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Median Filter
The median filter is a non-linear digital filtering technique, often used to remove noise from an image or signal. 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), 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 neighboring entries. 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 is just the first few preceding and following entries, whereas for two-dimensional (or higher-dimensional) data the window must include all entries within a given radius or ellipsoidal region (i.e. the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Median Filter Example
In statistics and probability theory, the median is the value separating the higher half from the lower half of a data sample, a 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 mean (often simply described as the "average") is that it is not skewed by a small proportion of extremely large or small values, and therefore provides a better representation of a "typical" value. Median income, for example, may be a better way to suggest what a "typical" income is, because income distribution can be very skewed. The median is of central importance in robust statistics, as it is the most resistant statistic, having a breakdown point of 50%: so long as no more than half the data are contaminated, the median is not an arbitrarily large or small result. Finite data set of numbers The median of a finite list of numbers is the "middle" number, when those numbers are l ... [...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. This noise can be caused by sharp and sudden disturbances in the image signal. It presents itself as sparsely occurring white and black pixels. An effective noise reduction method for this type of noise is a median filter or a morphological filter. For reducing either salt noise or pepper noise, but not both, a contraharmonic mean filter can be effective. See also * Defective pixel A defective pixel is a pixel on a liquid crystal display (LCD) that is not functioning properly. The ISO standard ISO 13406-2 distinguishes between three different types of defective pixels, while hardware companies tend to have further distingu ... References Noise (graphics) Digital photography Image noise reduction techniques {{Photo-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Signal Processing
Signal processing is an electrical engineering subfield that focuses on analyzing, modifying and synthesizing ''signals'', such as audio signal processing, sound, image processing, images, and scientific measurements. Signal processing techniques are used to optimize transmissions, Data storage, digital storage efficiency, correcting distorted signals, subjective video quality and to also detect or pinpoint components of interest in a measured signal. History According to Alan V. Oppenheim and Ronald W. Schafer, the principles of signal processing can be found in the classical numerical analysis techniques of the 17th century. They further state that the digital refinement of these techniques can be found in the digital control systems of the 1940s and 1950s. In 1948, Claude Shannon wrote the influential paper "A Mathematical Theory of Communication" which was published in the Bell System Technical Journal. The paper laid the groundwork for later development of information c ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Nonlinear Filters
In mathematics and science, a nonlinear 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 because 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 linear combination of the u ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Rosetta Code
Rosetta Code is a wiki-based programming website with implementations of common algorithms and solutions to various 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 paradigms, and how "the same" task is accomplished in different programming languages. , Rosetta Code has: ::* 1,121 computer programming tasks (or problems) ::* 303 additional draft programming tasks ::* 810 computer programming languages that are used to solve tasks ::* 83,043 computer programming ... [...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 (mathematics), 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. 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 function for ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Average With Limited Data Validity
In image analysis, the average with limited data validity is an image filter for feature-preserving 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_/math> 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 not fall in the same interval. For instance, given a pixel (x,y) of invalid data, its convolution kernel h becomes ::h_ = \begin 1 \quad I_ \notin _, I_\\ 0 \quad \text \end : This approach allows to effectively remove extraneous elements that have different inte ... [...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., range differences, such as color intensity, depth distance, etc.). This preserves sharp edges. 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 Gaussian function); : g_ ... [...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-idempotence ... [...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 dis ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Weighted Median
In statistics, a weighted median of a sample is the 50% weighted percentile. It was first proposed by F. Y. Edgeworth in 1888. Like the median, it is useful as an estimator of central tendency, robust against outliers. It allows for non-uniform statistical weights related to, e.g., varying precision measurements in the sample. Definition General case For n distinct ordered elements x_1, x_2,...,x_n with positive weights w_1, w_2,...,w_n such that \sum_^n w_i = 1, the weighted median is the element x_k satisfying :\sum_^ w_i \le 1/2 and \sum_^ w_i \le 1/2 Special case Consider a set of elements in which two of the elements satisfy the general case. This occurs when both element's respective weights border the midpoint of the set of weights without encapsulating it; Rather, each element defines a partition equal to 1/2. These elements are referred to as the lower weighted median and upper weighted median. Their conditions are satisfied as follows: Lower Weighted Median :\sum ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Image Noise
Image noise is random variation of brightness or color information in images, and is usually an aspect of electronic noise. It can be produced by the image sensor and circuitry of a Image scanner, scanner or digital camera. Image noise can also originate in film grain and in the unavoidable shot noise of an ideal photon detector. Image noise is an undesirable by-product of image capture that obscures the desired information. Typically the term “image noise” is used to refer to noise in 2D images, not 3D images. The original meaning of "noise" was "unwanted signal"; Noise (radio), unwanted electrical fluctuations in signals received by AM radios caused audible acoustic noise ("static"). By analogy, unwanted electrical fluctuations are also called "noise". Image noise can range from almost imperceptible specks on a digital photograph taken in good light, to Optical astronomy, optical and Radioastronomy, radioastronomical images that are almost entirely noise, from which a sma ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
