Matrices

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Matrices

• Image Processing With Matrices

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• Close gap between theory and application
• Digital images are matrices
• Matrices can be through various matrix operations
  along with scalars

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Manipulations to Be Covered

• Flip Vertical
• Flip Horizontal
• Rotate Left
• Rotate Right
• Invert
• Lighten/Darken
• Smooth/Sharpen

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Flip Horizontal

• Performed through multiplication with an inverted
  identity matrix
• AC

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Flip Vertical

• Performed through multiplication with an inverted
  identity matrix
• CA

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Rotate Left

• Performed by taking the transpose of the image

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Rotate Right

• Performed by multiplying by inverted identity
  then taking the transpose

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Inversion

• Performed by item by item subtraction from the
  maximum color value

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Lighten/Darken

• Performed through scalar multiplication
• Images appear darker or lighter through changes
  in light intensity

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Smooth/Sharpen

• Performed by multiplying matrix by a weight, then
  averaging each element with its 3x3 neighbors

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Special Thanks

• Carrie Mitsuyoshi Russell Miyazono
• Paul Haeberli
• ArtToday