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Re: What is the Maximum (linear) NOBs Encode-able into an 8-bit JPEG ?

Detail Man wrote:

Assume linearly encoded image-data.

Is "NOBs" in the title "number of bits"?

JPEG encoding applies gamma-correction (or operates upon already gamma-corrected image-data) prior to RGB > YCbCr color-space conversion.

Should that be Y'CbCr or are you remaining linear for the conversion?

(Even when no Chroma Sub-sampling or Quantization Data Compression are utilized), quantization to 8-bits takes place [within the Quantization Data Compression stage, limiting the processed data to 8-bits prior to loss-less "entropy coding" compression taking place].

I have no idea what "entropy coding" is. Don't really know what "Quantization Data Compression" is either.

To determine how many "extra bits" can be "squeezed-in" (due to the existing gamma-correction), I calculated the derivative of the non-linear transfer-function at the (non-discontinous) lowest value of non-linear compression (0.00313066844250063),

Bad link, error 404

which is 12.7033888061, and divided that value by the derivative of the non-linear transfer-function at the highest value of non-linear compression (which is 0.43958333333). Taking the logarithm to the base 2 of that ratio, the result is equal to an increase of 4.85293290926 [bits].

I'll have to take your word for it, the response is well beyond my ken, sorry

Add that to 8 bits, and I get a total of 12.85293290926 bits - which (may) exceed the (effective, meaningful) bit-depth of a de-mosaiced RAW (or TIFF) file to be JPEG-encoded.

OK

RMS Quantization Error of plus/minus 1/2 LSB equals 1 / ( (2)^(1/2) ) = 0.22675134595 LSB. Taking the logarithm to the base 2, I get a value of -1.79248125036 (relative to unity value of 1.0).

I'll take your word for it. the response is beyond my ken.

So it appears that the (potential) maximum (linearly encoded) input data-range that JPEG encoding can represent equals 12.85293290926 + 1.79248125036 = 14.6454141597 [bits].

An interesting result, thank you. So, now we have calculated a maximum bit range, can we consider a work-flow?

Suppose I work on a raw file with unspecified editing and export a 16-bit TIFF. Do I say that the TIFF data "bit maximum" for conversion to JPEG is 14bits or 15bits? Would that TIFF have to be linear, as I suspect.

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Those calculations do not adequately describe what the image-data "information...capacity" would be.

One of those links includes the camera lens abberations etc. and is again beyond my ken. The other is a discourse on the well-known discontinuity in sRGB gamma correction.

From the title change, it appears that the question is incorrect?