Images and Filtering

• Digital Image

• Bayer Filer：相机滤色版每个点有三个值，一个为传感器得到，两个为插值

• Image transformation

  Use of Filtering

  • Enhance an image
  • Extract infromation
  • Detect patterns

  Three views of filtering

  • Image filters in spatial domain
  • Image filters in frequency domain
  • Templates and Image Pyramids

• Image noise and image smoothing

• Convolution operation

• Media filter

Frequency Domain and Sampling

• Fourier Transform
• Sampling

Template matching

• correlation: bad

  $$h[m,n]=\sum_{k,l}g[k,l]f[m+k,n+l]$$

• Zero-mean filter: fastest but not a great matcher

  $$h[m,n]=\sum_{k,l}(g[k,l]-\overline{g})f[m+k,n+l]$$

• Sum Square Difference: next fastest, sensitive to overall intensity

  $$h[m,n]=\sum_{k,l}(g[k,l]-f[m+k,n+l])^2$$

• Normalized cross-correlation: slowest, invariant to local average intensity and contrast

  $$h[m,n]=\frac{\sum_{k,l}(g[k,l]-\overline{g})(f[m+k,n+l]-\overline{f}{m,n})^2}{(\sum{k,l}(g[k,l]-\overline{g})^2\sum_{k,l}(f[m+k][n+l]-\overline{f}_{m,n}))^{0.5}}$$

Image pyramids

• Gaussian Pyramids
  • Up or down sample images
  • Multi-resolution image analysis
• Laplacian Pyramids

Filter banks and texture analysis

• Texture: a phenomenon that is widespread, easy to recognize and hard to define
• Texture-related tasks
  • shape from texture
  • segmentation/classification
  • synthesis
• Filter banks: a collection of multiple filters
  • feature vectors will be d-dimensional