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'[OT]: Megapixels rerquired for document storage'
2002\02\09@051035 by

I wondered what digital camera resolution I required to archive documents of
various sizes.
This is simply stating the numerically fairly obvious in a way which may be
useful to others.
(Many could derive this themselves in 2 shakes of a lambs tail (if NZers
:-) ) - this saves the shaking.)

SUMMARY

This assumes the camera image is in approximately "A" format (long side is
1.414 x short side)

1.    Megapixels required to store an image of width W and "A" format aspect
ratio (A4, A5 etc)

MP = 1.4 x W^2R^2/1000000        ... [1]

W = width in units of your choice
R = resolution in pixels per unit of width
MP = megapixels

Rearranging

2.    Resolution required in pixels per unit width for an A format document
of width W

R = sqrt [ (MP x 1000000) / (1.4 x W^2) ] ... [2]

or        A4 sheet, 1 MP ==> 105 dpi
A4 sheet, 3 MP ==> 300 dpi

Conclude that 3 MP is fairly desirable if a camera is to be used for this
purpose.

___________________________________

Discussion:

An A4 sheet (or any sheet in the A series) has a height which is sqrt(2) =
1.414 greater than its width.
If short side has length L then area is L x L x 1.4

For a resolution of R dots per unit length (lets start with dots per inch =
dpi as it's commonly used) then total dots =

(L x R) x (L x R) x 1.414 = 1.414 x L^2R^2 = number of pixels

If this page is digitised this becomes the number of pixels resolution
needed for a given L and R or, as more commonly expressed, if we divide by 1
million, the megapixel rating required.

Megapixels = MP = 1.4 x L^2R^2/1000000        ... [1]

Rearranging        R = sqrt [ (MP x 1000000) / (1.4 x L^2) ] ... [2]

(1,000,000/1,414 = 707,000 near enough

Equations 1 & 2 are useful for determining either how good a "camera" we
need to archive a given document or how good a job a given "camera" will do.

A standard A4 sheet is 8" wide.
How many DPI will I get in a 1 MP image?

R = sqrt (707000/64) = 105 dpi

This is about poor fax quality

What about with a 3 MP camera
A 3 appears inside the sqrt so the figure increases by root(3) = 1.732 to
This is early laser quality but without the edge rounding and line smoothing
used in all modern laser printers (added first by HP AFAIK.)
ie a 3 megapixel camera will provide a reasonable copy of an A4 document but
the quality will still be less than ideal.

A 3 MP image saved at 1 byte per pixel (8 bit grey scale) requires 3 MByte
storage per image with no compression. JPEG will reduce this to 100k-300k
for a typical document with not too much quality loss.

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