Pixels

Last updated 2015. 03. 22

Heejune Ahn, SeoulTech

Outline What is Pixel-level processing? Pixel level Operations Transform

Histogram HE (Histogram Equalization) HA (histogram Matching)

Trhesholding

1. Pixel Processing in 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

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)

Blending(mixing): imadd(I1, I2)

Substraction: imsubstract(I1, I2) Difference : imabsdiff(I1, I2)

Multiplication, division : immultiply(I, const), imdivide(I, const)

Saturation issue Overflow & underflow problem in range [0, 255] matlab “im” functions handle the saturation

Logical operations 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

Thresholding for simple and complex image

4. transform Mostly for improving the contrast of images

(dynamic range) Logarithmic transform

Increase the contrast in “low” values

Exponential transform Increase contrast in high values

Gamma (power)

flexible r < 1 : log-style r > 1 : exp-style

4. Histograms Histogram

h(x) = # of pixels whose value is x. pmf (x) = h(x) / # of pixels

Thresholding Global Threshold selection

Bi-modal distribution (F3.12, previous slide) : easy to select

Multi-modal/complicated (F3.13) : not easy

Otsu’s Method: global optimal algorithm Threshold that minimizes the intra class standard

variance (a clustering algorithm)

level =graythresth(Img) in MATLAB

Intra-class variances

Inter-class variances

Minimizing

Maximizing

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

orignal

f

median

T

+ margin

still noise

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

Histogram equalization Equalization

Resultant histogram is flat/equal Nonlinear & dependent image histogram

Global method proof: Iout ~ py(y)Iin ~ px(x)

y = f(x)

Example Not exactly flat (in discrete values)

Histogram Matching Generalization of histogram equalization map output image’s histogram to a specific

function.

Iout ~ py(y) ~ Cy(y)

Iin ~ px(x) ~ Cx(x) y = f(x)

f(x) = C-1z[Cx(x)]

Adaptive histogram equalizer Similar reason as adaptive thresholding Local histogram generation

Sliding windows method Tile-based method

Low computation Blocking effects

inner window

outter window

Pizer’s approach Weighted histogram

Contrast limiting Not to over-amplificate noise pixels Concept

MATLAB J = adapthisteq

(I, [param1,val1]...) Params

ClipLimit : [0:1] (0.01) NumTiles: (8) Distribution

Target distist. (uniform)

Rayleigh

exponential uniform

A Real Application Budapest Castle (Hungary)

Taken by Galaxy S5 in the evening

gray/hsv

GHE

AHE

rgb