S2-11_EAZC473_ Lossless Image Compression

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WILP S2-11_EAZC473 Forums General Discussion Forum lossless image compression

lossless ima ge comp ressionby KALLURI RAJESH . - Monday, 2 April 2012, 04:53 PM

Friends,

There is a repeated question in old question papers to apply lossless image compression on a

table using predictor p6.

I wasted around 3 hours to find some worked out solution but in vain ...

if any body have some link please share with me ...

Any body can solve the problem

apply lossless image compression using predictor 6 for the table

10 10 15

10 15 20

15 20 25

Please solve ... its very imp guyz ...

Reply

Re: lossless image compre ssionby KALLURI RAJESH . - Tuesday, 3 April 2012, 12:29 PM

any inputs ?

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Re: lossless imag e compr essionby SRIRAM R . - Tuesday, 3 April 2012, 12:40 PM

http://taxila.bits-pilani.ac.in/mod/forum/discuss.php?d=4735

follow this forum, should be the same way i guess !!!

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Re: lossless image compre ssionby ABHAY DUTT PAROHA . - Tuesday, 3 April 2012, 01:02 PM

As per my understanding

This question is related to lossless mode of JPEG (different from baseline JPEG).

Steps to follow

_EAZC473: lossless image compression http://taxila.bits-pilani.ac.in/mod/forum/discuss.php

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1. Predictor

2. Entropy Encoding

Predictor

1. For each pixel a predictor (one of 7 possible) is used that best predicts the value

contained in the pixel as a combination of up to 3 neighbouring pixels.

2. The difference between the predicted value and the actual value (X) contained in the

pixel is used as the predictive difference to represent the pixel.

3. The predictor along with the predictive difference are encoded as the pixel's content.

4. The series of pixel values are encoded using Huffman Coding.

P1 A

P2 B

P3 C

P4 A+B+C

P5 A+floor[(B-C)/2]

P6 B+floor[(A-C)/2]

P7 floor[(A+B)/2]

Structure (pixel structure)

P P P P PP C B P P

P A X P P

P P P P P

P P P P P

A. The first pixel (0,0) will always use itself.

B. Pixels at the first row always use P1.

C. Pixel at the first column always use P2.

D. The best of the 7 predictions is always chosen for any pixel

So our image would be after predictor P6 (I am not sure about this...please verify once)P6 = B+floor[(A-C)/2]

10 10 10

10 10 17

10 17 22

then use entropy coding.

Hope, I am clear.

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Re: lossless imag e compr essionby KALLURI RAJESH . - Tuesday, 3 April 2012, 02:12 PM

Abhay,

thank you ...

i understand the procedure but only lack of confidence ... thats why i posted ... now i

feel i am in correct line ..

@sriram

This is different sriram ...


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Re: lossless image compressionby ABHAY DUTT PAROHA . - Tuesday, 3 April 2012, 02:23 PM

Hey Rajesh...I am not sure..same case with me also.. ..lack of confidence...Can

u pls verify my procedure......Can u post some steps of Entropy Encoding after

this?

I think, w e cant apply entropy coding ( w hich w e use with DCT based

compre ssion) because tha t encoding use DC ( predictive difference) and

AC coefficients (Run length coding)

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Re: lossless image compr essionby SRIRAM R . - Tuesday, 3 April 2012, 02:50 PM

Thank God. Guys i owe u all a drink !!

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Re: lossless imag e com pressionby ABHAY DUTT PAROHA . - Tuesday, 3 April 2012, 03:23 PM

Hey Sriram... ...

Can u explain

entropy coding (w hich w e use w ith DCT based compression)

for lossless JPEG ?

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Re: lossless image compr essionby TORTHI SUSMITHA . - Tuesday, 3 April 2012, 03:37 PM

I suppose, we have to find out the difference matrix between the original

matrix and the matrix obtained after applying prediction, find out the

frequency of the characters in the resultant matrix and just apply huffman

coding on that.

Correct me if i am wrong.

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Re: lossless imag e com pression

by KALLURI RAJESH . - Tuesday, 3 April 2012, 05:21 PM

@torthi

process is correct ... but here confusion is how to calculate the

predicted matrix ... please share if you know

@abhay

i also got the same answer ... As per my understanding no need to

apply any dc encoding ... but for ac coefficients, we can do zigzag scan

and apply run length encoding (as said in text book ... i did not

remember the procedure) ...


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Re: lossless imag e compr essionby TORTHI SUSMITHA . - Tuesday, 3 April 2012, 07:48 PM

Okay.

Here is my understanding..

