How Does A Median Filter Work

Median Filter

DT-Binarize

İmren Dinç , ... Marc 50. Pusey , in Emerging Trends in Image Processing, Calculator Vision and Blueprint Recognition, 2015

iii.2.1 Median filter

Median filter is one of the well-known social club-statistic filters due to its adept functioning for some specific noise types such as "Gaussian," "random," and "salt and pepper" noises [ three]. Co-ordinate to the median filter, the center pixel of a M × M neighborhood is replaced by the median value of the respective window. Notation that noise pixels are considered to exist very dissimilar from the median. Using this idea median filter can remove this blazon of noise bug [iii]. We use this filter to remove the noise pixels on the protein crystal images earlier binarization performance.

Read full chapter

URL:

https://www.sciencedirect.com/science/article/pii/B9780128020456000120

Multidimensional Systems: Bespeak Processing and Modeling Techniques

Makoto Ohki , ... Anastasios N. Venetsanopoulos , in Control and Dynamic Systems, 1995

A Median filters

Median filters are useful in reducing random noise, peculiarly when the noise aamplitude probability density has large tails, and periodic patterns. The median filtering procedure is accomplished by sliding a window over the paradigm. The filtered paradigm is obtained by placing the median of the values in the input window, at the location of the center of that window, at the output epitome. The median is the maximum likelihood estimator of location in the case of Laplacian racket distribution. For relatively uniform areas, the median filter estimates the gray-level value, with item success in the presence of long-tailed noise. As an edge is crossed, one side or the other dominates the window, and the output switches sharply between the values. Thus, the edge is not blurred. The disadvantages of such filters are that in the presence of modest indicate-to-noise ratios they tend to break up image edges and produce false noise edges, and they cannot suppress medium-tailed (Gaussian) noise distributions.

Median filters of both recursive and not-recursive types have been considered in the literature. Recursive median filters were shown to exist more than efficient than those of the non-recursive type. A useful special class of median filters are the separable median filters. These filters are specially piece of cake to implement, by performing successive operation over the rows and columns of the image.

Bovik, Huang and Munson [79] introduced a generalization of the median filter. They defined an order statistic (Bone) filter, in which the input value at a point is replaced by a linear combination of the ordered values in the neighborhood of the point. The class of OS filters includes every bit special cases the median filter, the linear filter, the α-trimmed mean filter, and the max (min) filter, which uses an extreme value instead of the median. For a constant betoken immersed in additive white noise, an explicit expression was derived for the optimal OS filter coefficients. Both qualitative and quantitative comparisons suggest that OS filters (designed for a abiding signal) can perform better than median and linear filters in some application.

Lee and Kassam [75], introduced another generalization of the median filter, which stems form robust estimation theory. According to different estimators the L filter and M filter were proposed, in which the filtering process uses a running L estimator and an M estimator, respectively. Considering the L figurer uses a linear combination of ordered samples for the interpretation of location parameters, the employ of a running L estimator for filtering resembles the use of an Os filter. Another variation of median filters is the modified trimmed mean (MTM) filter. This filter selects the sample median from a window centered around a point and then averages merely those samples inside the window shut to the sample median. MTM filters were shown to provide good overall characteristics. They tin preserve edges fifty-fifty better than median filters. The aforementioned authors also introduced a double-window modified trimmed mean (DWMTM) filter. In this filter a minor and a big window are used to produce each output betoken. The pocket-size window results in the retention of the fine details of the signal and the large window allows adequate additive noise suppression. The DWMTM filter has practiced performance characteristics. Even so, information technology often fails to shine out the signal dependent components. All these previous filters can be hands adjusted to 3-D filtering by defining a block mask (n ₁, north ₂, northward ₃), which can play the role of the traditional window of 2-D filters.

