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Gradient-domain Image Processing
Gradient domain image processing, also called Poisson image editing, is a type of digital image processing that operates on the differences between neighboring pixels, rather than on the pixel values directly. Mathematically, an image gradient represents the derivative of an image, so the goal of gradient domain processing is to construct a new image by integral, integrating the gradient, which requires solving Poisson's equation. Overview Processing images in the gradient domain is a two-step process. The first step is to choose an image gradient. This is often extracted from one or more images and then modified, but it can be obtained through other means as well. For example, some researchers have explored the advantages of users painting directly in the gradient domain, while others have proposed sampling a gradient directly from a camera sensor. The second step is to solve Poisson's equation to find a new image that can produce the gradient from the first step. An exact soluti ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Digital Image Processing
Digital image processing is the use of a digital computer to process digital images through an algorithm. As a subcategory or field of digital signal processing, digital image processing has many advantages over analog image processing. It allows a much wider range of algorithms to be applied to the input data and can avoid problems such as the build-up of noise and distortion during processing. Since images are defined over two dimensions (perhaps more) digital image processing may be modeled in the form of multidimensional systems. The generation and development of digital image processing are mainly affected by three factors: first, the development of computers; second, the development of mathematics (especially the creation and improvement of discrete mathematics theory); third, the demand for a wide range of applications in environment, agriculture, military, industry and medical science has increased. History Many of the techniques of digital image processing, or digita ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Image Gradient
An image gradient is a directional change in the intensity or color in an image. The gradient of the image is one of the fundamental building blocks in image processing. For example, the Canny edge detector uses image gradient for edge detection. In graphics software for digital image editing, the term gradient or color gradient is also used for a gradual blend of color which can be considered as an even gradation from low to high values, as used from white to black in the images to the right. Another name for this is ''color progression''. Mathematically, the gradient of a two-variable function (here the image intensity function) at each image point is a 2D vector with the components given by the derivatives in the horizontal and vertical directions. At each image point, the gradient vector points in the direction of largest possible intensity increase, and the length of the gradient vector corresponds to the rate of change in that direction. Since the intensity function of a d ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Derivative
In mathematics, the derivative of a function of a real variable measures the sensitivity to change of the function value (output value) with respect to a change in its argument (input value). Derivatives are a fundamental tool of calculus. For example, the derivative of the position of a moving object with respect to time is the object's velocity: this measures how quickly the position of the object changes when time advances. The derivative of a function of a single variable at a chosen input value, when it exists, is the slope of the tangent line to the graph of the function at that point. The tangent line is the best linear approximation of the function near that input value. For this reason, the derivative is often described as the "instantaneous rate of change", the ratio of the instantaneous change in the dependent variable to that of the independent variable. Derivatives can be generalized to functions of several real variables. In this generalization, the derivativ ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Integral
In mathematics Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics ..., an integral assigns numbers to functions in a way that describes Displacement (geometry), displacement, area, volume, and other concepts that arise by combining infinitesimal data. The process of finding integrals is called integration. Along with Derivative, differentiation, integration is a fundamental, essential operation of calculus,Integral calculus is a very well established mathematical discipline for which there are many sources. See and , for example. and serves as a tool to solve problems in mathematics and physics involving the area of an arbitrary shape, the length of a curve, and the volume of a solid, among others. The integrals enumerated here are those termed definite integrals, which can be int ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Poisson's Equation
Poisson's equation is an elliptic partial differential equation of broad utility in theoretical physics. For example, the solution to Poisson's equation is the potential field caused by a given electric charge or mass density distribution; with the potential field known, one can then calculate electrostatic or gravitational (force) field. It is a generalization of Laplace's equation, which is also frequently seen in physics. The equation is named after French mathematician and physicist Siméon Denis Poisson. Statement of the equation Poisson's equation is \Delta\varphi = f where \Delta is the Laplace operator, and f and \varphi are real or complex-valued functions on a manifold. Usually, f is given and \varphi is sought. When the manifold is Euclidean space, the Laplace operator is often denoted as and so Poisson's equation is frequently written as \nabla^2 \varphi = f. In three-dimensional Cartesian coordinates, it takes the form \left( \frac + \frac + \frac \right)\varphi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Conservative Vector Field
In vector calculus, a conservative vector field is a vector field that is the gradient of some function. A conservative vector field has the property that its line integral is path independent; the choice of any path between two points does not change the value of the line integral. Path independence of the line integral is equivalent to the vector field under the line integral being conservative. A conservative vector field is also irrotational; in three dimensions, this means that it has vanishing curl. An irrotational vector field is necessarily conservative provided that the domain is simply connected. Conservative vector fields appear naturally in mechanics: They are vector fields representing forces of physical systems in which energy is conserved. For a conservative system, the work done in moving along a path in a configuration space depends on only the endpoints of the path, so it is possible to define potential energy that is independent of the actual path taken. In ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Image Editing
