15-03-2010, 06:19 PM
Noise Reduction by Fuzzy Image Filtering
A new fuzzy filter is presented for the noise reduction of images corrupted with additive noise.It has two stages of operation: The first stage computes a fuzzy derivative for eight different directions. The next stage uses these fuzzy derivatives to perform fuzzy smoothing by weighting the contributions of neighboring pixel values.
INTRODUCTION
Fuzzy techniques have been applied in several domains of image processing like filtering, interpolation, and morphology. fuzzy techniques for image filtering are described here. Most fuzzy techniques in image noise reduction mainly deal with fat-tailed noise like impulse noise and are able to outperform rank-order filter schemes (like the median filter). a new technique for filtering narrow-tailed and medium narrow-tailed noise by a fuzzy filter is describe din this paper.
II. FUZZY FILTER
The general idea behind the filter is to average a pixel using other pixel values from its neighborhood, but simultaneously to take care of important image structures such as edges.distinguishing between local variations due to noise and due to image structure is a further objective of this filter. for each pixel we derive a value that expresses the degree in which the derivative in a certain direction is small.for each direction corresponding to the neighboring pixels of the processed pixel , Such a value is derived by a fuzzy rule.
A. Fuzzy Derivative Estimation:
for filtering we want a good indication of the edges, while to find these edges we need filtering.It is similar to a chicken-and-egg problem;In our approach, we start by looking for the edges. We try to provide a robust estimate by applying fuzzy rules.
III. ADAPTIVE THRESHOLD SELECTION:
Instead of making use of larger windows to obtain better results for heavier noise, we choose to apply the filter iteratively. The shape of the membership function 'small' is adapted each iteration according to an estimate of the (remaining) amount of noise.Here it is assumed that a percentage of the image can be considered as homogeneous and as such can be used to estimate the noise density.Compared to the direct calculation of the variance of (a part of) the image, the current scheme distinguishes between blocks containing mainly noise and blocks containing both image structure and noise. This is done by the sorting operation of the histogram operation on the homogeneity values.As a result, the estimate of the noise variance is based on smooth blocks only, for as long as the initial hypothesis remains true.
IV. RESULTS:
The proposed filter is applied to grayscale test images after adding Gaussian noise of different levels. Such a procedure allows us to compare and evaluate the filtered image against the original image. the proposed filter performs verywell. Only the fuzzy median (FM) gives a better MSE. filter is able to preserve the very small details (such as the narrow ropes).
for full details, refer this pdf:
http://citeseerx.ist.psu.edu/viewdoc/dow...1&type=pdf
