# Mathematics in Digital PhotographyResearch Paper

Pages: 3 (925 words)  ·  Bibliography Sources: 3  ·  File: .docx  ·  Level: Master's  ·  Topic: Education - Mathematics

SAMPLE EXCERPT . . .
Compression technology is the primary driver behind the vast expansion of digital photography. Compression allows large amounts of data to be stored in a relatively small area so that more intricate details of the photo can be accurately reconstructed.

Compression is a complicated process that involves several steps. The first step is to convert red, green, and blue color channels to Y, Cb, and Cr channels while partitioning blocks into size 8x8 pixels. For a JPEG image, the compression relies on the Discrete Cosine Transformation, which is exemplified by the equation: C = UBU^T, where B. is one of the 8x8 blocks and U. is a special 8x8 matrix. Applying certain methods of encoding enables compression of about 70% in most instances, or even more in some circumstances. The process can then be inverted to expand the image and view it in full, by finding B. For the previous equation:

B^' = U^T C^'U for each block ("Image Compression," 2011).

One downside of this compression technique for JPEG images is that decoupling can occur causing some parts of the image to appear blocky. While this loss of resolution is often within the range of acceptability, sometimes it is not good enough for certain publications, such as magazines or other media ("Image Compression," 2011). It is possible that the compression algorithms will continue to improve as both the mathematical concepts and computing power rendering them continue to improve.

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## Research Paper on Mathematics in Digital Photography the Assignment

There are many different applications of mathematics when it comes to digital photography. The equations are used for everything from the mathematical rendering of color to the compression of files down to a size that is easily stored and converted back to much more intricate images. The advances in both cameras and the software that helps to edit and alter the images have allowed many people to take pictures with their cell phones that would have required much more expensive cameras just a few short years ago. The realm of the professional photographer has been entered by every person sitting at home with a digital camera and a suite of photo editing programs, such as Adobe. Furthermore, the compression of the photos has allowed them to be easily shared over the Internet and between friends on their cell phones or Facebook pages. This marks a huge turning point in modern photography and one that will doubtless continue to push the boundaries of what is possible with digital cameras.

References

Higham, N. (2007). The mathematics of digital photography. Retrieved from:

http://www.maths.manchester.ac.uk/~higham/talks/digphot.pdf.

Hoggar, S.G. (2006). Mathematics of digital images. Cambridge, UK: Cambridge

Image Compression: How Math Led to the JPEG2000 Standard. (2011). Society for Industrial

And Applied Mathematics. Retrieved from:

http://www.whydomath.org/node/wavlets/basicjpg.html. [END OF PREVIEW] . . . READ MORE

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Mathematics in Digital Photography.  (2012, July 16).  Retrieved November 29, 2020, from https://www.essaytown.com/subjects/paper/mathematics-digital-photography/1810332

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"Mathematics in Digital Photography."  Essaytown.com.  July 16, 2012.  Accessed November 29, 2020.
https://www.essaytown.com/subjects/paper/mathematics-digital-photography/1810332.