image enhancement in the spatial domain
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Lecture 1: Image Enhancement -
Spatial Domain
BioE 244
Medical Image Processing and Analysis
T.R. McKnight, .R. McKnight,
Colin Studholme Colin Studholme
UCSF UCSF 22
Image Enhancement in the Spatial Domain
o Image Intensity/Contrast Transforms
o Image Histogram Analysis
o Arithmetic/Logical Image Operations
o Spatial Filtering (Klifa)
T.R. McKnight, .R. McKnight,
Colin Studholme Colin Studholme
UCSF UCSF 33
Spatial Domain Image Operations
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) ]
� f(x,y) - input image
� g(x,y) - output image
� T - spatial operator
T=
g(x,y) f(x,y)
T.R. McKnight, .R. McKnight,
Colin Studholme Colin Studholme
UCSF UCSF 44
Intensity/Contrast Transformations
o Point Pixel/Voxel Processing
� 1 x 1 neighborhood: s = T(r)
� �Intensity or graylevel transformation�, �pixel mapping�
� Typically implemented with a lookup table
r
S = T(r)
Dark Light
Dark
Lig
ht
r
S = T(r)
Dark Light
Dark
Lig
ht
Contrast StretchThreshold
r
S = T(r)
Input Image Value
Outp
ut Im
age V
alu
e
T.R. McKnight, .R. McKnight,
Colin Studholme Colin Studholme
UCSF UCSF 55
Contrast Stretching
r
S = T(r)
Dark Light
Dark
Lig
ht
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
syntax is equivalent to imadjust(I,stretchlim(I)).
T.R. McKnight, .R. McKnight,
Colin Studholme Colin Studholme
UCSF UCSF 66
Thresholding
r
S = T(r)
r
S = T(r)
Dark Light
Dark
Lig
ht
r
S = T(r)
thr1 = im2bw(byt,.35);
thr1 = im2bw(byt,.50);
thr1 = im2bw(byt,.75);
T.R. McKnight, .R. McKnight,
Colin Studholme Colin Studholme
UCSF UCSF 77
CT intensity Range and Intensity
Windowing
-1000HU to 1000 HU mapped to 128 gray levels
-0HU to 100 HU mapped to 128 gray levels
T.R. McKnight, .R. McKnight,
Colin Studholme Colin Studholme
UCSF UCSF 88
Gray Level Transforms
L - 1
L - 1
3L/4
L/4
L/2
0
3L/4L/4 L/20
o Image Negative, Inverse Transform
o s = L - 1 - r
S
r
imadjust(I, [0 ; 1], [1 ; 0]);
or
imcomplement(I)
T.R. McKnight, .R. McKnight,
Colin Studholme Colin Studholme
UCSF UCSF 99
Gray Level Transforms
o Log Transform
o s = c log(1+r)
o Compresses dynamic range of images that have large
variation in intensities
o Most common display for FFTs L - 1
L - 1
3L/4
L/4
L/2
0
3L/4L/4 L/20
S
r
T.R. McKnight, .R. McKnight,
Colin Studholme Colin Studholme
UCSF UCSF 1010
Gray Level Transforms
o Gamma Correction, Power-Law Transform
o s = c r �
� � = 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
L - 1
L - 1
3L/4
L/4
L/2
0
3L/4L/4 L/20
S
r
� = 0.4
� = 1
� = 2.5
� = 0.4 � = 2.5� = 1
imadjust(I, [ ], [ ], 0.4); imadjust(I, [ ], [ ], 2.5);
T.R. McKnight, .R. McKnight,
Colin Studholme Colin Studholme
UCSF UCSF 1111
Histogram Analysis
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 Histogram normalization: p(rk ) = nk /ntotal, for k = 0, 1, 2, �, L-1
o Useful for image enhancement, obtaining image statistics, segmentation, and
compression
T.R. McKnight, .R. McKnight,
Colin Studholme Colin Studholme
UCSF UCSF 1212
Histogram Equalization
o Image Transformations (T): s = T(r) 0 � r 1 � (normalized intensities)
o Histogram equalization: for k = 0, 1, 2, �, L-1
o Spreads the histogram of the input image over a larger range of intensities
sk=� j=0
k n j
n
Histogram
transformation function
(T)
T.R. McKnight, .R. McKnight,
Colin Studholme Colin Studholme
UCSF UCSF 1414
Histogram Matching
o Histogram matching, Histogram specification
o Histogram mapping of Image 1: for k = 0,1,2,�,L-1
o Histogram of Image 1: for k = 0,1,2,�,L-1
o Histogram matching to Image 2: for k = 0,1,2,�,L-1
sk=� j=0
k n j
n
z k=G�1 �s k �
G � z k �=�i=0
k
pz � zi �
T.R. McKnight, .R. McKnight,
Colin Studholme Colin Studholme
UCSF UCSF 1515
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. McKnight, .R. McKnight,
Colin Studholme Colin Studholme
UCSF UCSF 1616
Image subtraction in medical Imaging:
DSA: digital Subtraction Angiography
T.R. McKnight, .R. McKnight,
Colin Studholme Colin Studholme
UCSF UCSF 1717
Subtraction SPECT imaging (after
registration)
T.R. McKnight, .R. McKnight,
Colin Studholme Colin Studholme
UCSF UCSF 1818
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?
Simulated CEDActual CED
Difference (Actual - Sim)
- =
T.R. McKnight, .R. McKnight,
Colin Studholme Colin Studholme
UCSF UCSF 1919
Image Subtraction: Masking
- =
Difference |RealMask- SimMask|
Actual CED
Actual CED mask Simulated CED mask
Simulated CED
Quantify Volume of Difference or Standard Error
T.R. McKnight, .R. McKnight,
Colin Studholme Colin Studholme
UCSF UCSF 2020
Image Logic: Masking
Actual CED
& =
Simulated CED mask
T.R. McKnight, .R. McKnight,
Colin Studholme Colin Studholme
UCSF UCSF 2121
Spatial Filters
o Kernal
� Small 2D array eg 3x3 neighborhood
� �filter�, �kernal�, �template�, �window�
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