Point Operations Histogram Processing, Lecture notes of Digital Image Processing

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BBM 413

Fundamentals of

Image Processing

Erkut Erdem Dept. of Computer Engineering Hacettepe University

Point Operations

Histogram Processing

Today’s topics

• Point operations
• Histogram processing

Digital images

• Sample the 2D space on a regular grid
• Quantize each sample (round to nearest integer)
• Image thus represented as a matrix of integer values. Slide credit: K. Grauman, S. Seitz 2D 1D

Image Transformations

• g (x,y)= T [ f (x,y)] g (x,y): output image f (x,y): input image M: transformation function
  1. Point operations: operations on single pixels
  2. Spatial filtering: operations considering pixel neighborhoods
  3. Global methods: operations considering whole image

Image Transformations

• g (x,y)= M [ f (x,y)] g (x,y): output image f (x,y): input image M: transformation function
  1. Point operations: operations on single pixels
  2. Spatial filtering: operations considering pixel neighborhoods
  3. Global methods: operations considering whole image g ( x , y ) = M ({ f ( i , j ) |( i , j )Î N ( x , y )})

Point operations

• Smallest possible neighborhood is of size 1x
• Process each point independently of the others
• Output image g depends only on the value of f at a single point (x,y)
• Map each pixel’s value to a new value
• Transformation function T remaps the sample’s value: s = T(r) where
• r is the value at the point in question
• s is the new value in the processed result
• T is a intensity transformation function

Sample intensity transformation

functions

• Image negatives
• Log transformations
  • Compresses the dynamic range of images
• Power-law

transformations

• Gamma correction

Sample intensity transformation

functions

• Image negatives
• Log transformations
  • Compresses the dynamic range of images
• Power-law

transformations

• Gamma correction

Point Processing Examples

produces an image of higher contrast than the original by darkening the intensity levels below k and brightening intensities above k produces a binary (two-intensity level) image

Point Processing Examples

produces an image of higher contrast than the original by darkening the intensity levels below k and brightening intensities above k produces a binary (two-intensity level) image

Changing the image mean

Slide credit: Y. Hel-Or

Image Mean

v M(v) 255 255 M ( v ) = 255 - v Slide credit: Y. Hel-Or

Image Negative

Point Operations:

Contrast stretching and Thresholding

• Contrast stretching: produces an image of higher contrast than the original
• Thresholding: produces a binary (two-intensity level) image

Point Operations:

Contrast stretching and Thresholding

• Contrast stretching: produces an image of higher contrast than the original
• Thresholding: produces a binary (two-intensity level) image

Point Operations

• How we can process the image so that it has a better visual quality?
• Answer is contrast stretching!

Point Operations

• Let us devise an appropriate point operation.
• Shift all values so that the observable pixel range starts at 0.