Image Processing

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Image Processing 8Edge Detection Video
segmentation
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Edge detection
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Edge detection

• What are edges?
• Why are they interesting?
• How do we find them?
• Prewitt
• Sobel
• Laplacian
• Canny

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What are edges?

• Local intensity change
• Strong edge the steep areas in a 3D plot
• (show blobs-for-edge, surface plot)

Edge detection
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What are edges?
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Why are they interesting?

• Edges can (many times) represent the
• information in the image (the objects)
• A higher level of abstraction (less data to
  process!)
• Edges are features
• Independent from illumination. As opposed to
  e.g., color information
• Object recognition and detection (many times) use
  edge features
• This is true for computer vision as well as for
  biological vision systems!
• Excellent for measurements

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Edges detectors

• Different detectors, but all have three steps
• Noise reduction
• Edge enhancement
• Edge localisation

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Edges detectors

• Three steps
• Noise reduction
• E.g., median filter
• E.g., mean filter
• Dilemma
• Large filter gt remove noise ?
• Large filter gt remove edges ?
• Small filter gt keep edges ?
• Small filter gt keep noise ?
• Edge enhancement
• Edge localisation

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Edges detectors

• Three steps
• Noise reduction
• Edge enhancement
• Calculate candidates for the edges
• Edge localisation
• Decide which edge candidates to keep

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Edges detectors

• Well look at four methods (but others exist!)
• With respect to complexity (simplest first)
• Prewitt
• Sobel
• Laplacian
• Canny

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Edge Detectors Prewitt and Sobel
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Edge Detectors Prewitt and Sobel

• Simple to implement. Fast
• Based on the grey-level gradient
• A measure of the steepness of the
  image-landscape
• Calculated for each pixel gt Gradient image
  g(x,y)
• Use a 16-bit or 32-bit image to represent the
  gradients!
• The gradient is the first-order derivative
• Approximated in the x- and y-direction by

x
x1
x-1
y-1
y
y1
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Convolution (Foldning) with this kernel
-1
1
Normally this kernel to avoid bias
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Edge Detectors Prewitt and Sobel
gx , gy

• Gradient vector
• Magnitude (hvor kraftig er kanten længden af
  blå pil)

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Edge Detectors Prewitt and Sobel

• Noise reduction
• Mean of three gradients
• Edge enhancement
• Implementation of
• Convolution with Prewitt kernels or Sobel
  kernels
• Edge localisation
• If the magnitude g(x,y) gt TH gt edge found
  e(x,y)255
• Else no edge e(x,y)0
• (Show blobs-for-edge, 32-bit, convolution, abs,
  TH)

Sobel kernels
Prewitt kernels
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Prewitt and Sobel

• Conclusion
• Pros
• Simple to understand
• Simple to implement
• Fast
• Cons
• Produce wide edges
• Used a lot! (most common Sobel)

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Edge Detector Laplacian
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Edge Detector Laplacian

• Where exactly is the edge (width)?
• Second-order derivative
• The variation of the variation of the gray-level
  value!
• How fast does the gradient change?
• Find the zero-crossing
• Center of edge

Prewitt and Sobel
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Zero-crossing
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(No Transcript)
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Edge Detector Laplacian

• The second-order derivative is very sensitive to
  noise!

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Laplacian of Gaussian

• Solution
• Combined with a 2D Gaussian smoothing filter
• (show blobs-to-edge, 32-bit, gauss, convolution,
  plot profile)

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Examples

• Gauss filter width
• 5x5 pixels
• 9x9 pixels
• 12x12 pixels

Input
Gauss conv.
Edges
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Laplacian of Gaussian

• Conclusion
• Pros
• Edges well-defined due to zero-crossings
• Cons
• How do we find the zero-crossings?
• I.e., transitions from black to white and vice
  versa
• Laplacian is too sensitive to noise due to
  second-order derivative
• Simple to implement except for the search for
  zero-crossings!
• Not used so often

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Canny Edge Detector
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Canny Edge Detector

• Noise reduction
• 2D Gaussian used for smoothing
• Edge enhancement
• Magnitude of gradient vector
• Edge localisation

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Canny Edge Detector

• Edge localisation
• Wide edges
• Edges give rise to ridges in the gradient image
• Thin edges using the principle of non-maximal
  suppression
• Find gradients directions
• Each pixel is compared with its two
• neighbors in the gradient direction. The
• two smallest are suppressed gt set to zero
• The result is pixel-thin edges

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Thresholding Dilemma

• Define a threshold in the magnitude-image
• Assume high magnitudes originate from
  object-edges
• Dilemma (Show blobs-to-edge, edge, dilate(3),
  TH)
• Too high threshold
• Remove noise ?
• Remove small edges ?
• Too low threshold
• Keep noise ?
• Keep small edges ?
• How do we threshold the magnitude image so that
  noise is suppressed and the object-edges are
  not???

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Hysteresis Thresholding

• Concept think of object-edges as a connected
  group of edge pixels
• Use two thresholds Thmin and Thmax
• All magnitude edge-pixel below Thmin are sat to
  zero
• Choose Thmin so low that no object edges are
  eliminated
• Find all grouped edges (non-zero edge-pixels)
• Ignore all groups which are too small (in number)
• Ignore all groups which do not contain at least
  one edge-pixel with a magnitude above Thmax
• Choose Thmax so high that (most) noise edges are
  eliminated
• Similar to region growing
• Effect
• Isolated (noise) edge-pixels are ignored
• Both strong and weak edge-pixels are kept

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Examples
Gauss 5x5, Thmax 255, Thmin 1
Gauss 5x5, Thmax 255, Thmin 220
Gauss 5x5, Thmax 128, Thmin 1
Gauss 9x9, Thmax 128, Thmin 1
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Examples
Gauss 7x7, Thmax 200, Thmin 1
Gauss 5x5, Thmax 200, Thmin 1
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Examples

• Comparison on noisy image

Canny
Sobel
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Canny edge detector

• Conclusion
• Pros
• One pixel wide edges
• Edges are grouped together (often good for
  segmentation)
• Robust against noise!
• Cons
• Complicated to understand and implement
• Slow
• Used a lot!

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What to remember

• Edge Rapid intensity change
• Edge information is an important factor in Image
  Procesing and Human Vision
• Three steps in edge detection
• Noise reduction
• Edge enhancement
• Edge localisation
• Three types were presented
• Based on first-order derivative
• Prewitt and Sobel
• Based on second-order derivative
• Laplacian of Gaussian
• Based on groups of edges
• Canny

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Exercises

• Use ImageJ to generate a magnitude image using
  the Sobel kernels
• Discuss the PE-questions
• How wide will the edges be for the different edge
  detectors?
• Does this matter?
• Discuss the principle of non-maximal suppression