Read full affiliate

URL:

https://www.sciencedirect.com/science/commodity/pii/S0090526705800386

Video signal processing

In Digital Video and HD (Second Edition), 2012

Median filtering

A median filter is a nonlinear filter in which each output sample is computed equally the median value of the input samples nether the window – that is, the result is the center value after the input values have been sorted. Ordinarily, an odd number of taps is used. Median filtering oftentimes involves a horizontal window with 3 taps; occasionally, 5 or even seven taps are used. Sometimes spatial median filters are used (for case, iii×3).

In the rare case of an even-order median filter, the output is the average of the central 2 samples after sorting.

Any isolated extreme value, such as a large-valued sample due to impulse noise, volition never appear in the output sequence of a median filter: Median filtering can exist useful to reduce noise. Withal, a legitimate farthermost value volition non be included! I urge you to use great caution in imposing median filtering: If your filter is presented with image data whose statistics are non what you expect, you lot are very likely to degrade the paradigm instead of improving it.

Read full affiliate

URL:

https://world wide web.sciencedirect.com/scientific discipline/article/pii/B978012391926750031X

A cognitive perception on content-based image retrieval using an advanced soft computing paradigm

Chiliad. Martin Sagayam , ... Omer Deperlioglu , in Avant-garde Car Vision Paradigms for Medical Image Assay, 2021

3.2 Pre-processing

The pre-processing stage is the essential pace towards retaining the important information. The filtering and preparation of image will take a considerable amount of processing time. Epitome pre-processing includes cleaning, normalization, transformation, feature extraction and selection, etc. In social club to the improve the quality of the image, the raw paradigm is preprocessed and so equally to improve the efficiency and ease of the mining process. Preprocessing has a major impact on the quality of characteristic extraction and a profound output of image analysis. A dataset has a common feature descriptor method that corresponds to mathematical normalization in preprocessing.

3.ii.1 Median filtering

The median filter is the filtering technique used for noise removal from images and signals. Median filter is very crucial in the image processing field equally information technology is well known for the preservation of edges during noise removal. The prior duty of the filter is to browse every input data interceding the overall entries with the median function known equally "window" method. The window tends to exist a piffling fleck complex over the college-dimensional signals. The number of medians is set co-ordinate to the number of windows, falling under odd and fifty-fifty categories.

Read full chapter

URL:

https://www.sciencedirect.com/scientific discipline/commodity/pii/B978012819295500007X

Basic Image Filtering Operations

East.R. DAVIES , in Machine Vision (3rd Edition), 2005

three.eight.iii Shifts Arising with Hybrid Median Filters

Although median filters preserve edges in digital images, they are also known to remove fine image particular such as lines. For example, three × 3 median filters remove lines i pixel wide, and v × 5 median filters remove lines two pixels wide. In many applications such equally remote sensing and 10-ray imaging, this is exceedingly of import and efforts have been made to develop filters that overcome the problem. In 1987, Nieminen et al. reported a new class of "item preserving" filters. These employ linear subfilters whose outputs are combined by median operations. At that place are a great multifariousness of such filters, employing dissimilar subfilter shapes and having the possibility of several layers of median operations. Hence we cannot describe them fully here in the infinite available. Although these filters are aimed particularly at retentiveness of line item and are readily understood in this context, they turn out to accept some corner preserving properties and to exist resistant to the edge shifts that ascend when there is a nonzero curvature.

Perhaps the best of the filters in the new form, from the betoken of view of preserving border position, is the two-level "bi-directional" linear-median hybrid filter termed 2LH+ (Nieminen et al., 1987). Its operation in a 5 × five neighborhood may be illustrated every bit follows. It employs the subfilters A to I in the v × v region:

pixels marked as beingness in the same subfilter having their intensities averaged, and dashed pixels beingness ignored. Nonlinear filtering and then proceeds using two levels of median filtering, with the final middle-pixel intensity being taken as:

(3.18) ${\text{A}}^{\prime }=\text{med(A,med(A,B,D,F,H)},\text{med(A,C,East,M,I))}$

