Removal of noise by Median and Relaxed median filter
Volumn 3

Removal of noise by Median and Relaxed median filter

Sangita kulkarni

Department of Electronics (VLSI) .

Jhulelal Institute of Technology, Nagpur,India

Prof.Anil Bavaskar

Department of Electronics (VLSI) .

Jhulelal Institute of Technology, Nagpur,India


Digital images are normally corrupted by many types of noise.In dirrerent types of images there are different noise are present which shows poor quality of image.The noise in the image is the random variation of brightness.There are different types of noise salt and pepper noise,Gaussian noise,speckle noise etc.Noise removal is necessary to obtained the better quality of image. Many filtering technique are used to remove the noise from the image.Many linear and Non-linear technique.The non-linear filtering is better than linear filtering for removing noise in the presence of edges.In this paper we are using non-linear filtering.It shows how to remove salt and pepper noise from an image using a median filter and relaxed median filter to allow comparision of the result.These are most widely used filtering technique in digital image processing because it preserve edge while removing noise.

Key  words Median Filter ,Relaxed Median filter , Non-linear filtering ,Linear filtering, Impulse noise.  


Digital images are normally contains impulse noise also called as Salt and Pepper noise which take only the maximum and minimum value in the range (0,255). So even a small percent-age of impulse noise distorts the image greatly.Salt and pepper noise is impulse type of noise. Impulse noise removal using the standard Median Filter and it’s variants are analyzed extensive simulations have been carried out on a set of standard gray scale images[7].Noise can be added to the compound images during image capturing or image transmission .Different filtering technique are presented to remove noise. This paper  proposes relaxed median filter perform better for compound image[1]-[6]. Impulse noise is a basic noise which  present in medical image as well as binary and gray images which causes blurring  in the image, edge being distorted and  poor quality. so it is necessary to remove such noise from improved median filter is proposed. Clustering  performance of FCM algorithm on different median filter is analysed [8]. One of  the most  popular solution to deal with impulse noise is use non-linear filtering and works in spatial domain .The Non- linear filter compared to Liner one shows certain advantages :Edge  preservation and efficient noise attenuation with robustness against impulsive –type noise. In this paper we are using Median filter and Relaxed Median filter .The trade off   between noise elimination and detail preservation is widely analyzed.The Relaxed filter is obtained by relaxing the order statistic for pixel substitution. Noise attenuation properties as well as edge and line preservation are analyzed statistically. It is shown that relaxed median filter preserve details better the standard median filter and remove noise better than other median type filters[4]. Image filtering algorithms are applied on images to remove the different types of noise that are either present in the image during capturing or injected into the image during transmission. This paper deals with performance comparision of median and wiener filters in image de-noising for gaussion noise,salt and pepper, and speckle noise[3]. The method of wavelet thresholding for removing noise is used. This work proposes a spatially adaptive  wavelet thresholding method based on context modeling which yields superior image quality. In context–modeling it enbles a pixel wise estimation of signal variance and thus of best threshold[5].

2 .Median Filter:

Median filtering is a non-linear operation often used in image processing to reduce “salt and pepper” noise. A median filter is more effective than convolution when the goal is to simultaneously reduce noise and preserve edge .Median filters uses median value in it’s filtering process. A median filter works in a window of size WM X WN where WM and WN are both odd. Median filter provides better performance only at lower noise densities but for high noise density they can not perform well .T he median filter has been proven to be very useful in many image processing applications. In a median filter a window slides across the data and the median value of the samples inside the window is chosen to be the output of the filter. The median filter replaces the center pixel of the window (eg.(3×3)etc) considered by median of the window. If the Center pixel is either ‘0’(pepper) or’255’(salt).It is replaced by median of the window  which will be other than 0 or 255.It works as follows. window ={23,32,41,255,45,52,23,32,41} The window sorted in ascending order = {23,23,32,32,41,41,45,52,255} Median is the mid value after sorting. i.e. 41

Median filtering is non-linear method used to remove noise from images while preserving edges.It is particularly effective at removing ‘salt and pepper’type noise.The Median Filter works by moving through image pixel by pixel replacing each value with the median value of  neighbouring  pixel which is called window which slides pixel by  pixel over the entire image.If the window has an odd number of entries then median is simple to define.It is just the middle value after all the entries in the window are sorted numerically.For an even number of entries there is more than one possible median.Even though it is perfect filtering method it may remove fine details sharp corners and thin lines.  Replace each pixel value with the median of the gray value in the region of the pixel.

