Digital Image Processing at Multiple Scales

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Digital Image Processing at Multiple Scales
???
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Humans
Brain (Inside)
Eyes
Conclusion Ideally Suited for Image Processing
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computers
May Look Ideally Suited for Image Processing
But Theyre Not
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Filtering Images

• Creates new image
• Each pixel is based on the corresponding pixel
  and its neighbors in the old image
• Filters can be used to clean images

Average Filter Each pixel in new image will be
the average (mean) of a region of pixels in the
old image.
Median Filter Each pixel in new image will be
the median of a region of pixels in the old image.
Noisy Picture
Cleaned Picture
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Feature Detection

• What are features?
• A feature is something that catches our eye in an
  image

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Laplacian Filter

• Laplacian filter is a filter looking like this
• The Laplacian filter detects points (or areas)
  that are different from their surrounding.
• Us humans see the world
• Through Laplacian filter

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Feature detection in action
narrow filter small features
wide filter large features
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The Problem of Scale

• The computer can easily fill in small gaps in the
  image to clean up noise.
• There are problems with larger gaps.
• Solution Work on different scales.

Filter
Picture With Larger Bad Piece
Just Filtering is Not Effective!
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Gaussian Pyramids

• G0 Original Image
• GN, N gt 0 Reduced Image

Expand
Low Detail
Much Higher Detail
Expand
G0
G1
G2

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Using Filters As Pyramids

• Filters can accomplish the same blurring as
  Gaussian pyramids.
• Gaussian filters create this blurring effect by
  emphasizing the corresponding pixels neighbors
  more than the corresponding pixel

Apply Large, Strong Gaussian Filter
Apply Small, Weak Gaussian Filter
Much Higher Detail
Lower Detail
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Approximations

• G0s of similar images quite different
• GNs of similar images are closer than G0s

Find GNs with Large N
Very Slightly Similar
Slightly More Similar
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Image Completion

• Method for Image Completion
• Repeat with N from a large number to 0
• Obtain a filtered version of GN, enlarged to the
  original size (Using filters or a Gaussian
  pyramid)
• Reintroduce the good pixels from the incomplete
  image

Incomplete Image
Complete Image
Mask (Marks Valid Pixels)
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Another Example

• Can you see the Einstein in 100 random lines?

Incomplete Image
Complete Image
Mask (Marks Valid Pixels)
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Limitations

• This method does not work as well on drawings
  because drawings can have more unpredictable
  changes in color.

Incomplete Image
Complete Image
Mask (Marks Valid Pixels)
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Resizing Images

• Our task was making images smaller.
• Why?
• One reason is to transmit the image over the
  internet faster.

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But how do you resize an image?

• There a few methods to resize images and to
  reduce their number of pixels
• The simplest reduce method is to use the uniform
  grid

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Adaptive Sub-sampling

• To keep more pixels where details are finer
• Using Feature Detection to sample (take) more
  pixels near features
• Non-uniform grid

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Thank you!

• No questions please