Lecture Three
Chapters Two and threePhoto slides from Digital Image Processing, Gonzalez and Woods, Copyright 2002
Functional Represenation of Images
• Two-D function f(x,y), (x,y) pixel position. Postive and bounded
• Written as f(x,y)=i(x,y)r(x,y), i(x,y) illumination from light source, r(x,y) reflectance (bounded between 0 and 1) based on material properties. E.g r(x,y)=0.01 for black velvet, r(x,y) = 0.93 for snow.
• Intensity of monochrome image f(x,y) is synonymous with grey levels. By convention grey level are from 0 to L-1.
Spatial and Gray Level Resolution
• Spatial resolution is the smallest level of detail discernable in an image. Number of line pairs per millimeter, say 100 line pairs per millimeter.
• Gray-level resolution is the smallest discernable change in gray level. Very subjective.
Adjacency and Connectivity
• Adjacency- Two pixels p and q are adjacent if q is in N(p) where N(p) is the neighborhood of p and they have closely related pixel values. Three common definitions of neighborhood are
(1) 4-adjacency. If p=(x,y), values are similar, but q is either (x-1,y),(x+1,y),(x,y-1),(x,y+1)(2) 8-adjacency. It is possible for q to be one of the
diagonal points (x-1,y-1),(x-1,y+1),(x+1,y-1),(x+1,x+1).(3) m-adjacency. Either q is 4-adjacent to p, or q is a
diagonal point and the intersection of the four neighborhood of p and that of q have no similar pixel values.
Adjacency ,More Formally
Choose a set of gray values V. If f(p) and
f(q) are in V, and q is in the right kind of neighborhood of p, then p and q are adjacent.
I can model this relationship using 0-1 images, why??
Chapter Three
Image Enhancement in Spatial Domain
Find gray level transfomration function T(r) to obtain
g(x,y) =T(f(x,y)) processed image from input image.
Reasons
1. Contrast enhancement
2. Visual improvement
3. Image understanding
Negatives
Here
T(r) = L-1-r L-1 maximum gray level
Produces photographic negative. Some details are easier to spot if we go from black and white to white and black.
Mammogram
Notice that the white or gray detail in the dark region is more visible in the negative.
This shows a small lesion.
Log Transformation
T(r) = c log(1+s)
Inverse Log
T(r) = exp(r/c)-1
For the next picture, c=1. Used to display Fourier spectra.
CRT ExampleCRT devices have intensity to
value response functions that are power functions.
They vary in exponents from 1.8 to 2.5.
A logical transformation is
4.05.2/1)( rrrT