Visual Exploration of Uncertainty

in Remote-sensing Classification

This paper talks about uncertainty in classification of remotely sensed data. Remotely sensed data is like data collected by satellite. Classification of remotely sensed data can be used for extraction of information for cartographic purposes like generating thematic maps of land cover.

Why Uncertainty is an issue

Remotely sensed data naturally will ignore some fuzzy characteristics of environment; therefore, in classification of collected data uncertainty exists.

Representation of Uncertainty

The following probability vector will represent uncertainty in classification of remotely sensed data:
Pr(C = Ci | X)
Where Ci is one of the classes and X is our observed data

Measures of Uncertainty Based on Probability Vector

1. Maximum probability: expression of the strength of the class assignment.
2. Difference of maximum probability and second ranking probability: certainty of most probable class.
3. Entropy measure: (Weighted uncertainty)
   • Uncertainty of C being in class Ci: log Pr(C = Ci | X)
   • Able to summarize all the information contained in a vector of probabilities in a single number: Sum Pr(C = Ci | x) log Pr(C = Ci | X)
4. Quadratic score: (Weighted uncertainty)
   • Uncertainty of C being in class Ci: 1-Pr(C = Ci | X)
   • Sum Pr(C = Ci | x)(1-Pr(C = Ci | X))

Visualization of Uncertainty

• Static Visualization: use graphic variables for capturing uncertainty, like color hue, orientation, shape, size, texture, value, color saturation
  • Simplest: Gray scale map: color value to represent maximum probability measure: black for low maximum and white for high one
  • Color hue: use subjective association: for example traffic light
    • Green: high max probability, high difference
    • Yellow: high max probability, low difference
    • Red: low max probability, low difference
  • Color hue or Color Saturation: deviation from user threshold value: above the threshold with one color hue, below with another color hue
• Dynamic Visualization: add time dimension to static visualization
  • Clickable map: not directly visible uncertainty: activated after clicking
  • Sound visualization: for example use student noise to express reliability of each point of the map.
  • Animation: the higher a class probability for a pixel , the longer of time the class color is displayed
• Weighted Uncertainty Visualization
  • CAMOUTIUS package