CS5611 (Fuzzy Sets: Theory and Applications)

Final Report for CS5611 (Fuzzy Sets: Theory and Applications):

Neural Fuzzy on Block Truncation Coding

歐名峰 (mr854346, 資碩一)
李旭明 (mr854348, 資碩一)

Abstract	BTC	Data Set Description	Our Approach
Simulation Results	Conclusions	Computer Programs	Division of labor
References

Abstract

This report describes our attempt to apply ANFIS (Adaptive Neuro-Fuzzy Inference Systems) [Jang93] for the prediction of best threshold for the BTC (Block Truncation Coding) System. The preliminary results show that ANFIS is a competitive approach when compared to conventional approaches.

Block Truncation Coding

Introduction: BTC was developed at Purdue University. This technique uses a one bit nonparametruc quantizer adaptive over local regions of the images. The quantizer that shows great promise is one that preserves local statistics of the image.

Algorithm:

The image was divided into 4x4 pixel blocks

The blocks are coded individually, each into a two level signal.

The levels for each block are chosen such that the first two sample moments are preserved.

Let and let ,,…, be the values of the pixel in a block of the original picture. Then the first and second sample moments and the sample variance are , respectively ; ; As with the deign of any one bit quantizer, we find a threshold, , and two output levels, a and b, such that if for I=1, 2, …,m
For our first quantizer, we set = The output level a and b are found by solving the following equations: Let q = number of 's greater than (=) then to preserve and m=(m-q)a+qb and m=(m-q)+q Solving for a and b:

Example: suppose a 4x4 picture block is given by the following:

so =98.75 ; =92.95 ;q=7

and a=16.7≒17 ; b=204.2≒04

the bit plane is

The reconstructed block becomes:

And the sample mean and variance are preserved.

We try to use anfis to train the threshold.

Output: the best threshold

Problem Definition

This project tries to solve the problem of the threshold prediction using the ANFIS [Jang93] approach. We try to train the best threshold by ANFIS.

Data Set Description

Description: There are totally 4096 instances, each with 3 inputs and 1 output:

Input 1: block mean
Input 2: block variance
Input 3: block median
Output: the best threshold

Approach

ANFIS Structure:

3-input and each input with 2 Generalized bell member function

ANFIS Training: We use the data set from the 'lena' to train the ANFIS and use "fruit.raw","bridge.256" to check its performance.

Training and testing image

Simulation Results

Training Results:

Training data from 'lena'

Membership function before training

Membership function after training 100 epochs

Error curve

Step size

Difference between the prediction and target

Lena as training	Lena	Fruit.raw	Bridge
Optimal	30.5441	33.1529	28.3928
BTC	29.7393	32.6486	27.7932
FBTC with 20 epoch	30.0157	32.7851	27.9352
FBTC with 100 epoch	30.0120	32.7773	27.9271

Training data from 'lena'+'fruit.raw'+'bridge.256'

Membership function before training

Membership function after training 50 epochs

Error curve

Stepsize

Difference between prediction and target

Lena+fruit.raw+bridge.256 as training data	Lena	Fruit.raw	Bridge.256	Hat.256
Optimal	30.5441	33.1529	28.3928	30.9963
BTC	29.7393	32.6486	27.7932	30.4289
FBTC with 20 epochs	29.9896	32.8191	27.9789	30.6274
FBTC with 50 epochs	29.9826	32.8258	27.9803	30.6279

Concluding Remarks and Future Work

Concluding Remarks:

We think ANFIS is useful because it improve the PSNR about 0.25db
(Actually, an approach that can improve PSNR much is very hard to create.) It uses twice time to run FBTC than BTC but only uses one-third time to get optimal BTC.

Future Work:

We want to improve the performance by using another feature as inputs and run simulation with bigger image, maybe 512x512 or so…

Computer Programs

All the computer programs (including C and MATLAB) for this project are available at: program.exe self extractor

How to run my program: run getdata('lena') to get lena.dat for example then run trndata('lena.dat',20) using lena as training data and training epochs is 20 .final using fbtc('lena') to get the result