1. Last updated 2015. 03. 22 Heejune Ahn, SeoulTech
Pixels
Last updated
Heejune Ahn, SeoulTech

2. Outline What is Pixel-level processing? Pixel level Operations
Transform
Histogram
HE (Histogram Equalization)
HA (histogram Matching)
Trhesholding

3. 1. Pixel Processing in pixel level Information of pixel level
Not using information of neighbor pixels
Information of pixel level
visual color/intensity : camera data
IR (infrared) : emission from heat object, night-vision, surveillance
Medical image : density of tissue, CT (computed tomography), MRI (magnetic resonance imaging), 3D (stack of 2Ds)
Ladar/sonar
3-D imaging: 3D scanning, depth map
Scientific image

5. 2. Operations upon pixels
Individual, pixel-by-pixel
Iout (n,m) = f (Iin(n,m))
E.g. Iin(n,m) + IB(n,m) or Iin(n,m) + C
Arithmetic operation
contrast adjustment : imadd(I, const)

6. Blending(mixing): imadd(I1, I2)
Substraction: imsubstract(I1, I2)
Difference : imabsdiff(I1, I2)

7. Multiplication, division : immultiply(I, const), imdivide(I, const)
Saturation issue
Overflow & underflow problem in range [0, 255]
matlab “im” functions handle the saturation

8. Logical operations Thresholding Mostly for binary image
NOT: imcomplement(I)
OR, XOR, AND, NAND, NOR, NXOR
Thresholding
Gray scale to binary image : im2bw(I, thres)
Io = 1 if Iin > T or 0 o.w.
Used for extract fg from bg
variations

9. Thresholding for simple and complex image

10. 4. transform
Mostly for improving the contrast of images (dynamic range)
Logarithmic transform
Increase the contrast in “low” values

11. Exponential transform
Increase contrast in high values

12. Gamma (power)
flexible
r < 1 : log-style
r > 1 : exp-style

13. 4. Histograms Histogram h(x) = # of pixels whose value is x.
pmf (x) = h(x) / # of pixels

14. Thresholding Global Threshold selection
Bi-modal distribution (F3.12, previous slide) : easy to select
Multi-modal/complicated (F3.13) : not easy

15. Otsu’s Method: global optimal algorithm
Threshold that minimizes the intra class standard variance (a clustering algorithm)
level =graythresth(Img) in MATLAB
Minimizing
Intra-class variances
Maximizing
Inter-class variances

16. Adaptive thresholding
Reason: Illumination is not uniform, multiple objects
T(n, m) = f ( W[n,m] )
Threashold value “adapts” neighbors of pixel (n,m), W.
E.g of function
mean, median, floor((max – min/2) +C
still noise f
median
+ margin T
orignal

17. (value – c) (a-b)/(c-d) + a
Contrast Control
To enhance visual perception
Linear contrast stretching
Tips: outlier problem
Use c at 5%, d at 95%
[c, d]
[b= 0, a = 255]
(value – c) (a-b)/(c-d) + a

18. Histogram equalization
Resultant histogram is flat/equal
Nonlinear & dependent image histogram
Global method
proof:
Iin ~ px(x)
Iout ~ py(y)
y = f(x)

19. Example
Not exactly flat (in discrete values)

20. Histogram Matching Generalization of histogram equalization
map output image’s histogram to a specific function.
Iin ~ px(x)
~ Cx(x)
Iout ~ py(y)
~ Cy(y)
y = f(x)
f(x) = C-1z[Cx(x)]

21. Adaptive histogram equalizer
Similar reason as adaptive thresholding
Local histogram generation
Sliding windows method
Tile-based method
Low computation
Blocking effects
outter window
inner
window

22. Pizer’s approach
Weighted histogram
I = histogram for i

23. Contrast limiting MATLAB Not to over-amplificate noise pixels Concept
J = adapthisteq
(I, [param1,val1]...)
Params
ClipLimit : [0:1] (0.01)
NumTiles: (8)
Distribution
Target distist. (uniform)
Rayleigh
exponential
uniform

24. A Real Application Budapest Castle (Hungary)
Taken by Galaxy S5 in the evening
rgb
AHE
gray/hsv
GHE