Here we ignore the line-preserving properties of this filter and concentrate on its corner-preserving, low-edge-shift characteristics. Information technology is quite easy to see that the v × 5 regions

$\begin{array}{ccccc}0& 0& 0& 0& 0\\ 0& 0& 0& 0& 0\\ 0& 0& 1& 1& \mathrm{ane}\\ 0& 0& \mathrm{i}& \mathrm{ane}& \mathrm{one}\\ 0& 0& 1& \mathrm{one}& 1\end{array}\begin{array}{ccccc}0& 0& 0& 0& 0\\ 0& 0& 0& 0& 0\\ 0& 0& 1& 0& 0\\ 0& 1& 1& 1& 0\\ 1& 1& 1& 1& 1\end{array}$

are preserved past this filter, although these examples stand for limiting cases that could be disrupted past minor amounts of dissonance or slight changes of orientation. Thus, the filter seems guaranteed to preserve corners only if the internal angle is greater than 135°. This figure should be compared with the 180° obtained using similar arguments for the normal median filter in 5 × v regions such as

$\begin{array}{ccccc}0& 0& 0& \mathrm{ane}& 1\\ 0& 0& 0& 1& 1\\ 0& 0& \mathrm{i}& \mathrm{i}& \mathrm{one}\\ 0& 0& 1& \mathrm{one}& 1\\ 0& 0& 1& 1& 1\end{array}$

Figure 3.21 shows plots obtained with this filter under the same conditions as for the 5 × five median filters. Information technology always gives at least a fourfold improvement in edge shift over that for the median filter, and this operation improves with increasing radius of curvature b until there is zero shift for b > 4. (Note that b = four is approximately the figure that would be expected from the corner angle of 135^° noted to a higher place, within a 5 × 5 neighborhood.) Hence, such item-preserving filters amend the situation dramatically simply practise non completely overcome the underlying problem described earlier. In improver, this improvement may not take been obtained without toll, since in some cases the filter seems to insert structure where none exists (Davies, 1989b). The upshot is to cast some doubt on the usefulness of this type of filter in all possible situations. Nevertheless, its effect on existent images appears to be generally very good (see Figs 3.18c and three.22c).

Read total chapter

URL:

https://www.sciencedirect.com/science/article/pii/B978012206093950006X

Image Processing Basics

Lizhe Tan , Jean Jiang , in Digital Signal Processing (Third Edition), 2019

13.4.two Median Filtering

The median filter is the one type of nonlinear filters. Information technology is very effective at removing impulse noise, the "table salt and pepper" noise, in the image. The principle of the median filter is to replace the gray level of each pixel by the median of the gray levels in a neighborhood of the pixels, instead of using the average operation. For median filtering, we specify the kernel size, list the pixel values, covered by the kernel, and determine the median level. If the kernel covers an even number of pixels, the average of two median values is used. Before offset median filtering, zeros must exist padded around the row edge and the column edge. Hence, edge distortion is introduced at image purlieus. Permit the states look at Case thirteen.8.

Case xiii.8

Given a three   ×   3 median filter kernel and the following 8-fleck grayscale original and corrupted (noisy) images,

$4\times 4\text{original image}:\left[\begin{array}{cccc}100& 100& 100& 100\\ 100& 100& 100& 100\\ 100& 100& 100& 100\\ 100& 100& 100& 100\end{array}\right]$

$\mathrm{iv}\times \mathrm{iv}\text{corrupted image}\mathrm{by}\text{impulse noise}:\left[\begin{array}{cccc}100& 255& 100& 100\\ 100& 255& 100& 100\\ 255& 100& 100& 0\\ 100& 100& 100& 100\end{array}\right]$

$3\times 3\text{median filter kernel}:{\left[\begin{array}{ccc}& & \\ & & \\ & & \end{array}\right]}_{3\times \mathrm{iii}}$

Perform digital filtering, and compare the filtered image with the original one.

