More Image Processing Operations

1
More Image Processing Operations

• Some operations we want to cover
• Edge detection, enhancement, etc.
• Region growing

2
Edge Detection

• We want to find the boundary between two regions
  abrupt change
• Were looking for derivatives
• A derivative is a type of high-pass filter
• Whats a derivative in 2D?

3
Gradients

• An image gradient consists of the horizontal and
  vertical partial derivatives

4
Derivative Estimators

• Most trivial Simple difference
• Note All must add to zero
• Problems
• Derivatives enhance noise
• We desire some filtering
• We prefer odd sized filters, not even
• Note relation to high-pass filtering

Horz
Vert
5
Better Derivative Estimators

• Prewitt operator
• Sobel operator

Horz
Vert
Horz
Vert
TT
6
Steps (so far)

• Compute two Gx and Gy
• Using some derivative estimation filter

7
Determining edge locations

• We are interested in the magnitude of the
  gradient at each pixel
• For each pixel
• Determine magnitude based on gradient images
• Test against a threshold

8
Example code
// Filter that returns absolute values
Filter3x3A(inImg, hfilt, sobelH)
Filter3x3A(inImg, vfilt, sobelV) //
Determine where the edges are for(int r0
rltouImg.Height() r) for(int
c0 cltouImg.Width() 3 c)
double p1 hfiltrc double
p2 vfiltrc if(sqrt(p1 p1
p2 p2) gt m_threshold)
ouImg.Set(c/3, r, 255, 0, 0)

9
Improving Efficiency

• Square root per pixel is very expensive
• We can approximate using absolute values

if(abs(hfiltrc) abs(vfiltrc) gt
m_threshold)
ouImg.Set(c/3, r, 255, 0, 0)
TT
10
Region Growing

• Given a point in the image
• Use color at point as region color
• Flag point as in region
• Push point onto stack
• While(stack not empty)
• t lt- Pop stack
• For each neighbor of t
• if similar color and not visited before
• Flag point as in region
• push point onto stack

TT
11
Keeping track of the visited

• Dummy image
• Specific values in output image
• Destroying input image

12
Comparing Colors

• Vector distance
• Manhattan distance
• Maximum in any dimension

13
Alternative color systems and myths

• RGB is a poor perceptual system
• HLS is better for human color selection
• H Hue the color
• S Saturation How pure the color is
• L Luminance the Brightness
• HLS can be a poor choice for region growing (or
  other color comparisons)
• If S 0, H does not matter
• If L 0 or 100, H and S do not matter

14
The RGB color cube
Blu
What do our distance measures mean here?
Grn
Red
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RGB Color cube looking down the gray line
Blu
Magenta
Cyan
Grn
Red
Yellow
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The Hexacone HLS model

• Parameters
• H Angle relative to red
• L Height from black
• S Percentage of way from center

TT
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Combining region growing and edge detection

• Assume an image of only detected edges
• What if I click on a non-edge pixel?
• What if I click on an edge pixel?

18
Edge linking

• Following edges to decide which are contiguous
  and the paths
• How can we describe a path?