How to change the dpi of differently sized images within a pdf in order to realise a common "print size" for every page? - pdf

Question

I am new to the world of raster images, so I will first explain which definitions I use and hope that I will use them right:
- geometry (the total number of pixels of the image %w * %h)
- resolution (pixels per inch / ppi)
- size or "print size" (the display size (e.g. in inches) on screen or printer)
I have some PDF documents containing raster images of different geometry. When opening with evince they therefore all display (and I guess potentially print) with different sizes. I would like to define the print size within the pdf so that evince (or any other viewer) would display every page with the same size when opening the document.
How could this be realized? Geometry and print size of the image are linked by the resolution as far as I understand. Currently one of my pdf's shows to following ImageMagick:identify output:
$identify -units PixelsPerInch -format "%w x %h - %[resolution.x] x %[resolution.y] - %[fx:w/72] x %[fx:h/72] in\n" example.pdf
geometry - resol. - print size -
538 x 375 - 72 x 72 - 7.47 x 5.20 in
546 x 381 - 72 x 72 - 7.58 x 5.29 in
1210 x 1681 - 72 x 72 - 16.80 x 23.34 in
1658 x 1166 - 72 x 72 - 23.02 x 16.19 in
542 x 365 - 72 x 72 - 7.52 x 5.06 in
1673 x 1169 - 72 x 72 - 23.23 x 16.23 in
I would like to realize a constant print size (column 3) and I do not want to change the geometry of the image/ avoid to re-compress it, so that it does not loose quality. In order to proceed it seems to me that I need to understand the following which I cannot find any information about:
1) Which of these three values is actually saved in the pdf document and which one is calculated by identify?
2) Which software (and how) would allow me to batch process a number of pdf files in order to achieve my goal.
3) Guessing that geometry and resol are values of the pdf file and print size is derived from it, the software would need to calculate a resolution value for each image so that print size would qual over all pages?
Thank you very much!
Cheers,
Benjamin

Answer 1

1) I think only the first two are actually stored in the PDF, but the third value (print size) is directly related to resolution (538x375) and pixel density (72ppi aka 72dpi), so it can easily be calculated anyway.
2) It seems like you're going about this a little backward. There are plenty of applications that are perfectly suited to controlling image layout and printing. Adobe Illustrator is one of the most common and there are some free ones, too. But these are going to involve loading the images, visually arranging them on the page and adjusting the print sizes visually, rather than programmatically.
2) If you did want to do this programmatically, though, I think you're going to have a hard time finding software to solve that problem. GIMP and Photoshop both have some batching capability, and I know GIMP has a fairly robust CLI, so you might be able to use that.
3) Yes, you'll start with the print size you want, divide the number of pixels by the number of inches to get ppi/dpi.
NOTE: Keep in mind that dpi goes both directions. If you have a 200 x 300 image and a 400 x 400 image, and you want them both to print 10 inches square, then you're going to distort the 200 x 300 image, stretching it horizontally. The 200 x 300 image will also look poorer quality than the 400 x 400, because you have fewer pixels to work with.
For these and other reasons, I highly recommend a visual approach, rather than a coding approach.
Good luck!