Image Enhancement - Spatial Domain
Image Enhancement in the Spatial Domain Lecture 1: Image Enhancement Spatial Domain o o o o
Image Intensity/Contrast Transforms Image Histogram Analysis Arithmetic/Logical Image Operations Spatial Filtering (Klifa)
BioE 244 Medical Image Processing and Analysis
T.R. .R. McKnight, Colin Studholme
UCSF 2
1
Spatial Domain Image Operations
Intensity/Contrast Transformations o Point Pixel/Voxel Processing
o Spatial operators act directly on the pixels comprising the image, unlike frequency domain operators which act on the frequency representation of the image. o g(x,y) = T[ f(x,y) ]
1 x 1 neighborhood: s = T(r) Intensity or graylevel transformation, pixel mapping S = T(r) Output Image Value
f(x,y) - input image g(x,y) - output image T - spatial operator
g(x,y)
f(x,y)
Input Image Value
r
Typically implemented with a lookup table S = T(r)
S = T(r)
T
Contrast Stretching
r Dark
Contrast Stretch T.R. .R. McKnight, Colin Studholme
Light
UCSF 3
Threshold
Light
T.R. .R. McKnight, Colin Studholme
Dark
Dark
=
r
Light
Dark
Light
UCSF 4
Thresholding S = T(r)
thr1 = im2bw(byt,.35);
S = T(r) Dark
r S = T(r) Dark
Light
r Dark
thr1 = im2bw(byt,.50);
Light Light
r Dark
Light
S = T(r) J = imadjust(I) maps the values in intensity image I to new values in J such that 1% of data is saturated at low and high intensities of I. This increases the contrast of the output image J. This T.R. .R. McKnight, syntax is equivalent to imadjust(I,stretchlim(I)). Colin Studholme
thr1 = im2bw(byt,.75); T.R. .R. McKnight, Colin Studholme
UCSF 5
UCSF 6 r
CT intensity Range and Intensity Windowing
Gray Level Transforms o Image Negative, Inverse Transform o s=L-1-r
L-1 3L/4
S
L/2 L/4 0 0
L/4
L/2
3L/4
L-1
r imadjust(I, [0 ; 1], [1 ; 0]); or imcomplement(I)
-1000HU to 1000 HU mapped to 128 gray levels
-0HU to 100 HU mapped to 128 grayT.R. levels .R. McKnight, Colin Studholme
T.R. .R. McKnight, Colin Studholme
UCSF 7
UCSF 8
Gray Level Transforms
Gray Level Transforms
o Log Transform o s = c log(1+r) o Compresses dynamic range of images that have large variation in intensities L-1 o Most common display for FFTs
o o
Gamma Correction, Power-Law Transform s=cr = 1 => identity image < 1: maps narrow I range (dark) to a wider dynamic range > 1: maps wide range of I to narrow range o Predominantly used for image capture, display, and printing
3L/4
S
= 0.4 L-1 3L/4
S
=1 L/2 L/4 0 0
L/2
L/4
L/2
r
L/4
3L/4
0 0
L/4
L/2
3L/4
L-1
r =1 T.R. .R. McKnight, Colin Studholme
= 0.4
= 2.5
imadjust(I, [ ], [ ], 0.4);
T.R. .R. McKnight, Colin Studholme
imadjust(I, [ ], [ ], 2.5);
UCSF 9
Histogram Analysis
UCSF 10
Histogram Equalization
o The histogram (h) of an image with L graylevels is defined as h(rk) = nk, where rk is the k-th gray level and nk is the number of pixels with intensity rk
o Image Transformations (T): s = T(r)
o Histogram normalization: p(rk ) = nk /ntotal, for k = 0, 1, 2, , L-1
o Histogram equalization:
o Useful for image enhancement, obtaining image statistics, segmentation, and compression
o Spreads the histogram of the input image over a larger range of intensities
T.R. .R. McKnight, Colin Studholme
UCSF 11
k
s k = j=0
nj n
L-1
= 2.5
0 r 1 (normalized intensities) for k = 0, 1, 2, , L-1
Histogram transformation function (T)
T.R. .R. McKnight, Colin Studholme
UCSF 12
Histogram Matching o Histogram matching, Histogram specification o Histogram mapping of Image 1:
o Histogram of Image 1:
k
s k = j=0
nj
for k = 0,1,2, ,L-1
n for k = 0,1,2, ,L-1
k
G z k =i=0 p z z i
o Histogram matching to Image 2:
for k = 0,1,2, ,L-1
z k =G1 s k
T.R. .R. McKnight, Colin Studholme
UCSF 14
Image subtraction in medical Imaging: DSA: digital Subtraction Angiography
Arithmetic & Logic Image Operations o Pixel-by-pixel mathematical operations o Arithmetic (eg addition, subtraction, division, etc) o Logic (eg AND, OR, NOT) => used in masking operations
T.R. .R. McKnight, Colin Studholme
T.R. .R. McKnight, Colin Studholme
UCSF 15
UCSF 16
Subtraction SPECT imaging (after registration)
Image Subtraction Problem: We have used physiologic MRI data to simulate (predict) the distribution of gadolinium-labeled liposomes infused into pig brain by convection-enhanced delivery (CED). How do we evaluate the accuracy of our simulation?
