In reply to Gordon Stainforth:
> You need to get the right size for your projector (and at 72 or 96 dpi).
Dots per inch only has meaning when talking about a particular physical format display medium; a monitor screen of given physical and pixel dimensions, or printed page with given image physical dimensions. It has no meaning for a digital image (until that image is displayed). I'm sure I've tried to make this point before... ah yes, 8 Sept 2003....
I can take an HD image (1920 x 1080 pixels) and print it on a stamp (with a suitable printing technology; about 2000dpi), or project it on to the side of a building with an HD resolution projector. The visible dpi of these cases would be very different, but the image resolution would remain constant; that of the pixel dimensions of the image.
For the case of a projected image, we need to consider the resolution of the projector; if it can only display a VGA image (i.e. its pixel dimensions are 640x480), there's not much point in using images larger than VGA, since the additional detail cannot be displayed by the projector, and it will only be resampled away. And you're not in control of that resampling, since it's done by the page renderer of whatever tool you're using for your presentation.
On the other hand, if we take an image with a small pixel size (low resolution), and force it to fill a larger pixel dimension (high resolution) screen, each of the source image pixels must be scaled up to fill multiple pixels in the display screen, but giving a blocky appearance.
Strictly, when we talk about resolution, we ought to bear in mind the visual acuity of the eye, which is about 0.5 to 1 minute of arc. So, find the distance between eye and displayed image, calculate the angle each pixel subtends, and, if it's better (smaller) than the visual acuity of the eye, that will be as good an image resolution as you need... Unsurprisingly, the eye's visual acuity, which is determined by the cone density in the fovea, is pretty close to that determined by the Rayleigh criterion for the eye's lens; nature has optimally adapted the eye so the the sense elements are no smaller than the resolution of the optical lens system in front of it.
As for my comments about image sizes last night, I don't know what I was thinking, as I completely neglected the possibility that the image was compressed. And since I've worked on motion JPEG video compression systems in the past, that's a bit of an oversight...
JPEG is lossy, yes. But the degree of loss depends on the quality factor (level of compression). The higher the quality factor, the more image detail will be retained. Image size depends on pixel dimensions of the image, on image complexity (or detail), and on the quality factor. So a JPEG image of a white sheet will be quite small (no detail), whereas a JPEG image of a bed of moss could be quite large (lots of fine detail).
If you start with a raw RGB image, I'd first re-size (scale) the image using a decent resampling filter to fit 1:1 in the allocated image area of the display space (so, if you're going to allocate 1000x500 pixels on the page for the image, scale & crop the image to 1000x500 pixels). Only then would I compress. And I'd play with the JPEG quality factor until I was happy with the image quality and size (sometimes you are limited on the data size of an image). Or use PNG's lossless compression and accept the larger data size.