Image Rotation and Warping

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Image Rotation and Warping

• By Chris Dapkus and Zach Goff

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Pixel Rotation Problem

• All images are represented as a matrix with
  values in discrete locations
• Direct rotation does not result in the new
  location of each pixel to a discrete location
• Rotation equations
• x2cos(t)(x1-x0)-sin(t)(y1-y0)x0
• y2sin(t)(x1-x0)cos(t)(y1-y0)y0
• where (x0,y0) is the image center

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Pixel Values

• Matlab has 3 different methods in assigning
  values to the discrete matrix values
• Nearest neighbor
• Bilinear
• Bicubic
• All remaining matrix positions are set to 0

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Examples
Original
Nearest Neighbor
Bilinear
Bicubic
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Differences
Threshold0
Threshold5
Bicubic to Nearest neighbor
Bicubic to Bilinear
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Image Warping

• Camera lenses and perspective distorts 2d
  representation
• To match features exactly, images must be warped.
• Corresponding control points between 2 images are
  selected to control warping
• Image is warped using homography

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Warped Image