Solution:

Step one: The 3 × iii kernel requires zero padding iii/two   =   1 column of zeros at the left and right edges while 3/two   =   i row of zeros at the upper and bottom edges:

Step two: To process the first element, we comprehend the 3 × 3 kernel with the middle pointing to the first element to be processed. The sorted data within the kernel are listed in terms of its value every bit.

$0,0,0,0,0,0,100,100,255,255.$

The median value   =   median (0, 0, 0, 0, 0, 100, 100, 255, 255)   =   0. Zero will replace 100.

Step 3: Proceed for each element until the last is replaced.

Allow u.s. see the element at the location (1,1):

The values covered past the kernel are:

$100,100,100,100,100,100,255,255,255.$

The median value   =   median (100, 100, 100, 100, 100, 100, 255, 255, 255)   =   100. The final candy image is

$\left[\begin{array}{cccc}0& 100& 100& 0\\ 100& 100& 100& 100\\ 0& 100& 100& 0\\ 100& 100& 100& 100\end{array}\right].$

Some boundary pixels are distorted due to nothing padding effect. Nevertheless, for a large image, the distortion can be omitted versus the overall quality of the image. The 2 × ii middle portion matches the original paradigm exactly. The effectiveness of the median filter is verified via this example.

The image in Fig. 13.27A is corrupted by "salt and pepper" dissonance. The median filter with a 3 × three kernel is used to filter the impulse noise. The enhanced image shown in Fig. 13.27B has a significant quality comeback. Notwithstanding, the enhanced image too seems smoothed, thus, the high-frequency data is reduced. Annotation that a larger size kernel is not appropriate for median filtering, because for a larger prepare of pixels the median value deviates from the pixel value.

Fig. 13.27. (A) Noisy prototype (corrupted by "table salt and pepper"noise). (B) The enhanced prototype using the three   ×   3 median filter.

Read total chapter

URL:

https://www.sciencedirect.com/scientific discipline/article/pii/B9780128150719000130

Medical Image Processing Using GPU-Accelerated ITK Image Filters

Won-Ki Jeong , ... Massimiliano Fatica , in GPU Computing Gems Emerald Edition, 2011

46.iii.three Median Filter

The median filter is a nonlinear statistical filter that replaces the current pixel value with the median value of pixels in the neighboring region. A naive implementation outset creates a cumulative histogram for the neighbor region and and so finds the first index beyond half the number of pixels in the histogram. The major problem of this approach on the GPU is that each thread needs to compute a complete histogram, and therefore 256 histogram bins have to be allocated per pixel for an viii-bit prototype. This is inefficient on current GPUs because there are not plenty hardware registers available for each thread, and using global memory for histogram ciphering is just too slow.

To avert this trouble, our implementation is based on a bisection search on histogram ranges proposed in [6]. This method does not compute the actual histogram just iteratively refines the histogram range that includes the median value. During each iteration, the electric current valid range is divided into two halves, and the half that has the larger number of pixels is called for the next circular. This process is repeated until the range converges to a unmarried bin. This approach requires log₂(number of bins) iterations to converge. For example, an prototype with an eight-chip pixel depth (256 bins) requires merely 8 iterations to compute the median. Effigy 46.vii shows an instance of this histogram bisection scheme for eight histogram bins.

Figure 46.vii. A pictorial example (left) and pseudocode (right) of the histogram bisection scheme. This case is based on viii histogram bins (i.due east., iii bits per pixels). Left: Dark grey arrows indicate the electric current valid range, and the calorie-free grey arrow (described as pivot in the pseudocode on the right) indicates the location of the median bin.

Because we do not want to store the entire histogram but want to keep rail of only a valid range for each thread, nosotros have to scan all the neighbour pixels in each iteration to refine the range. This leads to a computational complexity of O(mlog₂ n), where n is the number of histogram bins (a constant for a given pixel format) and m is the number of neighboring pixels to compute the median (a variable depending on the filter size). To minimize the O(g) factor, we store neighboring pixels in shared retentiveness and reuse them multiple times. Similar performance can be achieved using texture memory instead of shared retention.

