- Signal Processing is a very advanced which comes very close to its apogee by the undeniable attempts to reach the best performances. This process is noticed by the orientation with the digital signal processing. This article aims to study and design a median filter. Firstly, we highlighted the behavioral study for this filter using MATLAB software. Secondly, we passed to the functional study of the median with MODELSIM software (VHDL).
The digitized image processing has become in recent years
a very important area of research both for image restoration,
image coding or feature extraction for pattern recognition
features. Whatever the sensor used, especially when it comes
to a video camera, the quality of acquired images is often
affected. In general, the images are degraded by the presence
of noise, and the other edges or ridges forms present in some
areas may fade. To remedy this situation, many filtering
techniques have been proposed. The objective of the digitized
image filtering is to eliminate the noise in order to make more
uniform gray levels while preserving the main features such as
edges or ridges. The techniques commonly used include
replacing the gray level of each point of the image processed
by the value resulting from an analysis of local neighborhood
of this point [
This analysis can be predefined, this is the case when using a convolution mask whose size and the coefficients are set at the outset. But, although the noise is eliminated relatively well, it results an attenuation of the transition lines or ridge lines that can be fatal for the extraction of primitives.
In this context, falls the design of median filter. In fact,
median filtering is used extensively in smoothing and
denoising applications for images and video [
II.
The median filter, a sub-class of the rank order filter sorts
the pixels in a region by luminance, finds the median value
and replaces the central pixel with that value [
Rank operations also include the maximum and minimum operators, which find the brightest or darkest pixels in each neighborhood and place that value into the central pixel. By loose analogy to the erosion and dilation operations on binary images, these are sometimes called grey scale erosion and dilation [8].
One important variable in the use of a rank operator is the size of the neighborhood. Generally, rectangular (for convenience of computation) or circular (to minimize directional effects) shapes are used. As the size of the neighborhood is increased, however, the computational effort in performing the ranking increases rapidly.
In fact, a median filter is a non-linear digital filter which is able to preserve sharp signal changes and is very effective in removing impulse noise (or salt and pepper noise). An impulse noise has a gray level with higher or lower value that is different from the neighborhood point. Linear filters have no ability to remove this type of noise without affecting the distinguishing characteristics of the signal. Median filters have remarkable advantages over linear filters for this type of noise. Max Min
Median that an additional sorting is implied if groups of identical adjacent characters appear in the array). This implies that in practice, it is possible to reduce more than the number of steps to solve the suffix problem.
b) Minimum Exchange Strategy: The graph of Fig.3 shows the minimum exchange network required to produce a median from nine input pixels by performing a partial sort. Each node is a two element sort, with the lower input exiting the node on the left, the higher input leaving on the right.
P1 P2 P3 P4 P5 P6 P7 P8 P9 Therefore median filter is very widely used in digital signal and image/video processing applications [9].
A standard median operation is implemented by sliding a window of odd size (e.g. 3x3 window) over an image. At each window position the sampled values of signal or image are sorted, and the median value of the samples replaces the sample in the center of the window as shown in Fig.1.
A 3x3 window 10 14 15 5 3 25 20 11 2
Center pixel replaced with median value 11 2 3 5 10 11 14 15 20
25
Median filters remove isolated pixels, whether they are bright or dark. Prior to any hardware design, the software versions of the algorithms are created in MATLAB. Using MATLAB procedural routines to operate on images represented as matrix data, these software algorithms were designed to resemble the hardware algorithms as closely as possible. While a hardware system and a matrix- manipulating software program are fundamentally different, they can produce identical results, provided that care is taken in development. This approach was taken because it speeds understanding of the algorithm design. In addition, this approach facilitates comparison of the software and synthesized hardware algorithm outputs [10].
In this part, we used two strategy of median filter, the parallel sorting strategy and the minimum exchange strategy.
a) Parallel Sorting Strategy : The parallel strategy leads to a significant reduction compared to the wave sorter approach.
P1 P2 P3 P4 P5 P6 P7 P8 P9
Furthermore, in additional sorts the necessary number of steps for sorting is equal to the number of characters in the biggest group of identical characters divided by 2 (remember Median
And
We will compare two bits ai and bi if the bits ai+1 and bi+1 are equal (It is mean that tei= rei+1 = 1). For that, we supposed that the values of tei are “1” in this table.
In addition, rmxi=1 only if ai>bi. Based on the logic table, we have these equations:
rmx i = tei • a i • bi rei = te i • (a i • b i + a i • b i ) = te i • (a i b i ) (1) (2)
In this functional study, the two strategies are based on principal element. It is the comparison module (CM). The figure Fig.4 shows this module.
Firstly, in order to explain the functioning of this module, A and B are two 8 bits pixels. We will compare every time two bits so we need to 8 modules unitary comparison module (UCM). MCU is based to the following logic table:
The figure Fig.6 shows the logic schematic of CM.
The behavioral study is very important; it shows the operation of this filter and presents its effect on a noisy image. That is why we have taken any image, and then we have the noisy image. Figure Fig.1 shows the original image and the noisy image. original Image Nosy Image rmxi rei 50 100 150 200 250 50 100 150 200 250
Impulse noise is visibly reduced. Median filtering of a pixel P, on a neighborhood V(P) of size (MxN), directs the pixel values of V(P) in ascending order, and assigned the median value at the output of this neighborhood to the pixel P (non-linear operation).
Using the previous example: the pixel values are arranged in ascending order: 0, 8, 8, 8, 8, 8, 8, 8, 255. The median is 8. To this non-linear operation, the pulses 0 and 255 did not affect the median. Median filtering is therefore suitable for reducing impulse noise.
Neighborhood 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 0 8 8 8 8 8 8 8 8 8 8 8 8 255 8 8 8 8 8 8
50
By increasing the filter size, the image becomes blurred. The following figure illustrates four images filtered by various median filters.
Filtered image by the median filter 3x3 Filtered image by the median filter 5x5 Filtered image by the median filter 7x7 Filtered image by the median filter 9x9 Filtered image by the median filter 11x11
We simulated each time a strategy. Indeed, we used an arbitrary matrix (3x3) and we applied our filter on this matrix and we had the following results using MODELSIM using VHDL.
In this paper, we have approached the study of architecture very important in the field of signal processing. This architecture called Median Filter, finds its application in various fields. In this study, we have achieved a behavioral study of this filter which allowed us to determine the suitable settings and the proper functioning of this filter. Based on these parameters established, we simulated the architecture designed by MODELSIM.
As perspective, we aim to optimize the architecture of our filter and study its performances. Then, choose the optimal and efficient structure. Finally, implement this architecture on an FPGA board. (PAMI) 13(6):568-582. [10] D.Dhanasekaran and K.B. Bagan, High Speed Pipelined Architecture for Adaptive Median Filter, European Journal of Scientific Research ISSN 1450-216X Vol.29 No.4 (2009), pp. 454460