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Median Filter
The median filter is a non-linear digital filtering technique, often used to remove signal noise, noise from an image, signal, and video. Such noise reduction is a typical pre-processing step to improve the results of later processing (for example, edge detection on an image). Median filtering is very widely used in digital image processing because, under certain conditions, it preserves edges while removing noise (but see the discussion below for which kinds of noise), also having applications in signal processing. Algorithm description The main idea of the median filter is to run through the signal entry by entry, replacing each entry with the median of the entry and its neighboring entries. The idea is very similar to a moving average filter, which replaces each entry with the arithmetic mean of the entry and its neighbors. The pattern of neighbors is called the "window", which slides, entry by entry, over the entire signal. For one-dimensional signals, the most obvious window ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Median Filter Example
The median of a set of numbers is the value separating the higher half from the lower half of a Sample (statistics), data sample, a statistical population, population, or a probability distribution. For a data set, it may be thought of as the “middle" value. The basic feature of the median in describing data compared to the Arithmetic mean, mean (often simply described as the "average") is that it is not Skewness, skewed by a small proportion of extremely large or small values, and therefore provides a better representation of the center. Median income, for example, may be a better way to describe the center of the income distribution because increases in the largest incomes alone have no effect on the median. For this reason, the median is of central importance in robust statistics. Median is a 2-quantile; it is the value that partitions a set into two equal parts. Finite set of numbers The median of a finite list of numbers is the "middle" number, when those numbers are liste ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Salt-and-pepper Noise
Salt-and-pepper noise, also known as impulse noise, is a form of noise sometimes seen on digital images. For black-and-white or grayscale images, it presents as sparsely occurring white and black pixels, giving the appearance of an image sprinkled with salt and pepper. Cause Salt-and-pepper noise can be caused by sharp and sudden disturbances in the image signal. These may be from transmission errors, corrupted pixel elements in the camera sensors, or faulty memory locations in the storage media. Removal An effective noise reduction method for this type of noise is a median filter The median filter is a non-linear digital filtering technique, often used to remove signal noise, noise from an image, signal, and video. Such noise reduction is a typical pre-processing step to improve the results of later processing (for example ... or a morphological filter. For reducing either salt noise or pepper noise, but not both, a contraharmonic mean filter can be effective. Linear fil ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Nonlinear Filters
In mathematics and science, a nonlinear system (or a non-linear system) is a system in which the change of the output is not proportional to the change of the input. Nonlinear problems are of interest to engineers, biologists, physicists, mathematicians, and many other scientists since most systems are inherently nonlinear in nature. Nonlinear dynamical systems, describing changes in variables over time, may appear chaotic, unpredictable, or counterintuitive, contrasting with much simpler linear systems. Typically, the behavior of a nonlinear system is described in mathematics by a nonlinear system of equations, which is a set of simultaneous equations in which the unknowns (or the unknown functions in the case of differential equations) appear as variables of a polynomial of degree higher than one or in the argument of a function which is not a polynomial of degree one. In other words, in a nonlinear system of equations, the equation(s) to be solved cannot be written as a line ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Rosetta Code
Rosetta Code is a wiki-based programming chrestomathy website with implementations of common algorithms and solutions to various computer programming, programming problems in many different programming languages. It is named for the Rosetta Stone, which has the same text inscribed on it in three languages, and thus allowed Egyptian hieroglyphs to be deciphered for the first time. Website Rosetta Code was created in 2007 by Michael Mol. The site's content is licensed under the GNU Free Documentation License 1.2, though some components may be dual-licensed under more permissive terms. The Rosetta Code web repository illustrates how desired functionality is implemented very differently in various Programming_paradigm, programming paradigms, and how "the same" task is accomplished in different programming languages. , Rosetta Code has: * 1,266 computer programming tasks (or problems) * 404 additional draft programming tasks * 933 computer programming languages that are used to solve ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
High-pass Filter
A high-pass filter (HPF) is an electronic filter that passes signals with a frequency higher than a certain cutoff frequency and attenuates signals with frequencies lower than the cutoff frequency. The amount of attenuation for each frequency depends on the filter design. A high-pass filter is usually modeled as a linear time-invariant system. It is sometimes called a low-cut filter or bass-cut filter in the context of audio engineering. High-pass filters have many uses, such as blocking DC from circuitry sensitive to non-zero average voltages or radio frequency devices. They can also be used in conjunction with a low-pass filter to produce a band-pass filter. In the optical domain filters are often characterised by wavelength rather than frequency. High-pass and low-pass have the opposite meanings, with a "high-pass" filter (more commonly "short-pass") passing only ''shorter'' wavelengths (higher frequencies), and vice versa for "low-pass" (more commonly "long-pass"). De ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Unsharp Masking