Read full chapter

URL:

https://www.sciencedirect.com/science/commodity/pii/B9780123849885000462

Stack Filters: From Definition to Design Algorithms

Nina Due south.T. Hirata , in Advances in Imaging and Electron Physics, 2008

2 Rank-Club Filters

A straightforward extension of the median filters is the rank-guild filter (Justusson, 1981; Heygster, 1982; Nodes and Gallagher, 1982), based on order statistics. Given realizations u ₁, u ₂,…, u_d of d random variables, with d  ∈   ℕ, d   >  0, and r  ∈   ℕ, ane   ≤ r  ≤ d, the r-th smallest ² element in the samples u ₁, u _two,…, u_d is called the r-th gild statistic and is denoted u _(r). Thus, u ₍₁₎  ≤ u _(two) ≤…≤ u _(d). If d is odd, so u _{((d  +   one)/ii)} is the median. The order statistics u _(one) and u _(d) are, respectively, the minimum and the maximum.

By assigning a random variable to each point in the window and positioning it at any location of the input signal domain, the values of the signal under the window can exist seen as realizations of those random variables. The rank-order filters are those filters that, instead of the median, outputs the r-th club statistics among the observations, 1   ≤ r  ≤ d. This form includes the median filter, r  =   (d +   ane)/two, as a particular case. Applications of rank-order filters include filtering of cell pictures (Heygster, 1982), detection of narrow-ring signals (Wong and Chen, 1987), and document image analysis (Ma et al., 2002).

The weighted version of the rank-order filters are termed generalized rank-club filters (Wendt et al., 1986) and weighted gild statistic (WOS) filters (Yli-Harja et al., 1991). They work as follows: allow u ₁, u ₂,…, u_d be realizations of d random variables, d  ∈   ℕ, d   >  0, let Ω   =   (ω ₁, ω _two,…, ω_d ), ω _i   ∈   ℕ and ω_i  >  0 for all i, and let r  ∈   ℕ, 1   ≤ r  ≤   Σ ω_i . Each sample u_i is duplicated by its respective weight ω_i to obtain a sequence of Σ ω_i elements. The filter that outputs the element of rank r from this sequence is the WOS filter with weight Ω and rank r.

Note that the term social club statistic filters is more than commonly used to refer to filters defined by $\mathit{y}={\displaystyle \sum _{\mathit{j}=1}^{\mathit{d}}{\mathit{a}}_{\mathit{j}}{\mathit{u}}_{\left(\mathit{j}\right)}}$ , where a_j are real coefficients. They are also known as Fifty-filters. They generalize the rank-order, moving average, and other filters (run across Bovik et al., 1983; Pitas and Venetsanopoulos, 1992). The ii bones differences of these filters from WOS filters are: (1) WOS filters first duplicate each observation by the corresponding weight and so compute the society statistics, whereas lodge statistic filters do the inverse, and (2) weights of WOS filters are positive integers, whereas coefficients of order statistic filters are existent numbers.

Effigy 8 shows an example of a WOS filter. Duplication past a given weight vector can be understood as a mapping to a space of larger dimension. If all elements of same Hamming weight are depicted horizontally side by side, then a WOS filter corresponds to tracing a horizontal line in the expanded lattice diagram and mapping all elements above that line to 1 and all elements beneath it to 0. This fact is precisely what defines the characterization of WOS filters as a counting (threshold) function, as explained in the following text.

Figure 8. Weighted society statistic filter.

