Convolution

• a.k.a. Linear Filtering

Similar to Rank Filtering

• a way to filter keeping the spatial pattern of pixels
• I’ = g * I
  • where g is the kernel, I is the image and I’ is the convoluted image
• 
• where g(a,b) is the kernel of size axb
• convolution is associative

Kernel/Mask/Filter Window

• The moving window
• common kernels
  • Image smoothing
  • Edge Detection

Decomposable Kernels

• symmetric kernels are decomposable into 2 linear convolutions
• if the kernel 2D matrix can be written as the outer product of 2 vectors
  • n x n = n x 1 * 1 x n
  • convolving with nxn kernel is the same as 2 convolutions with n x 1 and 1 x n kernels
  • such convolutions are computationally cheaper
    • 2n multiplications instead of n² per pixel

Padding

• adding extra padding around the source image before convolution so that all the pixels in the source image get processed.
• Common padding techniques
  • Zero: Set all pixels outside image course to zero
  • Constant (border colour): set all pixels outside the source image to a specified border value
  • Mirror: reflect pixels across the image edge