This issue is getting very muddied up.  While everything Laurie says
below is correct, there is one point which might be lost on some
people.  Changing the image size in Photoshop without checking the
"resample" box, does absolutely nothing to the file outside of
Photoshop. It is an internal function that simply changes the display
within Photoshop, and how Photoshop see the size of the image relative
to the screen presentation and the printed size.  You will find outside
of photoshop, you still have the same file size image, and the image
will appear in whatever the dimensions the other program uses as a
default.  For instance, if you are using web graphics, the image will be
displayed at the nominal 72 or 86 or 90 dpi (depending on your screen
resolution) and will expand to accommodate that dpi, based upon the
pixel dimension of the image.

So, as an example, if I take a 10" square image, which is 240 dpi, and I
change it using image size (without the resampling box checked) to 1"
square, the new image will now (within photoshop) show as a 1" square
image at 2400 dpi.  The file size will be identical, since there are
still the same number of pixels in the image.
If I print that image, it will print as a 1" square image, but since the
printer can only use somewhere between 200-400 dpi (in general) the rest
will be tossed during spooling, but it will be a very slow spooling
process. The image will be no sharper in the print then had it been
resampled to 1" x 1" at 200-400 dpi.  In fact, it might even have been
sharper, since most printer spoolers do a poor job of downsampling.

If I take that 1" x 1" 2400 dpi image, and place it on my web page, it
will appear on the web as an image about 33" x 33" (using the 72 dpi
screen resolution often quoted).

So, if your intention is to actually reduce the "size" of the image, for
web graphics, or for logical spooling for printing, or for storage, you
must use resampling, which is a form of interpolation.  But, it just so
happens Photoshop has a very well behaved form of resampling which does
a very nice job.

Art

Laurie Solomon wrote:
> 
> Resizing in Photoshop is not interpolation and does not use Bicubic,
> Bilinear, or any other resampling formula as long as you do not check the
> resampling check box in the dialog box.  It just resizes the image which
> will effectively increase or decrease the resolution without interpolation.
> However, if you do check the resampling box, then you will be using a form
> of interpolation depending on your choice of interpolation method in the
> preferences file, which will either add new additional pixels so as to
> increase the actual resolution or will delete actual existing pixels so as
> to decrease the actual resolution.
> 
> The increase and decrease in effective resolution which takes place when you
> resize with the resampling box left unchecked is merely a function of
> increasing or decreasing the number of inches in the dpi formula but not the
> number of dots in the dpi formula such that by doubling the image size you
> have 1/2 the dot per inch and by halving the image size you have effectively
> doubled the dpi.
>


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