Determining the resulting pixel value before creating a compressed JPEG image

Question

Is it possible to determine the resulting pixel values and modify them before the compressed jpeg image is actually created?

For example, I'm at the stage where I already have the quantized DCT coefficients of the original image and I want to change all pixels of the resulting image with a (255, 255, 0) value to (255, 254, 0).

What I was thinking is, if this is possible I would need to:

1. Get the equivalent DCT coefficient of original image and do quantization
2. Determine the resulting pixel values and do desired changes
3. Obtain the new DCT coefficients that will result to it
4. Proceed to Huffman encoding

Can the following be done during Huffman encoding?

1. Get the equivalent DCT coefficient from YCbCr and do quantizations
2. Do Huffman encoding and modify the desired pixel

Answer 1

To give you an upfront answer your question you want to determine the $pixel-values$ from $DCT-Coefficients$ probably there is nothing on earth better than doing IDCT itself!

However, leaving aside some vagueness i can re-phrase your question:

If i have an algorithm x - that is defined to work on Pixels, here is what i do:
DCT-Coeffs -> IDCT -> pixels Algorithm_X -> pixels DCT -> DCT-Coeffs
(ignoring other stuff that is peripheral).

The question is: is there a short cut to this brute force where i am obviously undoing quite some stuff done in first stage?

What you are referring to is what is generally known as Compressed Domain Processing.

DCT-Coeffs -> Compressed_Domain_Algorithm_X -> DCT-Coeffs

Basically, all compressed domain algorithm exploits the linearity of DCT. For example

$$ Y = \alpha * X_1 + \beta * X_2 $$ then,
$$ DCT(Y) = \alpha * DCT(X_1) + \beta * DCT(X_2) $$ where $\alpha$ $\beta$ are scalars.

There are many things possible, and while many NOT. It is too vast to answer the set of all compressed domain algorithms which are possible, but i would recommend key readings that will set a great stage for you.

1. Compressed Domain Processing of JPEG-encoded images by Brian C. Smith , Lawrence A. Rowe Real-Time Imaging (1996)

2. A Survey of Compressed Domain Processing Techniques by Brian C. Smith Proc. NSF Workshop on Reconnecting Science

3. Algorithms for Manipulating Compressed Images, Brian C. Smith, Lawrence A. Rowe, IEEE Computer Graphics and Applications, Sept. 1993, vol.13, (no.5):34-42.

4. Manipulation and compositing of MC-DCT compressed video by Shih-Fu Chang, David G. Messerschmitt IEEE Journal on Selected Areas in Communications, 1995/1, Volume 13 Issue 1

5. Compressed-Domain Video Processing by Susie Wee, Bo Shen, John Apostolopoulo HP Labs Tech Report 2002.

Specifics: If you are using libjpeg you can actually get quantized DCT co-efficients directly. However, most above literature refers un-quantized DCT co-efficients.