Today there is an increasing need for an image transfer in : e-mail, internet, cellular phone and so on . Transmission rate depends on size that effected by the quality.
Abstract
Today there is an increasing need for an image transfer in : e-mail, internet, cellular phone and so on . Transmission rate depends on size that effected by the quality. Hence if we try to reduce the time that takes to transmit the image we will have to use communication channel with wider bandwidth (faster transfer rate). Usually there is a bandwidth limit, that’s why images are transmitted with a lower resolution (lower quality). In this work we are trying to find a suitable method for image enlargement. Low resolution ® high resolution (low quality ® high quality).
Block diagram
– We get low resolution image, filter it in case that it noisy , enlarge it with spline and improve the image with one of the methods
for edge enhancement mentioned below . Finally we have high resolution image.
Solution
After testing number of enlargement methods we chosen Spline.
Spline interpolation consists of the approximation of a function by means of series of n degree polynomials over adjacent intervals with continuous derivatives at the end-point of the intervals.
The continuous estimate of samples is : 
When 
n degree base spline functions , and c[i] spline coefficients of function 
calculated such way that in original points: 
, 
When found it can be sampled at any given frequency.
For filtering we used diffusion that is based on PDE : 
Inverse diffusion was used for edge enhancement:
where 
, Kf is given by user and Kb is a local value that is most suitable for the edges in the close area.
The second edge enhancement algorithm is also based on PDE :
, 
Kf given by user ; This is the alternative way for edge enhancement.
Conclusions
- The algorithm was found to be efficient and the results were satisfactory. In order to achieve the best results the algorithm has to be implemented in C/C++ environment, because in MATLAB it doesn’t get enough resources (like memory etc.)
- Two methods of edge enhancement can be used for a different type of images . The inverse diffusion is used for photographs, images with complicated texture. And the second method is very efficient on synthetic pictures , animations ,texts etc.
Results
Acknowledgments
Specially thanks to our supervisor Guy Gilboa for his support throughout the project .
The project was supported by the “Ollendorff Minerva Center” fund.