We need to apply lossless image compression using P6 on thebelow matrix

10 10 15

10 15 20

15 20 25

For P-6 predictor, the prediction is B+(A-C)/2

Neighboring pixels in a lossless JPEG are assumed to be as given

below

---|---|---|---|---

| | C | B |

---|---|---|---|---

| | A | X |

---|---|---|---|---

So if you want to predict value for an element at X, we consider its

neighboring pixels in the above form

Now, in the matrix, say M, given,

10 10 15

10 15 20

15 20 25

If you consider element at (0,0) no A,B,C exists... hence this value

doesnt change

for element at

(0,1) -> A=10, B and C dont exist --> apply the formula

B+(A-C)/2, X value is 10/2=5

(0,2) -> A=10, B and C dont exist -> X=10/2 = 5

For elements at position

(1,0) -> A and C don't exist, B=10 -> X=10

(2,0) -> A and C don't exist, B=10 -> X=10

(1,1) -> A=10, B=10, C=10 -> X= 10 + (10-10)/2 = 10(1,2) -> A=15, B=15, C=10 -> X= 15 + (15-10)/2 = 15 + 2.5 =

17.5

(2,1) -> A=15, B=15, C=10 -> X= 15 + (15-10)/2 = 17.5

(2,2) -> A=20, B=20, C=15 -> X= 20 + (20-15)/2 = 20 + 2.5 =

22.5

So the predictor matrix , say P, will be

10 5 5

10 10 17.5


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10 17.5 22.5

Now, my understanding is, we have to find the difference between

M and P

M-P gives, (not sure whether floor / ceil function is needed for

decimal values)

0 5 10

0 5 2.5

5 2.5 2.5

and, we have to apply Huffman coding on the above matrix,

considering the frequency of each character.

0 --> freq = 2

5 --> freq = 3

2.5 --> freq = 3

10 --> freq = 1

I am not confident about the above step.. someone please confirm

!!

This is my understanding--- please let me know if i didnot

understand the algorithm properly

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We need to apply lossless image compression using P6 on the

below table - M

10 10 15

10 15 20

15 20 25

For P-6 predictor, the prediction is B+ f loor [ (A-C) / 2 ]

---|---|---|---|---

| | C | B |

---|---|---|---|---

| | A | X |

---|---|---|---|---

Rules are below (I think, we need to apply below rulesduring our calculations)

A. The first pixel ( 0,0 ) w ill alw ays use itself.

B. Pixels at the first row alw ays use P1.

C. Pixel at t he first colum n alw ays use P2.

D. The best of the 7 pr edictions is alw ays chosen for any

pixel

P1 A

P2 B


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P3 C

P4 A+B+C

P5 A+floor[(B-C)/2]

P6 B+floor[(A-C)/2]

P7 floor[(A+B)/2]

So, the Predicator Table is - P

10 10 10

10 10 17

10 17 22

Difference : M-P

0 0 5

0 5 3

5 3 3

Huffman Coding

Count(0) = 3

Count(3) = 3Count(5) = 3

Torthi..Can you please confirm? (I used rules also, that's why

I am getting different matrix for P)

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Re: lossless image compr essionby TORTHI SUSMITHA . - Wednesday, 4 April 2012, 12:17 AM

Hi,

Are you sure we have to apply P1 and P2 on first row and

first column always ???

I was in an assumption that when P-6[=B+(A-C)/2] is

used,

for first row , the predicted values will be A/2

for first column, the predicted values will be B (u can say

P2)

this is wat i understood from the text book..

Please share the source where these rules are

mentioned.. i haven't come across anything like this inthe text book... or not sure if i had missed that point...

Also, are you sure, we have to use the FLOOR of the

value ??

btwn... i m Susmitha, Torthi is my surname.. ;)

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Re: lossless imag e com pressionby ABHAY DUTT PAROHA . - Wednesday, 4 April 2012, 09:45 AM

Hi Sushmitha,

I was assuming ur name as Torthi.. ...

Here are the links

Simon Fraser University Lectures

http://www.cs.sfu.ca/CourseCentral/365/mark

/material/notes/Chap4/Chap4.2/Chap4.2.html

http://www.ecpe.nu.ac.th/paisarn/Multimedia/week2

/M4L1.pdf

http://www.technicaljournalsonline.com

/jers/past%20issue/swapnillahudkar.pdf

http://www.cs.clemson.edu/~jzwang/1201863

/cpsc86303.pdf

Can you please mention the text book where you

read this?

I am 100% sure about FLOOR value..

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Re: lossless ima ge compr essionby TORTHI SUSMITHA . - Wednesday, 4 April 2012, 09:50

AM

Cool...

thanks a lot for the info...

i was referring to T1 - prescribed text book..

not sure if these points were mentioned there.. i

dont remember reading these rules in the text

book..

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Re: lossless image compressionby ABHAY DUTT PAROHA . - Wednesday, 4 April 2012,

10:21 AM

I came across one example also

Source

Image and video compression standards: algorithms

and architectures

By Vasudev Bhaskaran, Konstantinos

Konstantinides


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Concept

The prediction residual is computed modulo

2 power 16. The residual is not directly

Huffman Coded. Instead, it is expressed as

pair of symbols : the category and the

magnitude.

