Extra Notes on Vision from

  Ginsberg, "Essentials of AI", Chapter 16
  Ballard and Brown, "Computer Vision"

- edge detection
  - consider simple templates [FigG16.4, p329]
    - corresponds to [FigBB3.10, p77]
      - see others there also
  - edge(i,j) = sqrt([I(i+1,j+1) - I(i,j)]^2 + [I(i+1,j) - I(i,j+1)]^2)
  - general
    - given gradients
      - DX: measures intensity difference in x direction
      - DY: measures intensity difference in y direction
    - mag(x,y) = sqrt(DX^2 + DY^2)
    - orient(x,y) = arctan(DY,DX)
- edge completion
  - extend high-confidence edge pieces
  - extend zero regions 
    - region boundaries are edges
- Hough (pron. huff) transform
  - given model of curve
  - find location (if any) of such a curve in image
  - general alg
    - convert from image intensity space to model parameter space
      - H(model parms) = Sum({(i,j) satisfying model parms}) mag(i,j)
      - limit resolution of parameter space based on image resolution and
        size 
    - look for maxima in parameter space
  - e.g., lines [AlgBB4.1, p123]
    - point (i,j) is on line with slope m and y-intercept if
      - j = mi + c
    - transform to parameter space h(m,c)
      - h(m,c) = Sum({(i,j)|j=mi+c}) mag(i,j)
      - maxima in h(m,c) indicate lines
      - h(m,c) ~= number of image points on line
      - could remember which points for each (m,c)
        - extract end points of line
  - e.g., circles
    - point (i,j) is on circle at (x,y) with radius r if
      - (i - x)^2 + (j - y)^2 = r^2
    - transform to parameter space h(x,y,r)
      - h(x,y,r) = Sum({(i,j)|(i-x)^2+(j-y)^2=r^2}) mag(i,j)
      - maxima in h(x,y,r) indicate circles
        - above some threshold
    - given edge orientation as well (i,j,theta)
      - apply further constraint (j-y)/r = sin(theta - 90) = -cos(theta)
      - see [FigG16.8, p333]