How could I perfectly extract thin pencil line drawing from a uneven greyed background

If you want perfection, redraw it using vector tools. Time consuming but accurate.

Do you know what the sketch represents?  It’s highly ambiguous AFAICT which makes it difficult to judge which lines to ink and which to ignore.  I wonder what the Ai tools would make of it?

Once upon a time I would have tried Topaz Simplify.  I am away from home right now so can’t try it though. I would still be inclined to ask NB Gemini to take a stab at it. 

In the other thread you linked to, some of the ideas involve manually tracing with the vector tools. You said you have “tones of these kind of sketches to extract these lines.” You may find it too time-consuming to do the manual work across tons of sketches.

There is a background removal technique that comes from video editing, which uses layer blending modes. That technique is applied in step 1 of the demo below, combined with other adjustment layers to refine the sketch. These were the steps used:

1. Because the background is uneven, neutralize it using a linear Gradient Fill layer. At each end of the linear gradient, set the gradient stop colors by doing a one-click sample of the background color at that stop. Then apply the Divide layer blending mode. This will remove those exact colors, and the gradient creates a transition across the image. I had to add a third stop to match the middle exactly. (This technique usually uses a Solid Color Fill layer, but Gradient Fill had to be used here because of the uneven background color.)
2. (optional) Remove any remaining color using a Color and Vibrance adjustment layer with Saturation set to -100.
3. (optional) The sketch is a little light, so add a Curves adjustment layer to make it more visible. 
4. The top and bottom of the background were still a little darker than the middle, so I added one more Curves adjustment layer that blows out the white point. To contain the adjustment to the top and bottom, apply a linear gradient to the mask as needed. 

The point of doing it this way is to be easily able to adapt to how each sketch is slightly different, without having to start from scratch each time. 

You can reuse the stack of added layers with other sketches by simply dragging and dropping them to the other documents. Simply adjust the layer settings to match how each sketch background is different. I recommend grouping the layers so that there’s only one thing to drag to the other documents.

To avoid most of this work, go back to the artist and tell them to digitize them on a scanner — no handheld phone pictures. That would make the backgrounds uniform and the sketch lines sharp, not blurry/pixelated. 

You also talked about “extracting” the lines. In the thread you linked to, this is where you were advised to use the vector drawing tools like the Line and Pen. Using those tools means you will always have to draw every line yourself by hand…a lot of manual work per sketch. Depending on why you need those lines, it might help to use the Image Trace feature in Adobe Illustrator (shown below) to automate this process. But if Image Trace does not do what you want, then you might be back to a time-consuming all-manual drawing process in Photoshop or Illustrator. Again, you should be more specific about why you need “extracted” lines and what it is you want to do with them, then maybe we can think of an easier way.

In the demo below I set Image Trace to Black and White, but you could set it to Grayscale if that gets you the line quality you want.

​@Charles91 

You don’t need to select anything. Selecting is never a good idea in cases like this.

First fix the uneven lighting and desaturate to get rid of the yellow color cast.

Then lift the white point with Curves.

This is from the original, with no selection. If you need to darken the fainter lines, use Curves.

The image may be pixelated, but I’m not sure anyone could expect better results from 1) pencil drawing (not illustration apps) 2) scanning (what dpi/ppi?) 3) adjusting the base paper color.

I took your second image, pushed the black slider to 1.0, midtone/gamma slider to 200+.

Other related topics : https://www.photoshopgurus.com/forum/threads/how-to-clean-up-scanned-sketch.47441/?utm_source=chatgpt.com