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Guided Filter
A Guided filter is an edge-preserving smoothing light filter. As with a bilateral filter, it can filter out noise or texture while retaining sharp edges. Comparison Compared to the bilateral filter, the guided image filter has two advantages: bilateral filters have high computational complexity, while the guided image filter uses simpler calculations with linear computational complexity. Bilateral filters sometimes include unwanted gradient reversal artifacts and cause image distortion. The guided image filter is based on linear combination, making the output image consistent with the gradient direction of the guidance image, preventing gradient reversal. Definition One key assumption of the guided filter is that the relation between guidance I and the filtering output q is linear. Suppose that q is a linear transformation of I in a window \omega_k centered at the pixel k. In order to determine the linear coefficient (a_k, b_k), constraints from the filtering input p are req ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Edge-preserving Smoothing
Edge-preserving smoothing or edge-preserving filtering is an image processing technique that smooths away noise or textures while retaining sharp edges. Examples are the median, bilateral, guided, anisotropic diffusion, and Kuwahara filters. Introduction In many applications, e.g., medical or satellite imaging, the edges are key features and thus must be preserved sharp and undistorted in smoothing/denoising. Edge-preserving filters are designed to automatically limit the smoothing at “edges” in images measured, e.g., by high gradient magnitudes. For example, the motivation for anisotropic diffusion (also called nonuniform or variable conductance diffusion) is that a Gaussian smoothed image is a single time slice of the solution to the heat equation, that has the original image as its initial conditions. Anisotropic diffusion includes a variable conductance term that is determined using the differential structure of the image, such that the heat does not propagate over the ... [...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] |
Computational Complexity
In computer science, the computational complexity or simply complexity of an algorithm is the amount of resources required to run it. Particular focus is given to computation time (generally measured by the number of needed elementary operations) and memory storage requirements. The complexity of a problem is the complexity of the best algorithms that allow solving the problem. The study of the complexity of explicitly given algorithms is called analysis of algorithms, while the study of the complexity of problems is called computational complexity theory. Both areas are highly related, as the complexity of an algorithm is always an upper bound on the complexity of the problem solved by this algorithm. Moreover, for designing efficient algorithms, it is often fundamental to compare the complexity of a specific algorithm to the complexity of the problem to be solved. Also, in most cases, the only thing that is known about the complexity of a problem is that it is lower than the c ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Linear
Linearity is the property of a mathematical relationship (''function'') that can be graphically represented as a straight line. Linearity is closely related to '' proportionality''. Examples in physics include rectilinear motion, the linear relationship of voltage and current in an electrical conductor (Ohm's law), and the relationship of mass and weight. By contrast, more complicated relationships are ''nonlinear''. Generalized for functions in more than one dimension, linearity means the property of a function of being compatible with addition and scaling, also known as the superposition principle. The word linear comes from Latin ''linearis'', "pertaining to or resembling a line". In mathematics In mathematics, a linear map or linear function ''f''(''x'') is a function that satisfies the two properties: * Additivity: . * Homogeneity of degree 1: for all α. These properties are known as the superposition principle. In this definition, ''x'' is not necessarily a real ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Gradient
In vector calculus, the gradient of a scalar-valued differentiable function of several variables is the vector field (or vector-valued function) \nabla f whose value at a point p is the "direction and rate of fastest increase". If the gradient of a function is non-zero at a point , the direction of the gradient is the direction in which the function increases most quickly from , and the magnitude of the gradient is the rate of increase in that direction, the greatest absolute directional derivative. Further, a point where the gradient is the zero vector is known as a stationary point. The gradient thus plays a fundamental role in optimization theory, where it is used to maximize a function by gradient ascent. In coordinate-free terms, the gradient of a function f(\bf) may be defined by: :df=\nabla f \cdot d\bf where ''df'' is the total infinitesimal change in ''f'' for an infinitesimal displacement d\bf, and is seen to be maximal when d\bf is in the direction of the gradi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Loss Function
