Lecture Three Chapters Two and three Photo slides from Digital Image Processing, Gonzalez and Woods, Copyright 2002
Chapter 2: Digital Image Fundamentals
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.
Chapter 2: Digital Image Fundamentals
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.
Chapter 2: Digital Image Fundamentals
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.
Chapter 3 Image Enhancement in the Spatial Domain Chapter 3 Image Enhancement in the Spatial Domain
Chapter 2: Digital Image Fundamentals
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
Chapter 3 Image Enhancement in the Spatial Domain Chapter 3 Image Enhancement in the Spatial Domain
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.
Chapter 3 Image Enhancement in the Spatial Domain Chapter 3 Image Enhancement in the Spatial Domain
Mammogram Notice that the white or gray detail in the dark region is more visible in the negative. This shows a small lesion.
Chapter 3 Image Enhancement in the Spatial Domain Chapter 3 Image Enhancement in the Spatial Domain
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.
Chapter 3 Image Enhancement in the Spatial Domain Chapter 3 Image Enhancement in the Spatial Domain
Power Law or Gamma Transformations This the gamma correction
Chapter 3 Image Enhancement in the Spatial Domain Chapter 3 Image Enhancement in the Spatial Domain
CRT Example CRT 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
Chapter 3 Image Enhancement in the Spatial Domain Chapter 3 Image Enhancement in the Spatial Domain
MRI of Fractured Spine Transformation is With gamma = 0.6,0.4,0.3
Chapter 3 Image Enhancement in the Spatial Domain Chapter 3 Image Enhancement in the Spatial Domain
Chapter 3 Image Enhancement in the Spatial Domain Chapter 3 Image Enhancement in the Spatial Domain
Chapter 3 Image Enhancement in the Spatial Domain Chapter 3 Image Enhancement in the Spatial Domain
Chapter 3 Image Enhancement in the Spatial Domain Chapter 3 Image Enhancement in the Spatial Domain
Chapter 3 Image Enhancement in the Spatial Domain Chapter 3 Image Enhancement in the Spatial Domain
Chapter 3 Image Enhancement in the Spatial Domain Chapter 3 Image Enhancement in the Spatial Domain
Chapter 3 Image Enhancement in the Spatial Domain Chapter 3 Image Enhancement in the Spatial Domain