| |
| author |
Kayla Rockhill
| | title |
Image Approximation by means of Error Minimization
| | abstract |
Function approximation has many uses across many areas of physics,
mathematics, and computer science. It can be used to break up problems
into more manageable pieces and create solutions that are easier to understand. Function approximation can also be used to simplify data which
allows for a faster and easier transmission of the data. This method is
also useful for clearing out any noise from data. An image can be represented as a two dimensional function and can therefore be approximated.
To visualize the results of function approximation and gradient descent,
the methods can be implemented in computing software. The platforms
used in this paper were Octave and Python. The one and two dimensional cases of function approximation was implemented in both Octave
and Python. The one and two dimensional cases for gradient descent were
implemented in Python. Octave is a mathematical based platform while
Python is a more general language with a wider range of applications.
The function approximation method was implemented first in Octave and
was then translated to Python. The translation to Python was done so
that a comparison between the two could be made. Implementation into
Python also allows for the incorporation of hardware since a serial connection between Python and Arduino can be made. Both Python and
Octave provided accurate approximations for various target functions in
the one and two dimensional cases. An extension to using hardware was
started but further work is needed to fix the issues that arose.
| | school |
The College of Liberal Arts, Drew University
| | degree |
B.S. (2021)
|
| advisor |
Minjoon Kouh
|
| committee |
Jim Supplee
Barry Burd
|
| full text | KRockhill.pdf |
| |
