Why do images 'grow' when imported into Inkscape?

There is a limitation in the way Inkscape imports raster/bitmap images (e.g JPEG, PNG, TIFF images): it cannot read the image resolution. Inkscape assumes a 1-to-1 relation at 90dpi, so any imported image with a different resolution will appear to be scaled. For example, an image of resolution 180 dpi, when imported into Inkscape, will appear twice as big (180 = 90 x 2) in absolute units as it is in other programs. Note that this just scales the pixels of the image, but never adds or removes any pixels.

When exporting back to a PNG image, changing the resolution will only resample the image, not resize it. The only way to keep the image at the same size is to scale it inside Inkscape, once it is imported. For this you need to know the size (in pixels, cm, inches,...) of the image you import. Then select it and in the selector's toolbar, click the lock between the width and height fields, select the unit of the image size and enter either the width or height in the appropriate field. When exporting, if you don't want to lose information from your image, use a resolution larger or equal to the resolution of the original image.

Example: Import an image of size 800*600 pixels and resolution 150 dpi. It will appear to be 1333 pixels wide and 1000 pixels high in Inkscape. Select it, click the lock in the selector's toolbar, enter 800 in the width field. Add some stuff on the image. Export the document to PNG with resolution 150 dpi. The exported image will be identical to the original one expect for the stuff you added on it.