Transcript Scale - Medical Image Processing Group

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
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 (2D, 3D, 4D,…)
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
abg : body coordinate
system
a
abc: scanner coordinate
system
x
b
w
u
xyz: scene coordinate
system
v
uvw: structure coordinate
system
a
t
r
rst: display coordinate
system
voxel
z
c
s
y
pixel
b
structure
scene domain
10
CAVA Operations
Img processing:
Visualization
Manipulation
Analysis
Volume of interest
Filtering
Interpolation
Registration
Segmentation
11
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.
12
Global Scale
Not clear how to combine results from multiple scales.
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
S  (C , f )  S F   C , f F 
Gaussian: fF(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:
fF(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.
17
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.
V  f
V  intensity flow (vector field)
  conductance
f  gradient of f (vector field)
18
Suppressive Filtering - Diffusion
Conductance t(c, d) controlling flow Vt from voxel c
to voxel d at the t-th iteration is:
2

 t f  c, d  

 t  c, d   exp  
2
 2  s  c, d   

 

Vt  c, d    t  c, d  f  c, d 
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:
 f c
for t  0,
  
ft  c   
 f  c   A  V  c, d  • D  c, d  , t  0
t -1
 t -1
dN c
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
original
ROI
regular
diffusion
regular diffusion
b-diffusion
b-diffusion
t-diffusion
22
FOC curve (200 iterations)
gBD
# iterations
bD
NCD
23
Enhancive Filtering
S  C, f   SF  C, f F 
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 LM1,…., LMn on
each of a set of images.
(2) Choose a standard scale, say [0, 4000].
(3) Map LM1,…., LMn from each input image on to
standard scale.
s
LM
(4) Find average location
i on standard scale for
each landmark.
27
Enhancive Filtering: Intensity Standardization
image
scale
standard
scale
LM 1


LM 1s
LM 2

  