Image editing encompasses the processes of altering images, whether they are digital photographs, traditional photo-chemical photographs, or illustrations. Traditional analog image editing is known as photo retouching, using tools such as an airbrush to modify photographs or editing illustrations with any traditional art medium. Graphic software programs, which can be broadly grouped into vector graphics editors, raster graphics editors, and 3D modelers, are the primary tools with which a user may manipulate, enhance, and transform images. Many image editing programs are also used to render or create computer art from scratch. The term “image editing” usually refers only to the editing of 2D images, not 3D ones. Basics of image editing Raster images are stored in a computer in the form of a grid of picture elements, or pixels. These pixels contain the image's color and brightness information. Image editors can change the pixels to enhance the image in many ways ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Finite Difference
A finite difference is a mathematical expression of the form . If a finite difference is divided by , one gets a difference quotient. The approximation of derivatives by finite differences plays a central role in finite difference methods for the numerical solution of differential equations, especially boundary value problems. The difference operator, commonly denoted \Delta is the operator that maps a function to the function \Delta /math> defined by :\Delta x)= f(x+1)-f(x). A difference equation is a functional equation that involves the finite difference operator in the same way as a differential equation involves derivatives. There are many similarities between difference equations and differential equations, specially in the solving methods. Certain recurrence relations can be written as difference equations by replacing iteration notation with finite differences. In numerical analysis, finite differences are widely used for approximating derivatives, and the term " ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sobel Operator
The Sobel operator, sometimes called the Sobel–Feldman operator or Sobel filter, is used in image processing and computer vision, particularly within edge detection algorithms where it creates an image emphasising edges. It is named after Irwin Sobel and Gary Feldman, colleagues at the Stanford Artificial Intelligence Laboratory (SAIL). Sobel and Feldman presented the idea of an " Isotropic 3 × 3 Image Gradient Operator" at a talk at SAIL in 1968. Technically, it is a discrete differentiation operator, computing an approximation of the gradient of the image intensity function. At each point in the image, the result of the Sobel–Feldman operator is either the corresponding gradient vector or the norm of this vector. The Sobel–Feldman operator is based on convolving the image with a small, separable, and integer-valued filter in the horizontal and vertical directions and is therefore relatively inexpensive in terms of computations. On the other hand, the grad ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Image Stitching
Image stitching or photo stitching is the process of combining multiple photographic images with overlapping fields of view to produce a segmented panorama or high-resolution image. Commonly performed through the use of computer software, most approaches to image stitching require nearly exact overlaps between images and identical exposures to produce seamless results, although some stitching algorithms actually benefit from differently exposed images by doing high-dynamic-range imaging in regions of overlap. Some digital cameras can stitch their photos internally. Applications Image stitching is widely used in modern applications, such as the following: * Document mosaicing *Image stabilization feature in camcorders that use frame-rate image alignment *High-resolution photomosaics in digital maps and satellite imagery *Medical imaging *Multiple-image super-resolution imaging *Video stitching *Object insertion Process The image stitching process can be divided into three ma ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Non-photorealistic Rendering
Non-photorealistic rendering (NPR) is an area of computer graphics that focuses on enabling a wide variety of expressive styles for digital art, in contrast to traditional computer graphics, which focuses on photorealism. NPR is inspired by other artistic modes such as painting, drawing, technical illustration, and animated cartoons. NPR has appeared in movies and video games in the form of cel-shaded animation (also known as " toon" shading) as well as in scientific visualization, architectural illustration and experimental animation. History and criticism of the term The term ''non-photorealistic rendering'' is believed to have been coined by the SIGGRAPH 1990 papers committee, who held a session entitled "Non Photo Realistic Rendering". The term has received some criticism: * The term "photorealism" has different meanings for graphics researchers (see "photorealistic rendering") and artists. For artists—who are the target consumers of NPR techniques—it refers to a schoo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Deblocking
A deblocking filter is a video filter applied to decoded compressed video to improve visual quality and prediction performance by smoothing the sharp edges which can form between macroblocks when block coding techniques are used. The filter aims to improve the appearance of decoded pictures. It is a part of the specification for both the SMPTE VC-1 codec and the ITU H.264 (ISO MPEG-4 AVC) codec. H.264 deblocking filter In contrast with older MPEG- 1/ 2/ 4 standards, the H.264 deblocking filter is not an optional additional feature in the decoder. It is a feature on both the decoding path and on the encoding path, so that the in-loop effects of the filter are taken into account in reference macroblocks used for prediction. When a stream is encoded, the filter strength can be selected, or the filter can be switched off entirely. Otherwise, the filter strength is determined by coding modes of adjacent blocks, quantization step size, and the steepness of the luminance gradient betw ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
