Title: Image%20Editing%20by%20Point%20Operatons
1Image Editing by Point Operatons
- Fall 2001
- Martin Jagersand
23D reality -gt captured 2D image
x
z
y
y
x
z
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x
3Pinhole cameras
4Examples of image sources
- Analog cameras
- Digital cameras
- Optic Scanners (linear image sensors)
- Laser scanners (2 and 3D images)
- Radar
- X-ray
- NMRI
5Image display
- VDU
- Raster
- Vector
- LCD
- Printer
- Photo process
- Plotter (x-y table type)
6THE ORGANIZATION OF A 2D IMAGE
Pixel Binary 1 bit Grey 1 byte Color 3 bytes
7Mathematical / Computationalimage models
- Continuous mathematical
- I f(x,y)
- Discrete (in computer) adressable 2D array
- I matrix(i,j)
- Discrete (in file) e.g. ascii or binary sequence
- 023 233 132 232
- 125 134 134 212
8Image representation for display
(R,G,B) (R,G,B) (R,G,B) (R,G,B)
9Image representation for display
(I) (I) (I) (I)
(R,G,B) (R,G,B) (R,G,B)
10Point operations on images
- Point operations perform some operation on one
pixel at a time (independent on the neighboring
pixels) - For each (x,y)
- I2(x,y) f(I(x,y))
- Contrast to image transforms (later in course)
perform operations on the whole image
11Common point operations
- Brightness adjustment
- Contrast adjustment
- Dynamic range compression
- Gray level slicing
- Histogram equalization
- Image (sequence) averaging
- Background subtraction
12Linear brightness and contrast adjustment
- As seen on TV!
- Brightness
- For each (x,y)
- I2(x,y) I(x,y)const
- Contrast
- I2(x,y) constI(x,y)
13Contrast adjustment example
14Special purpose contrast adjustments
- Dynamic range limitation
- I2(x,y) sqrt(I(x,y))
- I2(x,y) log(I(x,y))
- Inverted image
- I2(x,y) 1-I(x,y)
- Gray level slicing
15Image histogram
- For a discrete image quantized e.g. on 0..255
- Let n total number of pixels
- Let nk number of pixels with value k
- Histogram pk nk / n
- Analogy Consider the image a sample of a random
variable. Then pk is probability of a pixel
having value k
16Histogram examples
narrow contrast Wide contrast
17Histogram equalization
- Let p(k) image histogram on k 0..1
- Goal find a contrast stretching transform T(k)
so that I2 T(I) and p2 1(uniform)
p2
p(k)
18Histogram eq.
19Discrete histogram equalization
- Compute discrete histogram summing bins
- Compute cumulative sum
- Map image intensities through cumulative
histogram - Question is discrete histogram uniform?
20Background subtraction
- Subtract out static background to capture changes
-
What process actually happened?
21Image averaging
- Average several images of the same scene
- Is(x,y) sum(I(x,y))/n
- Can remove noise