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Attempting to write a definition of DPI has lead me to:

DPI (dots), PPI (points), LPI (lines) all refer to the same concept hereafter referred to as DPI.

DPI is a device dependent measurement. It says, "This is the resolution of this device."

Vector based files are not tied to any one DPI (they expand and contract to conform to a certain resolution).

When that vector based file is rendered to a "bitmap" based format - (bmp, png, tiff, jpg) etc... that "bitmapped" file is created at a certain DPI for printing (or display) on "banding" or "scanline" based devices that output at that specific DPI.

Now, some would argue that DPI does not exist in "bitmapped" based files.

I'm looking for a definition of DPI and how or why it would be considered to not exist in a bitmapped image?

A: 

Certain file formats will contain a DPI value, but it can be ignored for most purposes. What you care about is the ratio of the size in pixels over the size you're displaying or printing. Lower levels generally result in a blurrier picture.

Mark Ransom
A: 

A bitmapped image would specify each dot, and leave the DPI and therefore the rendering up to some other part of the system. I could draw a sixteen by sixteen bitmap up on the wall with a projector and claim im getting one dot per inch. More advanced file formats will specify how to render them because they care how they look.

Karl
+1  A: 

Because a bitmapped image has no physical size, it has no dpi. If you have a file format where physical size is modeled, you can have a (modeled) dpi.

You might want to make a distinction between addressability and covered area. If a dot is not square but a circle, the covered area is larger.

b.t.w. LPI is a different but related concept. A 100 LPI screen for a 600 DPI printer means there are squares of 6*6 pixels available to create 37 different levels of gray (with a 0 degree rotation).

Stephan Eggermont
A: 

If the bitmap image has it's DPI specified we can print/display it as "intended" if we also know the DPI of the display/printer.

I think one should think less about DPI and more about the intended size in cm/inch. One good thing about DPI is that it can give us a measurement of how good the output will look.

mliesen