The digitized image and its properties

Image functions

  • A projected point (x, y, z) has coordinates (x’, y’) in the 2D image plane where:

where f is the focal length of the camera.

  • The brightness of a pixel depends on several independent factors:
  1. Object surface reflectance.
  2. Illumination properties.
  3. Object surface orientation with respect to a viewer and the light source.
  • Separating the components of brightness is another ill-posed problem.


  • In general, functions may be categorized into:














  • The quality of the digital image grows in proportion to the image resolution:
  1. Spatial resolution: given by the proximity of the image samples in the image plane.
  2. Spectral resolution: given by the bandwidth of light frequencies captured by the sensor.


  3. Radiometric resolution: corresponds to the number of distinguishable graylevels.
  4. Time resolution: given by the interval between time samples at which images are captured.

Image digitization

  • Two questions should be answered in connection with image function sampling:
  1. The sampling period:
  • Based on Shannon sampling theorem. The sampling interval should be chosen in size such that it is less than half of the smallest interesting detail in the image.
  • Decreasing the sampling period degrades the image quality. Much of the degradation is caused by aliasing in the reconstruction of the continuous image function for display. The display can be improved by the reconstruction algorithm interpolating brightness values in neighboring pixels.
  1. The geometric arrangements of the sample points:




Color (multi-spectral) images

  • For k = 256, the number of distinct colors is: 256 x 256 x 256 = 224.

  • Advantages the HIS model:
  1. Decouples the intensity information from color information.
  2. Hue and saturation correspond to human perception.

If b/i > g/i. set h=2p -h.

  • These measurements are normalized to the range [0,1] if h is set to h/2p .
  • If r=g=b, h is undefined and if i=0, s is undefined.

Case 0 < H £ 2p /3

Case 2p /3 < H £ 2 x 2p /3

Case 2 x 2p /3 < H £ 2p

Digital image properties




Pixel adjacency