In mathematical optimization and decision theory, a loss function or cost function (sometimes also called an error function) is a function that maps an event or values of one or more variables onto a real number intuitively representing some "cost" associated with the event. An optimization problem seeks to minimize a loss function. An objective function is either a loss function or its opposite (in specific domains, variously called a reward function, a profit function, a utility function, a fitness function, etc.), in which case it is to be maximized. The loss function could include terms from several levels of the hierarchy. In statistics, typically a loss function is used for parameter estimation, and the event in question is some function of the difference between estimated and true values for an instance of data. The concept, as old as Laplace, was reintroduced in statistics by Abraham Wald in the middle of the 20th century. In the context of economics, for example, this i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
MATLAB
MATLAB (an abbreviation of "MATrix LABoratory") is a proprietary multi-paradigm programming language and numeric computing environment developed by MathWorks. MATLAB allows matrix manipulations, plotting of functions and data, implementation of algorithms, creation of user interfaces, and interfacing with programs written in other languages. Although MATLAB is intended primarily for numeric computing, an optional toolbox uses the MuPAD symbolic engine allowing access to symbolic computing abilities. An additional package, Simulink, adds graphical multi-domain simulation and model-based design for dynamic and embedded systems. As of 2020, MATLAB has more than 4 million users worldwide. They come from various backgrounds of engineering, science, and economics. History Origins MATLAB was invented by mathematician and computer programmer Cleve Moler. The idea for MATLAB was based on his 1960s PhD thesis. Moler became a math professor at the University of New Mexico and starte ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
OpenCV
OpenCV (''Open Source Computer Vision Library'') is a library of programming functions mainly aimed at real-time computer vision. Originally developed by Intel, it was later supported by Willow Garage then Itseez (which was later acquired by Intel). The library is cross-platform and free for use under the open-source Apache 2 License. Starting with 2011, OpenCV features GPU acceleration for real-time operations. History Officially launched in 1999 the OpenCV project was initially an Intel Research initiative to advance CPU-intensive applications, part of a series of projects including real-time ray tracing and 3D display walls. The main contributors to the project included a number of optimization experts in Intel Russia, as well as Intel's Performance Library Team. In the early days of OpenCV, the goals of the project were described as: * Advance vision research by providing not only open but also optimized code for basic vision infrastructure. No more reinventing the wheel ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
FFmpeg
FFmpeg is a free and open-source software project consisting of a suite of libraries and programs for handling video, audio, and other multimedia files and streams. At its core is the command-line ffmpeg tool itself, designed for processing of video and audio files. It is widely used for format transcoding, basic editing (trimming and concatenation), video scaling, video post-production effects and standards compliance (SMPTE, ITU). FFmpeg also includes other tools: ffplay, a simple media player and ffprobe, a command-line tool to display media information. Among included libraries are libavcodec, an audio/video codec library used by many commercial and free software products, libavformat (Lavf), an audio/video container mux and demux library, and libavfilter, a library for enhancing and editing filters through a Gstreamer-like filtergraph. FFmpeg is part of the workflow of many other software projects, and its libraries are a core part of software media players such as VLC, an ... [...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] |
Computer Graphics
Computer graphics deals with generating images with the aid of computers. Today, computer graphics is a core technology in digital photography, film, video games, cell phone and computer displays, and many specialized applications. A great deal of specialized hardware and software has been developed, with the displays of most devices being driven by computer graphics hardware. It is a vast and recently developed area of computer science. The phrase was coined in 1960 by computer graphics researchers Verne Hudson and William Fetter of Boeing. It is often abbreviated as CG, or typically in the context of film as computer generated imagery (CGI). The non-artistic aspects of computer graphics are the subject of computer science research. Some topics in computer graphics include user interface design, sprite graphics, rendering, ray tracing, geometry processing, computer animation, vector graphics, 3D modeling, shaders, GPU design, implicit surfaces, visualization, scientific c ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