Unsharp masking (USM) is an image sharpening technique, first implemented in darkroom photography, but now commonly used in digital image processing software. Its name derives from the fact that the technique uses a blurred, or "unsharp", negative image to create a mask of the original image. The unsharp mask is then combined with the original positive image, creating an image that is less blurry than the original. The resulting image, although clearer, may be a less accurate representation of the image's subject. In the context of signal processing, an unsharp mask is generally a linear or nonlinear filter that amplifies the high-frequency components of a signal. Photographic darkroom unsharp masking For the photographic darkroom process, a large-format glass plate negative is contact-copied onto a low-contrast film or plate to create a positive image. However, the positive copy is made with the copy material in contact with the back of the original, rather than emulsio ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sharpening
Sharpening is the process of creating or refining a blade, the edge joining two non-coplanar faces into a converging apex, thereby creating an edge of appropriate shape on a tool or implement designed for cutting. Improving sharpness is done by removing material on an implement with an abrasive substance harder than the material of the implement, followed sometimes by processes to polish/hone the sharp surface to increase smoothness. Tools and materials There are many ways of sharpening tools. Malleable metal surfaces such as bronze, iron and mild steel may be formed by beating or peening a flat surface into a sharp edge. This process also causes work hardening. An abrasive material may be rubbed against the cutting edge to be sharpened. The most traditional abrasive material is a natural stone such as sandstone or granite. Modern synthetic grinding wheels and flat sharpening stones can be manufactured in precise grades of abrasiveness according to the intended pr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Smoothing
In statistics and image processing, to smooth a data set is to create an approximating function that attempts to capture important patterns in the data, while leaving out noise or other fine-scale structures/rapid phenomena. In smoothing, the data points of a signal are modified so individual points higher than the adjacent points (presumably because of noise) are reduced, and points that are lower than the adjacent points are increased leading to a smoother signal. Smoothing may be used in two important ways that can aid in data analysis (1) by being able to extract more information from the data as long as the assumption of smoothing is reasonable and (2) by being able to provide analyses that are both flexible and robust. Many different algorithms are used in smoothing. Compared to curve fitting Smoothing may be distinguished from the related and partially overlapping concept of curve fitting in the following ways: * curve fitting often involves the use of an explicit functio ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Average With Limited Data Validity
In image analysis Image analysis or imagery analysis is the extraction of meaningful information from images; mainly from digital images by means of digital image processing techniques. Image analysis tasks can be as simple as reading barcode, bar coded tags or a ..., the average with limited data validity is an image filter for feature-preserving image noise, noise removal, consisting in a smoothing filter that only involves pixels satisfying some validity criterion. If some feature of noise elements is known, it is possible to use it to define a criterion to detect invalid pixels, and selectively smooth only invalid pixels using data coming only from valid pixels, thus avoiding to affect other features of the image. Possible criteria are: * based on image intensity, by defining an interval [I_, I_] of invalid data, with the filter only modifying pixels in that interval and only averaging data from other pixels from its neighbourhood that are valid, i.e. their intensity does no ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bilateral Filter
A bilateral filter is a non-linear, edge-preserving, and noise-reducing smoothing filter for images. It replaces the intensity of each pixel with a weighted average of intensity values from nearby pixels. This weight can be based on a Gaussian distribution. Crucially, the weights depend not only on Euclidean distance of pixels, but also on the radiometric differences (e.g., variations in color intensity or depth). This dual dependency preserves sharp edges while suppressing noise. Definition The bilateral filter is defined as : I^\text(x) = \frac \sum_ I(x_i)f_r(\, I(x_i) - I(x)\, )g_s(\, x_i - x\, ), and normalization term, , is defined as : W_p = \sum_ where : I^\text is the filtered image; : I is the original input image to be filtered; : x are the coordinates of the current pixel to be filtered; : \Omega is the window centered in x, so x_i \in \Omega is another pixel; : f_r is the range kernel for smoothing differences in intensities (this function can be a Gaussi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lulu Smoothing
In signal processing, Lulu smoothing is a nonlinear mathematical technique for removing impulsive noise from a data sequence such as a time series. It is a nonlinear equivalent to taking a moving average (or other smoothing technique) of a time series, and is similar to other nonlinear smoothing techniques, such as Tukey or median smoothing. LULU smoothers are compared in detail to median smoothers by Jankowitz and found to be superior in some aspects, particularly in mathematical properties like idempotence. Properties Lulu operators have a number of attractive mathematical properties, among them idempotence Idempotence (, ) is the property of certain operations in mathematics and computer science whereby they can be applied multiple times without changing the result beyond the initial application. The concept of idempotence arises in a number of pl ... – meaning that repeated application of the operator yields the same result as a single application – and co-idempotenc ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pseudomedian
In statistics, the pseudomedian is a measure of centrality for data-sets and populations. It agrees with the median for symmetric data-sets or populations. In mathematical statistics, the pseudomedian is also a location parameter for probability distributions. Description The pseudomedian of a distribution F is defined to be a median of the distribution of (Z_1+Z_2)/2, where Z_1 and Z_2 are independent, each with the same distribution F. When F is a symmetric distribution, the pseudomedian coincides with the median; otherwise this is not generally the case. The Hodges–Lehmann statistic, defined as the median of all of the midpoints of pairs of observations, is a consistent estimator of the pseudomedian. Like the set of medians, the pseudomedian is well defined for all probability distributions, even for the many distributions that lack modes or means. Pseudomedian filter in signal processing In signal processing there is another definition of pseudomedian filter for discret ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