In full general, decision of the element at a given rank requires that elements be first sorted. Most sorting algorithms have computational complication of O(d log d). However, for binary variables the chemical element at a given rank tin be determined based on counting the number of samples with value 1 (or 0). For example, given the samples 101101, in that location are 4 1   southward (and, therefore, two 0   southward). Thus, because descending gild, it tin can be hands inferred that element 1 occupies the beginning four ranks and the two concluding ranks are occupied by element 0. In other terms, for binary inputs u  =   (u ₁, u ₂,…, u_d ) ∈ {0, i} ^d , rank part for a given rank r (because descending gild) can be expressed by a counting function as follows:

(12) ${\mathit{\psi }}_{\mathit{r}}\left(\mathbf{u}\right)=\mathrm{one}\iff |\mathbf{u}|\ge \mathit{r},$

where | u | denotes the Hamming weight of u (i.e., the number of components equal to 1 in vector u).

According to this equation, for binary inputs, the median is given by

(thirteen) ${\mathit{\psi }}_{\left(\mathit{d}+\mathrm{one}\right)/2}\left(\mathbf{u}\right)=1\iff |\mathbf{u}|\ge \left(\mathit{d}+1\right)/2.$

With regard to WOS filters, in the binary domain they also can be expressed equally a counting-based function. Let Ω   =   (ω _ane, ω _ii,…,ω_d ) be a weight vector, a vector of positive integers. Denote d*   =   ∑ ω _i and allow 0   ≤ r*   ≤ d*. Define the function ${\mathit{\psi }}_{\mathrm{\Omega },{\mathit{r}}^{*}}$ by, for any u ∈ {0, 1} ^d ,

(14) ${\mathit{\psi }}_{\mathrm{\Omega },\mathit{r}*}\left(\mathbf{u}\right)=1\iff {\displaystyle \sum {\mathit{\omega }}_{\mathit{i}}{\mathit{u}}_{\mathit{i}}\ge \mathit{r}*}.$

According to this, Eq. (12) is a item case where Ω   =   (1, one,…, 1).

Binary functions that can exist expressed in the form of Eq. (14) with arbitrary (not-necessarily positive) integer weights are called linearly separable Boolean functions. If both weights and thresholds (rank) are positive, then they are linearly separable positive Boolean functions (Muroga, 1971). Thus, while stack filters stand for to PBFs, WOS filters represent to threshold functions (with positive weights and threshold). In addition, as a subclass of the stack filters, WOS (and thus median and rank-social club) filters possess the threshold decomposition construction.

For a fixed weight vector, different WOS filters may exist obtained by varying the threshold. Figure ix shows five WOS filters generated by weight vector Ω   =   (1, i, iii). An interesting question is to determine whether two filters ${\mathit{\psi }}_{{\mathrm{\Omega }}_2,{{\mathit{r}}^{*}}_1}$ and ${\mathit{\psi }}_{{\mathrm{\Omega }}_2,{{\mathit{r}}^{*}}_2}$ are identical (Astola et al., 1994). Of more involvement might be whether 2 weight vectors are equivalent in the sense that they generate the aforementioned set of filters.

Figure ix. WOS filters generated by the weight vector Ω   =   (1, ane, 3).

Notation also that some authors define WOS filters every bit the ones that duplicate the d input samples by their respective weights and outputs the r-th largest chemical element of the sequence. This implies descending order. However, other authors define the output of the filter every bit the r-th smallest element, which implies ascending order. This departure may generate some confusion. In full general, descending society is adopted because of the convenience of having the threshold value of the threshold function equal to the desired rank.

Since WOS are a subclass of the stack filters, not all PBFs tin can be expressed equally Eq. (14). Figure x illustrates a positive Boolean function with d  =   4 variables that does non correspond to whatever WOS filter (it is not linearly separable). To see that, consider the six elements with Hamming weight ii (0011, 0101, 1010, 1100, 0110, 1001). In that location must be a weight vector (a, b, c, d) such that the first four, when expanded by the weight vector, result in elements with Hamming weight larger than the weight of the two others. More than specifically, the post-obit viii inequalities must be satisfied:

Figure 10. A positive Boolean office that is not WOS.