  1. Take a 3×3 region centered around pixel ( i ,j).
  2. Sort the intensity values of the pixel in the region into ascending order.
  3. Select the middle value as the new value of pixel( i, j).

With this method there is No reduction in contrast across steps since output value available consist only of those present in the neighborhood. Median filtering does not shift boundaries. Since the median is less sensitive than the mean to extreme value, those extreme values are more effectively removed.

.In this paper we introduce Relaxed Median filter having  similar properties as above mentioned filter. While being simpler and easier to implement them .


It works as follows:-  Two bounds l and u – lower and upper respectively- define a sublist inside the [Wi] ,which contains the gray levels that we assume to be good enough not to be filtered .If the input belongs to the sublist ,then it remains unfiltered otherwise the standard median filter is output. The performance of the relaxed median filter should be described by using some statistics of the output. However this is not possible in general .Since accurate statistical description of the input images are difficult to obtain. But it is still possible to obtain the  probability distribution function of the output by making simple assumption about the original image. In this sense, the noise attenuation can be well assessed from homogeneous originals and detail preservation can be assessed from pure edge and lines.

The filter is obtained  by relaxing the order statistic for pixel substitution .Noise attenuation properties as well as edge and line preservation are analyzed statiscally .The trade off between noise elimination and detail preservation is widely analyzed .Let m=N+1 and l,u such that 1<l <m<u< 2N+1.The relaxed median filter with bounds l and u is defined as

Yi=RM lu {Wi}= {XiifXiE{[Wi](l),[Wi](u)}

                            {[Wi](m) otherwise

Where [Wi](m) is the median value of the samples inside the Window Wi.

It is  shown that relaxed median filter preserve details better than standard  median filter and remove noise better than other median type  filter.


In this case, we have taken  a original image and then we added some percentage of salt and pepper noise to them and then by using Median  filter and Relaxed median filter we can remove the noise and compare the result. we get  these  outputs.

Fig 1 Original Image
Fig. 2 Corrupted noisy image

Fig. shows comparative studies of different filters for salt and pepper noise. (1)Original image (2) Corrupted noisy image (3) Median filtered denoised image (4) Relaxed Median filtered denoised image

Fig 3 Median filtered denoised image
Fig 4 Relaxed Median filtered denoised image


This paper attempts to remove salt and pepper noise from images using Median and Relaxed Median filter .While comparing  these  filter we concluded  that Relaxed  Median Filter gives better result.


  1. D. Maheswari et. al., “Noise removal in compound image using median filter”(IJCSE) International Journal on Computer Science and Engineering,Vol.02,No.04,2010, 1359-1362.
  2. Md. Mosaddik Hasan, Md. Sohel Parvez, Jahirul Isalm, Shibnath Datta, “(IJECT) International Journal on Electronics & Communication Technology ” Vol. 2, SP-1, Dec . 2011 ISSN : 2230-7109.
  3. Suresh Kumar, Papendra Kumar, Manoj Gupta, Ashok Kumar Nagawat, “Performance Comparison of Median and Wiener Filter in Image De-noising”,International Journal of Computer Applications (0975 – 8887) Volume 12– No.4, November 2010.
  4. Abdessamad ben hamza, Pedro l luque-escamilla, Jos´e mart´inez-aroza, Ramon roman-roldan, ” Removing Noise and Preserving Details with Relaxed Median Filters” Journal of Mathematical Imaging and Vision 11, 161–177 (1999) Kluwer Academic Publishers. Manufactured in The Netherlands.
  5. Shi Zhong, ”Image Denoising using Wavelet Thresholding and Model Selection”, International Conference on Image Processing Proceedings, 2000, Volume: 3, 10-13 Sept
  6. Zinat Afrose,”Relaxed Median Filter:A Better Noise Removal Filter for Compound Images”Engg.Journals publications,July 7,2012..
  7. E.Jefamalar,Leavline,D.Asir,Gnana Singh,”Salt and Pepper Noise detection and Removal in Gray scale  images” International journal of signal processing,vol 6,no.5 2013
  8. J.M.Waghmare,B.D.Patil,”Removal of Noises from Images by Improved Median filter and Analysis of FCM Algorithm”,International Journal of Innovative Research and Development,vol 3,No.4,April 2014 ISSN,2278-0211.

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