LM 2s
LM n


  
LM ns
28
Enhancive Filtering: Intensity Standardization
Transformation:
std scale
(1) Identify landmarks
in image scale.
(2) Map them to standard
scale and determine
LM 2s
transformation.
(3) Map all intensities in
image scale as per this
transformation to
standard scale.
LM 1s
LM 1
LM 2
input image scale
29
Enhancive Filtering: Intensity Standardization
Choosing landmarks on intensity scale:
(1) On image histogram – median, mode, quartiles,
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
32
Enhancive Filtering: Intensity Standardization
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
regions across patients.
WM
before
after
FSE PD
14.61
2.03
GM
FSE T2
14.83
2.59
FSE PD
14.59
1.07
FSE T2
14.33
2.60
CSF
FSE PD FSE T2
15.18
15.78
3.18
5.12
Scanner dependent inter-patient variations are
considerably reduced after standardization.
37
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
N3 (Sled et al.)
SBC
38
Enhancive Filtering: Intensity Non Uniformity
Correction
Goal: To develop a general method for correcting the
variations that fulfills:
(R1) no need for user help per scene
(R2) no need for accurate prior segmentation
(R3) 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 CB1, CB2, ..., 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
b j  x
bi  x 
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   b1  c   b 2  c   .
2
cC
2. Combine the two inhomogeneity maps b1 and b2 to obtain a new
discrete inhomogeneity map bd(c): C  [0, ) such that for any
cC,
  c, O2 
  c, O1 
bd c 
b1  c  
b 2  c 
  c, O1     c, O2 
  c, O1     c, O2 
3. Determine a 2nd degree polynomial b that constitutes a LSE fit to bd .
The above steps merge O1 and O2 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
N3 (Sled et al.)
WM
SBC
WM and GM modes are improved with correction.
45
Non Uniformity Correction – SBC Method
WM GM
Original
N3 (Sled et al.)
SBC
WM and GM modes are improved with correction.
46
Non Uniformity Correction – SBC Method
WM GM
Original
N3 (Sled et al.)
SBC
WM and GM modes are improved with correction.
47
Non Uniformity Correction – SBC Method
Set
Normal
Modality
T1
T2
PD
T1
MS
T2
PD
Inhomo.
20%
40%
20%
40%
20%
40%
20%
40%
20%
40%
20%
40%
%CV (GM)
Original N3 SBC
11.0
13.5
18.4
20.3
6.3
9.7
11.2
13.7
10.9
13.7
5.8
9.4
9.9
10.0
18.0
20.0
4.6
4.6
10.1
10.2
10.0
10.1
3.9
4.9
9.9
9.9
17.9
17.9
4.5
4.5
10.1
10.1
9.8
9.8
3.8
3.9
%CV (WM)
Original N3 SBC
6.7
9.2
12.0
13.3
5.5
7.5
6.9
9.3
8.7
10.6
5.3
7.4
5.1
5.2
11.8
13.0
4.7
4.6
5.3
5.3
8.3
8.2
4.4
4.3
5.1
5.2
11.7
11.8
4.7
4.6
5.3
5.4
8.1
8.2
4.3
4.3
48
Non Uniformity Correction – SBC Method
Modality
T2
PD
% CV (GM)
% CV (WM)
Original
N3
Original
N3
SBC
SBC
16.7(1.61) 14.9(1.18) 14.7(1.23) 12.9(1.12) 11.5(1.07) 11.2(0.98)
7.1(0.32 5.9(0.20) 5.6(0.19) 7.8(0.72) 6.6(0.62) 6.2(0.51)
The % cv values for the SBC method are smaller than that
for the N3 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 or Std Cor or
Cor Std Cor Std ... or Std Cor Std Cor…
• Does correction affect standardness or vice versa?
• How does noise filtering affect correction/
standardization and vice versa?
Cor Std Flt or Std Flt Cor or ….
Non Uniformity Correction – Interplay Between
Standardization and Correction
MTR
g-scale corrected
MTR scenes
gB-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
image analysis.
(3) Local (b-, t-, g-)scale based strategies are effective
in overcoming all these artifacts.
(4) Correction can introduce non standardness and
enhance noise.
(5) The best order of operation: Cor, Std, Fltr.
52
Key References
Background, Classification of Methods
1)
Udupa, J.K.: “Three-Dimensional Image Processing, Analysis, and Visualization: Methods and Techniques,”
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, J.K., G.T. Herman, (Editors): 3D Imaging In Medicine, 2nd Edition, CRC Press, Inc., Boca Raton,
Florida, 2000.
Scale
3)
Koenderink, J.J., A.J. van Doorn: “Representation of Local Geometry in the Visual System,” Biological
Cybernetics, 55:367-375, 1987.
4)
Wang, J.Y.-P., S.L. Lee: “Scale-Space Derived from B-Splines,” IEEE Transactions on Pattern Analysis and
Machine Intelligence, 20(10):1040-1055, 1998.
5)
Burt, P.: Fast Filter Transform for Image Processing,” Computer Graphics and Image Processing, 16:20-51,
1981.
6)
Burt, P. and E.H. Adelson: “The Laplacian Pyramid as a Compact Image Code,” IEEE Transactions on
Communications, 31(4):532-540, 1983.
7)
Witkin, A.P.: “Scale-Space Filtering,” in Proceedings of the 8th International Joint Conference on Artificial
Intelligence , pp. 1019-1022, 1983.
8)
Lindeberg, J.T.: “Automatic Scale Selection as Pre-Processing Stage for Interpreting the Visual World,”
Proceedings of Fundamental Structural Properties in Image and Pattern Analysis, 130:9-23, 1999.
9)
Olson, C.F.: “Adaptive-Scale Filtering and Feature Detection Using Range Data,” IEEE Transactions on
Pattern Analysis and Machine Intelligence, 22(9):983-991, 2000.
10)
Plantier, J., S. Lelandais and L. Boutte: “A Shape from Texture Method Based on Local Scales Extraction:
Precision and Results,” International Conference on Image Process, 2:261-264, 2001.
11)
Lindeberg, T.: Scale-Space Theory in Computer Vision, Kluwer Academic Publishers: Delhi, 1993.
12)
Lowe, D.G.: “Object Recognition from Local Scale-Invariant Features,” The Proceedings of the Seventh IEEE
International Conference on Computer Vision, 2(2):1150-1157.
13)
Elder, J.H. and S.W. Zucker: “Local Scale Control for Edge Detection and Blur Estimation,” IEEE
