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While encoding a raw image to a jpeg image, a 8x8 data unit is level shifted, transformed using a 2-D DCT, quantized and Huffman encoded.

I have first performed the Row DCT and then the column DCT and i have rounded the result to the nearest integer. I sent this block to quantization module. While quantizing i have used the following Q Tables. These tables are recommended by IJG for quality factor of 99.

Luma Tables

1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1
1 1 1 1 1 2 2 1
1 1 1 1 1 2 2 2
1 1 1 1 2 2 2 2
1 1 2 2 2 2 2 2
1 2 2 2 2 2 2 2

Chroma Tables

1 1 1 1 2 2 2 2
1 1 1 1 2 2 2 2
1 1 1 2 2 2 2 2
1 1 2 2 2 2 2 2
2 2 2 2 2 2 2 2
2 2 2 2 2 2 2 2
2 2 2 2 2 2 2 2
2 2 2 2 2 2 2 2

During quantization while dividing by '2' i have rounded the result away from zero. Example: 11/2 = 6. Hence an error of +1 will be added to every odd number during de-quantization while decoding.

In another set up i have changed my rounding technique. Here i am rounding the result towards zero. Example: 11/2 = 5. Hence an error of -1 will be added to every odd number during de-quantization while decoding.

In the second case i am getting very less file size (less by almost 100 kb for a 768x512 image) and more PSNR. I was able to explain the less file size by saying that all the AC coefficients which are '1' when quantized by 2 will now become 0 instead of 1. Hence RLE makes the file size lesser. But i am unable to explain why the encoding image quality is increasing. It is increasing by a factor of 2-3 dB and it happening for all the images i tested.

My argument is as the DCT is basically A * DCTmatrix equal error on either side should yield equal loss. But this is not the case here.

Ram
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  • JPEG assumes that the DCT values have been rounded towards 0. Do you treat negative numbers differently or would you produce -6 from -11/2? This different handling of negative values could account for your extra error. – BitBank Feb 24 '12 at 18:04
  • Thanks for the reply. But could you give me a source of the statement where "JPEG assumes that the DCT values have been rounded towards zero". I am treating both the postive and negative values the same way.That is to say either the values are rounded towards zero or rounded away from zero. – Ram Mar 04 '12 at 11:16
  • My point is that the decoder is rounding differently from your encoder. If they matched in their rounding technique, then you would get less error. – BitBank Mar 04 '12 at 16:26

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