Spatial Filtering

Spatial Filtering in Computer Vision

1. Spatial Frequency

• Concept: Spatial frequency refers to the rate at which pixel intensity values change within an image.

  • High Spatial Frequency: Represents rapid changes in intensity over a short distance. This corresponds to sharp details, edges, and textures in an image.
  • Low Spatial Frequency: Represents gradual changes in intensity over a larger distance. This corresponds to smooth regions, overall shapes, and the general background of an image.

• Bit Planes:

  • In some applications, analyzing the bit planes of an image is important.
  • Each bit plane represents a specific bit position (e.g., most significant bit, least significant bit) across all pixels in the image.
  • Higher-order bit planes often contain information about the overall structure and lower spatial frequencies, while lower-order bit planes might reveal finer details and higher spatial frequencies.

2. Spatial Filtering

• Concept: Spatial filtering is the process of modifying an image by applying a filter (kernel) directly to its pixels in the spatial domain (i.e., directly on the image grid).
• Process:
  • The notes show a simplified diagram:
    • Org img (Original Image) ⇒ Transfer (Filter/Kernel applied) ⇒ Spectral Domain or Image
    • The “Transfer” step represents a function, typically a kernel, that transforms the original image. It can either lead to the Spectral Domain, which is the representation of the image in frequency space (we’ll cover that next), or it results in a modified image directly in the spatial domain (as with the filters discussed in previous notes).
• Relationship to Frequency:
  • High frequencies correspond to edges and details.
  • Low frequencies correspond to smoothness and general shapes.
  • Spatial filters can be designed to selectively enhance or suppress certain spatial frequencies.

3. Frequency Domain (Spectral Domain)

• Concept: While spatial filtering operates directly on pixel values, the frequency domain offers an alternative representation of an image.
• Transformation:
  • Mathematical transforms, most notably the Fourier Transform, are used to convert an image from the spatial domain to the frequency domain.
  • The Fourier Transform decomposes an image into its constituent frequencies (like decomposing a musical chord into its individual notes).
• In the Frequency Domain:
  • The center of the frequency domain representation typically corresponds to low frequencies.
  • Pixels further away from the center represent higher frequencies.
• Filtering in the Frequency Domain:
  • Filters can be designed to operate in the frequency domain as well.
  • For example, a low-pass filter would allow low frequencies to pass through (keeping smooth areas) while attenuating high frequencies (reducing noise and detail).
  • A high-pass filter would do the opposite, preserving edges and details while suppressing smooth regions.