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distance between pixels = a fixed measurement (inch, foot etc)?

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distance between pixels = a fixed measurement (inch, foot etc)

Let's say the distance from my camera to my object is 3 feet. The object is a 6 foot long pole. The pole has a mark every inch. Will the number of pixels between the bottom 1 inch be the same number of pixels of the top 1 inch? Will I be able to say that at a 3 foot distance from my camera and any object that for example 100 vertical pixels is an inch, across the entire vertical view of the image?

I did a simple test. I took a picture of some graph paper, then converted to jpg to a pbm. At the bottom if the image, 30 pixels was 1/10 of an inch. But at the to of the image, it was more like 37 pixels for the 1/10 of an inch.

Was there a problem in the way i did my simple experiment. The jpg was taken with my cellphone. Would I see similar results with my Canon G11 Powershot?