$\begin{array}{l}\mathit{c}+\mathit{d}>\mathit{b}+\mathit{c}\mathit{b}+\mathit{d}>\mathit{b}+\mathit{c}\\ \mathit{c}+\mathit{d}>\mathit{a}+\mathit{d}\mathit{b}+\mathit{d}>\mathit{a}+\mathit{d}\\ \mathit{a}+\mathit{c}>\mathit{b}+\mathit{c}\mathit{a}+\mathit{b}>\mathit{b}+\mathit{c}\\ \mathit{a}+\mathit{c}>\mathit{a}+\mathit{d}\mathit{a}+\mathit{b}>\mathit{a}+\mathit{d}\end{array}$

Information technology is like shooting fish in a barrel to verify that there are no positive integers that satisfy the to a higher place inequalities. Therefore, the filter shown higher up is not a WOS filter. The number of WOS filters, equally well as of stack filters, is not known for a general dimension d. Finding the number of monotone Boolean functions on d variables is an open problem known as Dedekind's trouble (Kleitman, 1969; Kleitman and Markowsky, 1975).

Read full chapter

URL:

https://www.sciencedirect.com/science/article/pii/S1076567008006010

Morphological Amoebas and Partial Differential Equations

Martin Welk , Michael Breuß , in Advances in Imaging and Electron Physics, 2014

3.5 Multivariate Median Filtering on a Continuous Domain

Like M-smoothers, multivariate median filters were introduced in subsection 2.5 past a minimization approach. Thus, translation to the infinite-continuous setting again consists of replacing discrete sums by integrals over structuring elements: Given a multivariate smooth office $\mathit{u}:\Omega \to {\mathrm{ℝ}}^d,$ a compact structuring element $\mathcal{A}\subset \Omega \text{,}$ and a vector norm $\Vert .\Vert$ , the median of u in $\mathcal{A}$ is

(19) $\underset{(x,y)\in \mathcal{A}}{\text{med}}\mathit{u}(x,y):=\underset{z\in {\mathrm{ℝ}}^d}{\text{argmin}}\underset{\mathcal{A}}{\int \int }\parallel \mathit{z}-\mathit{u}(x,y)\parallel \text{d}x\text{d}y.$

A median filtering step for u assigns to each location $\left({\mathit{x}}_0,y_0\right)\in \Omega$ equally its new function value $\left[\tilde{\mathit{u}}({\mathit{x}}_0,y_0)\right]$ the median of values inside the respective amoeba; i.e.,

(20) $\tilde{\mathit{u}}({\mathit{x}}_0,y_0):=\underset{(\mathrm{10},y)\in \mathcal{A}({\mathit{x}}_0,y_0)}{\text{med}}\mathit{u}(x,y).$

Read full chapter

URL:

https://www.sciencedirect.com/science/article/pii/B9780128001448000033

Image Segmentation Techniques

Chaoxin Zheng , Da-Wen Lord's day , in Computer Vision Technology for Food Quality Evaluation, 2008

2.1.2 Median filter

Another pop filter that is widely used is the median filter. The intensity values of pixels in a pocket-sized region within the size of the filter are examined, and the median intensity value is selected for the central pixel. Removing noise using the median filter does not reduce the difference in brightness of images, since the intensity values of the filtered image are taken from the original image. Furthermore, the median filter does non shift the edges of images, as may occur with a linear filter ( Russ, 1999). These 2 primary advantages have led to corking employ of the median filter in the food industry (Du and Dominicus, 2004, 2006a; Faucitano et al., 2005).

Read full chapter

URL:

https://www.sciencedirect.com/scientific discipline/article/pii/B9780123736420500053

How Does A Median Filter Work,

Source: https://www.sciencedirect.com/topics/computer-science/median-filter

Posted by: kempclumse.blogspot.com

Share this post