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Box Blur
A box blur (also known as a box linear filter) is a spatial domain linear filter in which each pixel in the resulting image has a value equal to the average value of its neighboring pixels in the input image. It is a form of low-pass ("blurring") filter. A 3 by 3 box blur ("radius 1") can be written as matrix :\frac\begin 1 & 1 & 1 \\ 1 & 1 & 1 \\ 1 & 1 & 1 \end. Due to its property of using equal weights, it can be implemented using a much simpler accumulation algorithm, which is significantly faster than using a sliding-window algorithm. Box blurs are frequently used to approximate a Gaussian blur. By the central limit theorem, repeated application of a box blur will approximate a Gaussian blur.code doc In the frequency domain, a box blur has zeros and negative components. That is, a sine wave with a period equal to the size of the box will be blurred away entirely, and wavelengths shorter than the size of the box may be phase-reversed, as seen when two bokeh circles touch to ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
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Box Blur Filter Example - Pixlr Photo Editor
A box (plural: boxes) is a container with rigid sides used for the storage or transportation of its contents. Most boxes have flat, parallel, rectangular sides (typically rectangular prisms). Boxes can be very small (like a matchbox) or very large (like a shipping box for furniture) and can be used for a variety of purposes, from functional to decorative. Boxes may be made of a variety of materials, both durable (such as wood and metal) and non-durable (such as corrugated fiberboard and paperboard). Corrugated metal boxes are commonly used as shipping containers. Boxes may be closed and shut with flaps, doors, or a separate lid. They can be secured shut with adhesives, tapes, string, or more decorative or elaborately functional mechanisms, such as catches, clasps or locks. Packaging Several types of boxes are used in packaging and storage. * A corrugated box is a shipping container made from corrugated fiberboard, most commonly used to transport products from a wareho ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
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Gaussian Blur
In image processing, a Gaussian blur (also known as Gaussian smoothing) is the result of blurring an image by a Gaussian function (named after mathematician and scientist Carl Friedrich Gauss). It is a widely used effect in graphics software, typically to reduce image noise and reduce detail. The visual effect of this blurring technique is a smooth blur resembling that of viewing the image through a translucent screen, distinctly different from the bokeh effect produced by an out-of-focus lens or the shadow of an object under usual illumination. Gaussian smoothing is also used as a pre-processing stage in computer vision algorithms in order to enhance image structures at different scales—see scale space representation and scale space implementation. Mathematics Mathematically, applying a Gaussian blur to an image is the same as convolving the image with a Gaussian function. This is also known as a two-dimensional Weierstrass transform. By contrast, convolving by a circ ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
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Central Limit Theorem
In probability theory, the central limit theorem (CLT) states that, under appropriate conditions, the Probability distribution, distribution of a normalized version of the sample mean converges to a Normal distribution#Standard normal distribution, standard normal distribution. This holds even if the original variables themselves are not Normal distribution, normally distributed. There are several versions of the CLT, each applying in the context of different conditions. The theorem is a key concept in probability theory because it implies that probabilistic and statistical methods that work for normal distributions can be applicable to many problems involving other types of distributions. This theorem has seen many changes during the formal development of probability theory. Previous versions of the theorem date back to 1811, but in its modern form it was only precisely stated as late as 1920. In statistics, the CLT can be stated as: let X_1, X_2, \dots, X_n denote a Sampling ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
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Frequency Domain
In mathematics, physics, electronics, control systems engineering, and statistics, the frequency domain refers to the analysis of mathematical functions or signals with respect to frequency (and possibly phase), rather than time, as in time series. While a time-domain graph shows how a signal changes over time, a frequency-domain graph shows how the signal is distributed within different frequency bands over a range of frequencies. A complex valued frequency-domain representation consists of both the magnitude and the phase of a set of sinusoids (or other basis waveforms) at the frequency components of the signal. Although it is common to refer to the magnitude portion (the real valued frequency-domain) as the frequency response of a signal, the phase portion is required to uniquely define the signal. A given function or signal can be converted between the time and frequency domains with a pair of mathematical operators called transforms. An example is the Fourier transfo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
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Sine Wave
A sine wave, sinusoidal wave, or sinusoid (symbol: ∿) is a periodic function, periodic wave whose waveform (shape) is the trigonometric function, trigonometric sine, sine function. In mechanics, as a linear motion over time, this is ''simple harmonic motion''; as rotation, it corresponds to ''uniform circular motion''. Sine waves occur often in physics, including wind waves, sound waves, and light waves, such as monochromatic radiation. In engineering, signal processing, and mathematics, Fourier analysis decomposes general functions into a sum of sine waves of various frequencies, relative phases, and magnitudes. When any two sine waves of the same frequency (but arbitrary phase (waves), phase) are linear combination, linearly combined, the result is another sine wave of the same frequency; this property is unique among periodic waves. Conversely, if some phase is chosen as a zero reference, a sine wave of arbitrary phase can be written as the linear combination of two sine wa ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
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Bokeh