Actual CED
Difference (Actual - Sim)
Simulated CED
-
=
T.R. .R. McKnight, Colin Studholme
T.R. .R. McKnight, Colin Studholme
UCSF 17
UCSF 18
Image Subtraction: Masking Actual CED
Image Logic: Masking
Simulated CED Quantify Volume of Difference or Standard Error
Simulated CED mask
Actual CED
Actual CED mask
-
&
Difference |RealMask- SimMask|
Simulated CED mask
= T.R. .R. McKnight, Colin Studholme
T.R. .R. McKnight, Colin Studholme
UCSF 19
UCSF 20
Spatial Filters o Kernal Small 2D array eg 3x3 neighborhood filter, kernal, template, window
y
y
y
y
y
. . . x
x y
x y
x
x
y
y
y
. . . x
x
=
x
x
y
x
x
T.R. .R. McKnight, Colin Studholme
UCSF 21
Image Intensity/Contrast Transforms Image Histogram Analysis Arithmetic/Logical Image Operations Spatial Filtering (Klifa)
BioE 244 Medical Image Processing and Analysis
T.R. .R. McKnight, Colin Studholme
UCSF 2
1
Spatial Domain Image Operations
Intensity/Contrast Transformations o Point Pixel/Voxel Processing
o Spatial operators act directly on the pixels comprising the image, unlike frequency domain operators which act on the frequency representation of the image. o g(x,y) = T[ f(x,y) ]
1 x 1 neighborhood: s = T(r) Intensity or graylevel transformation, pixel mapping S = T(r) Output Image Value
f(x,y) - input image g(x,y) - output image T - spatial operator
g(x,y)
f(x,y)
Input Image Value
r
Typically implemented with a lookup table S = T(r)
S = T(r)
T
Contrast Stretching
r Dark
Contrast Stretch T.R. .R. McKnight, Colin Studholme
Light
UCSF 3
Threshold
Light
T.R. .R. McKnight, Colin Studholme
Dark
Dark
=
r
Light
Dark
Light
UCSF 4
Thresholding S = T(r)
thr1 = im2bw(byt,.35);
S = T(r) Dark
r S = T(r) Dark
Light
r Dark
thr1 = im2bw(byt,.50);
Light Light
r Dark
Light
S = T(r) J = imadjust(I) maps the values in intensity image I to new values in J such that 1% of data is saturated at low and high intensities of I. This increases the contrast of the output image J. This T.R. .R. McKnight, syntax is equivalent to imadjust(I,stretchlim(I)). Colin Studholme
thr1 = im2bw(byt,.75); T.R. .R. McKnight, Colin Studholme
UCSF 5
UCSF 6 r
CT intensity Range and Intensity Windowing
Gray Level Transforms o Image Negative, Inverse Transform o s=L-1-r
L-1 3L/4
S
L/2 L/4 0 0
L/4
L/2
3L/4
L-1
r imadjust(I, [0 ; 1], [1 ; 0]); or imcomplement(I)
-1000HU to 1000 HU mapped to 128 gray levels
-0HU to 100 HU mapped to 128 grayT.R. levels .R. McKnight, Colin Studholme
T.R. .R. McKnight, Colin Studholme
UCSF 7
UCSF 8
Gray Level Transforms
Gray Level Transforms
o Log Transform o s = c log(1+r) o Compresses dynamic range of images that have large variation in intensities L-1 o Most common display for FFTs
o o
