udupa and X. Zhang: “New Variants of a Method of MRI Scale Standardization, ” IEEE Transactions on Medical Imaging, 19: 143 -150, 2000. 47) Ge, Y. , J. K. Udupa, L. G. Nyul, L. Wei and R. I. Grossman: “Numerical Tissue Characterization in MS via Standardization of the MR Image Intensity Scale, ” Journal of Magnetic Resonance Imaging, 12: 715 -721, 2000. 48) Madabhushi, A. and J. K. Udupa: “New Methods of MR Image Intensity Standardization via Generalized Scale, ” SPIE Proceedings, 5747(2): 1143 -1154, 2005. 49) Madabhushi, A. : “ Generalized Scale: Theory, Algorithms, and Applications in Image Analysis, ” Ph. D. Thesis, Department of Bioengineering - University of Pennsylvania, Philadelphia, Pennsylvania, 2004. 50) 56