In photography, bokeh ( or ; ) is the aesthetic quality of the blur produced in out-of-focus parts of an image, whether foreground or background or both. It is created by using a wide aperture lens. Some photographers incorrectly restrict use of the term bokeh to the appearance of bright spots in the out-of-focus area caused by circles of confusion. Bokeh has also been defined as "the way the lens renders out-of-focus points of light". Differences in lens aberrations and aperture shape cause very different bokeh effects. Some lens designs blur the image in a way that is pleasing to the eye, while others produce distracting or unpleasant blurring ("good" and "bad" bokeh, respectively). Photographers may deliberately use a shallow focus technique to create images with prominent out-of-focus regions, accentuating their lens's bokeh. Bokeh is often most visible around small background highlights, such as specular reflections and light sources, which is why it is ofte ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
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Mario Klingemann
Mario Klingemann (born 1970 in Laatzen, Lower Saxony) is a German artist best known for his work involving neural networks, code, and algorithms. Klingemann was a Google Arts and Culture resident from 2016 to 2018, and he is considered as a pioneer in the use of computer learning in the arts. His works examine creativity, culture, and perception through machine learning and artificial intelligence, and have appeared at the Ars Electronica Festival, the Museum of Modern Art New York, the Metropolitan Museum of Art New York, the Photographers’ Gallery London, the Centre Pompidou Paris, and the British Library. Today he lives in Munich, where, in addition to his art under the name "Dog & Pony", he still runs a creative free space between gallery and Wunderkammer with the paper artist Alexandra Lukaschewitz. In 2018 his work ''The Butcher's Son'' ''w''on the Lumen Prize Gold Award 2018 by working with figurative visual input. Mario Klingemann is part of ONKAOS, the new media art ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
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Separable Filter
A separable filter in image processing can be written as product of two more simple filters. Typically a 2-dimensional convolution operation is separated into two 1-dimensional filters. This reduces the computational costs on an N\times M image with a m\times n filter from \mathcal(M\cdot N\cdot m\cdot n) down to \mathcal(M\cdot N\cdot (m + n)). Examples 1. A two-dimensional smoothing filter: : \frac \begin 1 \\ 1 \\ 1 \end * \frac \begin 1 & 1 & 1 \end = \frac \begin 1 & 1 & 1 \\ 1 & 1 & 1 \\ 1 & 1 & 1 \end 2. Another two-dimensional smoothing filter with stronger weight in the middle: : \frac \begin 1 \\ 2 \\ 1 \end * \frac \begin 1 & 2 & 1 \end = \frac \begin 1 & 2 & 1 \\ 2 & 4 & 2 \\ 1 & 2 & 1 \end 3. The Sobel operator, used commonly for edge detection: : \begin 1 \\ 2 \\ 1 \end * \begin 1 & 0 & -1 \end = \begin 1 & 0 & -1 \\ 2 & 0 & -2 \\ 1 & 0 & -1 \end This works also for the Pr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
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Finite Impulse Response
In signal processing, a finite impulse response (FIR) filter is a filter whose impulse response (or response to any finite length input) is of ''finite'' duration, because it settles to zero in finite time. This is in contrast to infinite impulse response (IIR) filters, which may have internal feedback and may continue to respond indefinitely (usually decaying). The impulse response (that is, the output in response to a Kronecker delta input) of an Nth-order discrete-time FIR filter lasts exactly N+1 samples (from first nonzero element through last nonzero element) before it then settles to zero. FIR filters can be discrete-time or continuous-time, and digital or analog. Definition For a causal discrete-time FIR filter of order ''N'', each value of the output sequence is a weighted sum of the most recent input values: :\begin y &= b_0 x + b_1 x -1+ \cdots + b_N x -N\\ &= \sum_^N b_i\cdot x -i \end where: * x /math> is the input signal, * y /math> is the outpu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
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Summed-area Table
A summed-area table is a data structure and algorithm for quickly and efficiently generating the sum of values in a rectangular subset of a grid. In the image processing domain, it is also known as an integral image. It was introduced to computer graphics in 1984 by Frank Crow for use with mipmaps. In computer vision it was popularized by Lewis and then given the name "integral image" and prominently used within the Viola–Jones object detection framework in 2001. Historically, this principle is very well known in the study of multi-dimensional probability distribution functions, namely in computing 2D (or ND) probabilities (area under the probability distribution) from the respective cumulative distribution functions. The algorithm As the name suggests, the value at any point (''x'', ''y'') in the summed-area table is the sum of all the pixels above and to the left of (''x'', ''y''), inclusive: I(x,y) = \sum_ i(x',y') where i(x,y) is the value of the pixel at (''x' ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
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Cascaded Integrator–comb Filter
In digital signal processing, a cascaded integrator–comb (CIC) is a computationally efficient class of low-pass finite impulse response (FIR) filter that chains N number of integrator and comb filter pairs (where N is the filter's order) to form a decimator or interpolator. In a decimating CIC, the input signal is first fed through N integrator stages, followed by a down-sampler, and then N comb stages. An interpolating CIC (e.g. Figure 1) has the reverse order of this architecture, but with the down-sampler replaced with a zero-stuffer (up-sampler). Operation CIC filters were invented by Eugene B. Hogenauer in 1979 (published in 1981), and are a class of FIR filters used in multi-rate digital signal processing. Unlike most FIR filters, it has a down-sampler or up-sampler in the middle of the structure, which converts between the high sampling rate of f_s used by the integrator stages and the low sampling rate of \tfrac used by the comb stages. Transfer function At ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
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Gaussian Filter
In electronics and signal processing, mainly in digital signal processing, a Gaussian filter is a filter (signal processing), filter whose impulse response is a Gaussian function (or an approximation to it, since a true Gaussian response would have infinite impulse response). Gaussian filters have the properties of having no Overshoot (signal), overshoot to a step function input while minimizing the rise and fall time. This behavior is closely connected to the fact that the Gaussian filter has the minimum possible group delay. A Gaussian filter will have the best combination of suppression of high frequencies while also minimizing spatial spread, being the critical point of the Fourier transform#Uncertainty principle, uncertainty principle. These properties are important in areas such as Oscilloscope#The vertical amplifier, oscilloscopes and digital telecommunication systems. Mathematically, a Gaussian filter modifies the input signal by convolution with a Gaussian function; thi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |