Shannon's uncertainty question

  • Thread starter Thread starter Calmstorm
  • Start date Start date
  • Tags Tags
    Uncertainty
Click For Summary
SUMMARY

The discussion focuses on measuring uncertainty in a two-tone image transmission, specifically using Shannon's entropy formula. The proposed formula for uncertainty is H(X) = - W{ Pi log(Pi) } - B{ Qj log(Qj) }, where W represents the number of white pixels and B represents the number of black pixels. The probabilities Pi and Qj correspond to the likelihood of encountering a white or black pixel, respectively. The length of the transmitted sequence for an NxN image is established as N^2, given that each pixel is transmitted independently.

PREREQUISITES
  • Understanding of Shannon's entropy and information theory
  • Familiarity with pixel representation in digital images
  • Basic probability concepts, including independent events
  • Knowledge of two-tone image formats and their characteristics
NEXT STEPS
  • Research Shannon's entropy in depth, focusing on its applications in image processing
  • Explore pixel probability calculations in binary images
  • Learn about data compression techniques for two-tone images
  • Investigate the implications of independent pixel transmission on data integrity
USEFUL FOR

Students studying information theory, image processing professionals, and anyone interested in the mathematical foundations of data transmission and uncertainty measurement.

Calmstorm
Messages
4
Reaction score
0

Homework Statement

:

If I were to use a two-tone image e.g. fax, and were to transmit it line-by-line, where the the individual pixels which make up the line were independent of each other, how would I measure the uncertainty at the transmitter? Also what would the length of the the transmited sequence be if the image was a square NxN image?


2. The attempt at a solution

I think the uncertainty is H(X)= - W{ Pilog(Pi) } -B{Qj log (Qj)}
where:
W=number of white pixels in the sequence
Pi=probability of a white pixel.
B=number of black pixels in seqence
Qj=probability of a black pixel.

Any ideas would be very helpful...thank you in advance!
 
Physics news on Phys.org
Please do not cross-post.
 

Similar threads

  • · Replies 2 ·
Replies
2
Views
5K
  • · Replies 1 ·
Replies
1
Views
3K
  • · Replies 2 ·
Replies
2
Views
3K
  • · Replies 4 ·
Replies
4
Views
2K
  • · Replies 7 ·
Replies
7
Views
2K
  • · Replies 2 ·
Replies
2
Views
2K
  • · Replies 3 ·
Replies
3
Views
6K
  • · Replies 2 ·
Replies
2
Views
6K
Replies
8
Views
6K
  • · Replies 18 ·
Replies
18
Views
4K