Transactions on Pattern Analysis and Machine Intelligence, 20(7):699-716, 1998.
14)
Saha, P.K., J.K. Udupa and D. Odhner: “Scale-Based Fuzzy Connected Image Segmentation: Theory,
Algorithms, and Validation,” Computer Vision and Image Understanding, 77(2):145-174, 2000.
15)
Saha, P.K.: “Novel Theory and Methods for Tensor Scale: A Local Morphometric Parameter,” Proceedings of
SPIE: Medical Imaging, 5032:743-753, 2003.
16)
Pizer, S.M., Eberly, D. and Fritsch, D.S.: “Zoom-Invariant Vision of Figural Shape: The Mathematics of Core,”
Computer Vision and Image Understanding, 69:55-71, 1998.
17)
Tabb, M. and N. Ahuja: “Multiscale Image Segmentation by Integrated Edge and Region Detection,” IEEE
Transactions on Image Processing, 6(5):642-655, 1997.
18)
Madabhushi, A., J.K. Udupa, and A. Souza: “Generalized Scale: Theory, Algorithms, and Application to Image
Inhomogeneity Correction,” Computer Vision and Image Understanding, 101(2):100-121, 2006.
Filtering
19)
Wong, Y.I.: “Nonlinear Scale-Space Filtering and Multi-Resolution System,” IEEE Transactions on Image
Processing, 4(6):774-787, 1995.
20)
Zuerndorfer, B. and G.H. Wakefield: “Extensions of Scale-Space Filtering to Machine-Sensing Systems,” IEEE
Transactions on Pattern Analysis and Machine Intelligence, 12(9):868-882, 1990.
53
21)
Shi, J.Y. and H.T. Tsui: “Scale Space Filtering by Fejér Kernel,” International Symposium on Speech Image
Process and Neural Networks, 2:638-641, 1994.
22)
Saha, P.K. and J.K. Udupa: “Scale-Based Image Filtering Preserving Boundary Sharpness and Fine Structures,”
IEEE Transactions on Medical Imaging, 20(11):1140-1155, 2001.
23)
Perona, P. and J. Malik: “Scale-Space and Edge Detection Using Anisotropic Diffusion,” IEEE Transactions on
Pattern Analysis and Machine Intelligence, 12(7):629-639, 1990.
24)
Whitaker, R.T. and S.M. Pizer: “A Multi-Scale Approach to Nonuniform Diffusion,” Computer Vision Graphic
and Image Processing: Image Understanding, 57(1):99-110, 1993.
25)
Weikert, J., et al.: “Theoretical Foundations of Anisotropic Diffusion in Image Processing,” Theoretical
Foundations of Computer Vision, Computing, Supplement 11:221-236, 1996.
26)
Parker, G.J.M. and J.A. Schnabel: “Enhancement of Anisotropic Diffusive Filtering of MR Images Using
Approximate Entropy,” in Proceedings of International Society for Magnetic Resonance in Medicine, 7:175,
1999.
27)
Gerig, G., O. Kubler, R. Kikinis and F.A. Jolesz: “Nonlinear Anisotropic Filtering of MRI Data,” IEEE
Transaction on Medical Imaging, 11(2):221-232, 1992.
28)
Souza, A., J.K. Udupa and A. Madabhushi: “Generalized Scale-Based Image Filtering,” SPIE Proceedings,
5747(2):732-742, 2005.
Inhomogeneity Correction
29)
Axel, L., J. Costantini and J. Listerud: “Intensity Corrections in Surface-Coil MR Imaging,” American Journal
of Roentgenology, 148:418-420, 1987.
30)
Haselgrove, J. and M. Prammer: “An Algorithm for Compensation of Surface-Coil Images for Sensitivity of the
Surface Coil,” Magnetic Resonance Imaging, 4:469-472, 1986.
31)
Meyer, C.R., P.H. Bland and J. Pipe: “Retrospective Correction of Intensity Inhomogeneities in MRI,” IEEE
Transactions on Medical Imaging, 14:36-41, 1995.
54
32)
Dawant, B.M., A.P. Zjidenbos and R.A. Margolin: “Correction of Intensity Variations in MR Images for
Computer-Aided Tissue Classification,” IEEE Transactions on Medical Imaging, 12:770-781, 1993.
33)
Tincher, M., C.R. Meyer, G. Gupta and D.M. Williams: “Polynomial Modelling and Reduction of RF Body
Coil Spatial Inhomogeneity in MRI,” IEEE Transactions on Medical Imaging, 12:361-365, 1993.
34)
Lai, S. and M. Fang: “A New Variational Shape-from-Orientation Approach to Correcting Intensity
Inhomogeneity in MR Images,” Medical Image Analysis, 3(4):409-424. 1999.
35)
Wells, W.M., E.L. Grimson, R. Kikinis and F.A. Jolesz: “Adaptive Segmentation of MRI Data,” IEEE
Transactions on Medical Imaging, 15:429-442, 1996.
36)
Guillemaud, R. and M. Brady: “Estimating the Bias Field of MR Images,” IEEE Transactions on Medical
Imaging, 16:238-251, 1997.
37)
Van Leemput, K., F. Maes, D. Vandermeulen and P. Suetens: “Automated Model-Based Bias Field Correction
of MR Images of the Brain,” IEEE Transactions on Medical Imaging, 18:885-896, 1999.
38)
Sled, J.G., A. P. Zjidenbos and A.C. Evans: “A Nonparametric Method for Automatic Correction of Intensity
Nonuniformity in MRI Data,” IEEE Transactions on Medical Imaging, 17:87-97, 1998.
39)
Styner, M., C. Brechbuhler, G. Szekely and G. Gerig: “Parametric Estimate of Intensity Inhomogeneities
Applied to MRI,” IEEE Transactions on Medical Imaging, 19:153-165, 2000.
40)
Likar, B., M.A. Viergever and F. Pernus: “Retrospective Correction of MR Intensity Inhomogeneity by
Information Minimization,” IEEE Transaction on Medical Imaging, 20:1398-1410, 2001.
41)
Madabhushi, A. and J.K. Udupa: “The Interplay Between Intensity Standardization and Inhomogeneity
Correction in MR Image Processing,” IEEE Transactions on Medical Imaging, 24(5):561-576, 2005.
42)
Zhuge, Y., J. K. Udupa, J. Liu and P.K. Saha: “An Intensity Standardization-Based Method for Image
Inhomogeneity Correction in MRI,” in Proceedings of SPIE: Medical Imaging, 6143:658-668, 2006.
43)
Madabhushi, A., J.K. Udupa and A. Souza: “Generalized Scale: Theory, Algorithms, and Application to Image
Inhomogeneity Correction,” SPIE Proceedings, 5370(2):765-776, 2004.
55
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.
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.
56