Gamma Correction, Power-Law Transform s=cr = 1 => identity image < 1: maps narrow I range (dark) to a wider dynamic range > 1: maps wide range of I to narrow range o Predominantly used for image capture, display, and printing
3L/4
S
= 0.4 L-1 3L/4
S
=1 L/2 L/4 0 0
L/2
L/4
L/2
r
L/4
3L/4
0 0
L/4
L/2
3L/4
L-1
r =1 T.R. .R. McKnight, Colin Studholme
= 0.4
= 2.5
imadjust(I, [ ], [ ], 0.4);
T.R. .R. McKnight, Colin Studholme
imadjust(I, [ ], [ ], 2.5);
UCSF 9
Histogram Analysis
UCSF 10
Histogram Equalization
o The histogram (h) of an image with L graylevels is defined as h(rk) = nk, where rk is the k-th gray level and nk is the number of pixels with intensity rk
o Image Transformations (T): s = T(r)
o Histogram normalization: p(rk ) = nk /ntotal, for k = 0, 1, 2, , L-1
o Histogram equalization:
o Useful for image enhancement, obtaining image statistics, segmentation, and compression
o Spreads the histogram of the input image over a larger range of intensities
T.R. .R. McKnight, Colin Studholme
UCSF 11
k
s k = j=0
nj n
L-1
= 2.5
0 r 1 (normalized intensities) for k = 0, 1, 2, , L-1
Histogram transformation function (T)
T.R. .R. McKnight, Colin Studholme
UCSF 12
Histogram Matching o Histogram matching, Histogram specification o Histogram mapping of Image 1:
o Histogram of Image 1:
k
s k = j=0
nj
for k = 0,1,2, ,L-1
n for k = 0,1,2, ,L-1
k
G z k =i=0 p z z i
o Histogram matching to Image 2:
for k = 0,1,2, ,L-1
z k =G1 s k
T.R. .R. McKnight, Colin Studholme
UCSF 14
Image subtraction in medical Imaging: DSA: digital Subtraction Angiography
Arithmetic & Logic Image Operations o Pixel-by-pixel mathematical operations o Arithmetic (eg addition, subtraction, division, etc) o Logic (eg AND, OR, NOT) => used in masking operations
T.R. .R. McKnight, Colin Studholme
T.R. .R. McKnight, Colin Studholme
UCSF 15
UCSF 16
Subtraction SPECT imaging (after registration)
Image Subtraction Problem: We have used physiologic MRI data to simulate (predict) the distribution of gadolinium-labeled liposomes infused into pig brain by convection-enhanced delivery (CED). How do we evaluate the accuracy of our simulation?
Actual CED
Difference (Actual - Sim)
Simulated CED
-
=
T.R. .R. McKnight, Colin Studholme
T.R. .R. McKnight, Colin Studholme
UCSF 17
UCSF 18
Image Subtraction: Masking Actual CED
Image Logic: Masking
Simulated CED Quantify Volume of Difference or Standard Error
Simulated CED mask
Actual CED
Actual CED mask
-
&
Difference |RealMask- SimMask|
Simulated CED mask
= T.R. .R. McKnight, Colin Studholme
T.R. .R. McKnight, Colin Studholme
UCSF 19
UCSF 20
Spatial Filters o Kernal Small 2D array eg 3x3 neighborhood filter, kernal, template, window
y
y
y
y
y
. . . x
x y
x y
x
x
y
y
y
. . . x
x
=
x
x
y
x
x
T.R. .R. McKnight, Colin Studholme
UCSF 21
