Is there a way to extract handwriting?

As the question has a recommended answer, I’ll offer a different perspective that you, or anyone who wanders here, may find of use. If you have an iPad and Apple Pencil you can stay in the digital realm and use the native Notes and Preview apps. As an example:

Open the Notes app on iPad. Create a new note. If you want to use guidelines, tap the Share button, tap Lines & Grids and make a selection. Tap the Markup button and select pen, marker or pencil. Select the stroke thickness and opacity. Tap the close button to hide the tools. Write your note.

If you’ve enabled Notes sync for iCloud, the note will sync to your Mac. Open the Notes app on your Mac. Click and hold the handwriting in the synced note and drag it to the Desktop. This will create an image file on the Desktop.

Open the file in Preview. If Preview is the default application, double-click the file to open it. Press the Command + A keys to select all. Press the Command + C keys to copy. Close the image file. Open the image file you want to overlay with your handwriting. Press the Command + V keys to paste your handwriting image. Tap the handwriting image to bring up the blue control handles. Drag a control handle to resize. Use the hand cursor to reposition. If you have a trackpad you can rotate two fingers to rotate the handwriting image. When satisfied, save the file. Keep in mind that once the file is saved and closed you won’t be able to make further adjustments.

If you don’t have an iPad and it’s not a requirement to use your own handwriting, but you still want the warmer aesthetic of handwriting, you can use an online handwriting font generator to create an image file to use for overlay. Follow the relevant steps above to copy, paste and manipulate in Preview.

If you want to separate the writing from its background (the paper and the printing showing through from the back) you'll need bitmap graphics software (it isn't a Mojave question). Among the many options that you could use: GIMP is free, Photoshop isn't.

For an image with this much contrast, you could select the handwriting part by selecting for black pixels with a fairly low tolerance. That would give you the handwriting against a transparent background.

If you wanted to keep a background, you could re-map the levels or adjust contrast and brightness to make the background uniformly white.

To separate the image from the background you use the 'magic wand' selection tool. This is available in the free and built-in Preview tool as well. You then press the delete key on the keyboard and it will delete i.e. 'mask' the background.

You would do this on either a PNG format image or a JPEG2000 format image as these formats unlike ordinary JPEG support using an alpha mask.

Since you've got Photoshop, here's a guide to the selection process I was thinking of: https://helpx.adobe.com/photoshop/using/making-quick-selections.html

I'm not certain if this meets your needs but Scan or take a picture of the page. I just did a screen capture then of the area of the handwriting I wanted and saved it as an image. If there is something else you intended please let us know.

Another way, if you're writing these yourselves, is to skip the paper step and write them directly in Photoshop, especially if you've got a graphics tablet, are especially fluent with a mouse, or can do it on an iPad.

You would also need to inquire about any licensing, copyright or ownership issues, especially if the text/image is not commercially available. Also see the licensing agreement for Mojave (which is owned by Apple and you are only granted a license to use it).

https://www.apple.com/legal/sla/docs/macOS1014.pdf

I didn't know that Preview had a magic wand! Thanks for drawing attention to it.

A couple things to consider if going the analog to digital route is resolution and the weight of the line for legibility...