1. The first symbol represents the number

of bits needed to encode the magnitude.

(Only this value is Huffman coded)

Example: Prediction value for X is 42, then

from table (see at last), we determine that

this value belongs to category 6, that is we

need an additional 6 bits to uniquely

determine the value 42.

2. The prediction residual is then mapped

into 2 tuple (6, 6 bit code for 42)

3. Category 6 is Huffman Coded and the

compressed representation for the

prediction residual consists of this Huffman

codeword followed by this 6 bit

representation for the magnitude.

4. If the value of residual is positive: then

code for magnitude is its direct binary

representation.

5. If the value of residual is negative: then

code for the magnitude is one's complement

of the absolute value

Consider

- - - | - - - | - - - | - - - | - - -

| | C | B |

- - - | - - - | - - - | - - - | - - -

| | A | X |

- - - | - - - | - - - | - - - | - - -

Pixel values A=100, B=191, C=100 and

X=180.

Let Y = (A+B)/2; (which comes 145.5, butbecause we are using FLOOR, this will

become 145)

and the prediction residual is r = 145 - 180

= -35.

From Table , belongs to category 6.The

binary number for 35 is 100011, and its

one's complement is 011100. Thus, is

represented as(6,011100). If the Huffman

code for six is 1110, then is coded by the


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10-bitcodeword 1110011100. Without

entropy coding, would require 16 bits.

In the decoder, the category (that is, 6) is

extracted first.Thus, the next six bits,

011100, correspond to the magnitude of the

residual.Since the most significant bit is

zero, the residual is negative. After

takingthe one's complement of 011100, the

decoded value of the residual r is -35 . TheA and B bits have already been decoded;

thus Y = 145, as before, and X = Y+35 =

180

Category Prediction Residual

0 0

1 -1, 1

2 -3, -2, 2, 3

3 -7, , -4, 4, , 7

4 -15, , -8, 8, , 15

5 -31, ,-16, 16, , 31

6 -63, , -32, 32, , 63

7 -127, ..., -64, 64, , 127

8 -255, ..., -128, 128, ..., 255

9 -511, ..., -256, 256, ..., 511

10 -1023,..., -512, 512, ..., 1023

11 -2047, ..., -1024, 1024, ..., 2047

12 -4095, ..., -2048, 2048, ..., 4095

13 -8191, ..., -4096, 4096, ..., 8191

14-16383, ,-8192, 8192, ...,

16383


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15-32767, ..., -16384, 16384, ...,

32767

16 32768

Table: Prediction residual categories

forlossless JPEG compression.

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Re: lossless imag e compr essionby TUSHAR PAWAR . - Tuesday, 3 April 2012, 06:41 PM

Abhay

thanks for solution

can u pls explain how u get 17 and 22 after using p6 formula

10 10 10

10 10 17

10 17 22

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Hey Tushar...see my solution above ur post...

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Re: lossless image compr essionby SHETH TEJAS NIXIT . - Wednesday, 4 April 2012, 08:17 PM

thnaks abhay.. post was very helpfull

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Re: lossless image compressionby SARANG PADMAKAR GAIKI . - Tuesday, 3 April 2012, 11:47 PM

Hello All

Thanks for this.Even I was searching for such problems.However I have not

understood the concepts. Can some one tell me the source for this.Have you

gone thru lectures or it is better illustarted in book.Please let me know.

Regards

Sarang

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Re: lossless image compr essionby KALLURI RAJESH . - Wednesday, 4 April 2012, 10:33 AM


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abhay,

thank you ...

I am having only one doubt in the solution about this point ...

Point says "it uses only previously encoded neighbors, the very first pixel

I(0, 0) will have to use itself. Other pixels at the first row always use P1, at

the first column always use P2."

By this point ... do we have to apply the formula on predicted values or

original values ?

In the solution , We are doing on original values only ...

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Re: lossless imag e com pressionby ABHAY DUTT PAROHA . - Wednesday, 4 April 2012, 10:41 AM

You will apply the formula on original values only. After that, you will

get one differt matrix.

After this, you need to calculate predictive residuals matrix

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Re: lossless imag e compr essionby DHEERAJ SHARMA . - Wednesday, 4 April 2012, 11:00 AM

Appreciate your efforts for explanation Abhay.

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Re: lossless imag e compr essionby RAMYA N . - Wednesday, 4 April 2012, 03:07 PM

Thanks a lot Abhay...

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Re: lossless imag e compr essionby PANKAJ RAWAL . - Wednesday, 4 April 2012, 11:10 PM

Hi Abhay,

If we need to apply formula only on original values.

Then Value @ (0,2) i.e last row first column should apply P2->B

prediction so its value as per original values should come as 15 and

not 10.Please let me know if i am missing anything.

Final result

10 10 10

10 10 17

15 17 22

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