Remove background of a single contiguous color

Question

I have a PNG image which has two figures, bounded by black lines, against a purely white background. My figures have also some white "pixels" (dots, points) inside, not contiguous with background "pixels". Use of the word pixel is not meant to be technically strict. I mean to get an image with transparent instead of white background, same as if it were generated from the get-go, by removing all contiguous white pixels. This seems something attainable. Preferably with Inkscape.

I tried this, but the result was not good.

Later I found

Remove Background in Inkscape

Answer 1

I understand your desire to work in Inkscape, that is OK, however, I would edit the imported PNG in bitmap editor first, then use it in Inkscape for vector-like work.

For example in Gimp:

1) Open bitmap file

2) In the layers, right-click the only layer there and select "Add alpha channel" (this will allow transparency)

2) Click magic stick selection tool

3) Click to the white area (or more, with shift) you want to make transparent and press delete

4) Press CTRL+E for exporting edited bitmap and save as new PNG.

5) Use that PNG in Inkscape.

EDIT:

You've mentioned automated processing in your comment. You can do automated processing with GIMP (https://www.gimp.org/tutorials/Basic_Batch/). However I haven't done that before; even though I use GIMP for desktop editing, I used ImageMagic for batch conversions.

Here is how you batch-remove background with ImageMagic: https://imagemagick.org/Usage/masking/#bg_remove