Mean Filters :: essays research papers

  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚   Develop a Program that will implement the non-linear filters Abstract: The purpose of this project is to develop a program that implements non-linear filters. For this project we will research the mean filter and the Median filter. Introduction: The Idea of this project is to generate and image and implement different types of noise, then add them together and run them through a non-linear filter and see how the filter affects the output image. First we must locate and image then add the noise and run the image thru a non-linear filter to successfully remove all sort of noise corruption. We will compare two filters, the mean filter and the median filter, for a few simple cases. The purpose of the filtering operation is assumed to be an effective elimination or attenuation of the noise that is corrupting the desired images. In this report we will consider only the two-dimensional cases (image). The effects are better visualized with images. Background on non-linear filters: Non-linear filtering has been considered even in the fifties, since then, the field has seen a rapid increase of interest indicated. In our case the Multistage medians and median filters have been rather extensively studied from the theoretical point of view in the beginning of the seventies in the Soviet Union. These filters have been independently reinvented and put into wide practical use around 15 years later by western researchers. Non-linear FIR filters cannot be expressed as a linear combination of the input, but as some other (non-linear) function on the inputs. A simple example of a useful non-linear filter is a 5th order median filter. This is the filter represented by: This type of filter is extremely useful for data with non-Gaussian noise, removing outliers very efficiently. A significant amount of research effort has gone into the development of appropriate filters for various purposes. Statistics has taken a different tack to the problem: early approaches were similar to moving average filters. However, rather than using a simple moving average, the early work realized that linear regression could be used around the point we were trying to estimate; in other words, rather than simply averaging the five values around a point, a linear fit of the points, using a least squares estimate, could be used to give a better-looking result. Furthermore, we realized that 1)  Ã‚  Ã‚  Ã‚  Ã‚  Linear regression could be applied, so could other shapes, in particular splints. 2)  Ã‚  Ã‚  Ã‚  Ã‚  The weights for the instances used in regression could be changed.