wu :: forums
« wu :: forums - Mean Value Blurring »

Welcome, Guest. Please Login or Register.
Oct 5th, 2024, 6:50pm

RIDDLES SITE WRITE MATH! Home Home Help Help Search Search Members Members Login Login Register Register
   wu :: forums
   riddles
   cs
(Moderators: ThudnBlunder, Grimbal, SMQ, towr, william wu, Eigenray, Icarus)
   Mean Value Blurring
« Previous topic | Next topic »
Pages: 1  Reply Reply Notify of replies Notify of replies Send Topic Send Topic Print Print
   Author  Topic: Mean Value Blurring  (Read 1951 times)
Barukh
Uberpuzzler
*****






   


Gender: male
Posts: 2276
Mean Value Blurring  
« on: Apr 8th, 2014, 9:00am »
Quote Quote Modify Modify

Consider a representation of a visual image as rectangular matrix NxN, where every element represents the color of a pixel – a positive real number in interval [0..R].
 
This image undergoes an iterative process of blurring according to the following procedure:
 
At iteration i, every pixel color is replaced by an arithmetic mean of colors of itself and all its neighbours (horizontal, vertical, diagonal) at the iteration i-1.
 
Assume that all operations are performed mathematically.
 
We are interested in the following question: What happens after infinite number of blurring iterations?
 
Specifically, is it necessarily the case that the final image will be homogeneous (that is, every pixel has the same color)?
 
Consider also the following variants of image representation:
 
A. Colors are positive integers, and integer arithmetic is used.
B. Colors are positive integers, but this time floating point arithmetic is used, and the result is round to the nearest integer.
« Last Edit: Apr 8th, 2014, 9:01am by Barukh » IP Logged
Barukh
Uberpuzzler
*****






   


Gender: male
Posts: 2276
Re: Mean Value Blurring  
« Reply #1 on: Apr 9th, 2014, 1:37am »
Quote Quote Modify Modify

Just to be clear: In image processing, the procedure described above is called Mean Filtering with 3x3 square kernel.
« Last Edit: Apr 9th, 2014, 1:38am by Barukh » IP Logged
towr
wu::riddles Moderator
Uberpuzzler
*****



Some people are average, some are just mean.

   


Gender: male
Posts: 13730
Re: Mean Value Blurring  
« Reply #2 on: Apr 9th, 2014, 10:23am »
Quote Quote Modify Modify

How do we treat the edge cases?  
In the original statement, well, there's just fewer neighbours on the edges; but if you use a 3x3 kernel, then it matter what you do with the non-existent values beyond the border. (If you set the beyond-border values to zero, or extend to infinity, then all color bleeds off eventually.)
IP Logged

Wikipedia, Google, Mathworld, Integer sequence DB
Barukh
Uberpuzzler
*****






   


Gender: male
Posts: 2276
Re: Mean Value Blurring  
« Reply #3 on: Apr 9th, 2014, 10:36am »
Quote Quote Modify Modify

on Apr 9th, 2014, 10:23am, towr wrote:
How do we treat the edge cases?

You count only the neighbours in the image (so, for instance, the corner pixel will have 3 neighbours).
IP Logged
Pages: 1  Reply Reply Notify of replies Notify of replies Send Topic Send Topic Print Print

« Previous topic | Next topic »

Powered by YaBB 1 Gold - SP 1.4!
Forum software copyright © 2000-2004 Yet another Bulletin Board