|
Steerable Filter
In applied mathematics, a steerable filter is an orientation-selective convolution kernel used for image enhancement and feature extraction that can be expressed via a linear combination of a small set of rotated versions of itself. As an example, the oriented first derivative of a 2D Gaussian is a steerable filter. The oriented first order derivative can be obtained by taking the dot product of a unit vector oriented in a specific direction with the gradient. The basis filters are the partial derivatives of a 2D Gaussian with respect to x and y. The process by which the oriented filter is synthesized at any given angle is known as ''steering'', which is used in similar sense as in beam steering for antenna arrays. Applications of steerable filters include edge detection Edge detection includes a variety of mathematical methods that aim at identifying edges, curves in a digital image at which the image brightness changes sharply or, more formally, has discontinuities. Th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Applied Mathematics
Applied mathematics is the application of mathematical methods by different fields such as physics, engineering, medicine, biology, finance, business, computer science, and industry. Thus, applied mathematics is a combination of mathematical science and specialized knowledge. The term "applied mathematics" also describes the professional specialty in which mathematicians work on practical problems by formulating and studying mathematical models. In the past, practical applications have motivated the development of mathematical theories, which then became the subject of study in pure mathematics where abstract concepts are studied for their own sake. The activity of applied mathematics is thus intimately connected with research in pure mathematics. History Historically, applied mathematics consisted principally of applied analysis, most notably differential equations; approximation theory (broadly construed, to include representations, asymptotic methods, variational ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Kernel (image Processing)
In image processing, a kernel, convolution matrix, or mask is a small matrix used for blurring, sharpening, embossing, edge detection, and more. This is accomplished by doing a convolution between the kernel and an image. Details The general expression of a convolution is g(x,y)= \omega *f(x,y)=\sum_^a, where g(x,y) is the filtered image, f(x,y) is the original image, \omega is the filter kernel. Every element of the filter kernel is considered by -a \leq dx \leq a and -b \leq dy \leq b. Depending on the element values, a kernel can cause a wide range of effects. . The above are just a few examples of effects achievable by convolving kernels and images. Origin The origin is the position of the kernel which is above (conceptually) the current output pixel. This could be outside of the actual kernel, though usually it corresponds to one of the kernel elements. For a symmetric kernel, the origin is usually the center element. Convolution Convolution is the pr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Dot Product
In mathematics, the dot product or scalar productThe term ''scalar product'' means literally "product with a scalar as a result". It is also used sometimes for other symmetric bilinear forms, for example in a pseudo-Euclidean space. is an algebraic operation that takes two equal-length sequences of numbers (usually coordinate vectors), and returns a single number. In Euclidean geometry, the dot product of the Cartesian coordinates of two vectors is widely used. It is often called the inner product (or rarely projection product) of Euclidean space, even though it is not the only inner product that can be defined on Euclidean space (see Inner product space for more). Algebraically, the dot product is the sum of the products of the corresponding entries of the two sequences of numbers. Geometrically, it is the product of the Euclidean magnitudes of the two vectors and the cosine of the angle between them. These definitions are equivalent when using Cartesian coordinates. In mo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Beam Steering
Beam steering is a technique for changing the direction of the main lobe of a radiation pattern. In radio and radar systems, beam steering may be accomplished by switching the antenna elements or by changing the relative phases of the RF signals driving the elements. In recent days the beam steering is playing significant role in 5G communication because of quasi-optic nature of 5G frequencies. In acoustics, beam steering is used to direct the audio from loudspeakers to a specific location in the listening area. This is done by changing the magnitude and phase of two or more loudspeakers installed in a column where the combined sound is added and cancelled at the required position. Commercially, this type of loudspeaker arrangement is known as a line array. This technique has been around for many years but since the emergence of modern Digital Signal Processing technology there are now many commercially available products on the market. Beam steering and directivity Control u ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Edge Detection
Edge detection includes a variety of mathematical methods that aim at identifying edges, curves in a digital image at which the image brightness changes sharply or, more formally, has discontinuities. The same problem of finding discontinuities in one-dimensional signals is known as ''step detection'' and the problem of finding signal discontinuities over time is known as ''change detection''. Edge detection is a fundamental tool in image processing, machine vision and computer vision, particularly in the areas of feature detection and feature extraction. Motivations The purpose of detecting sharp changes in image brightness is to capture important events and changes in properties of the world. It can be shown that under rather general assumptions for an image formation model, discontinuities in image brightness are likely to correspond to: * discontinuities in depth, * discontinuities in surface orientation, * changes in material properties and * variations in scene illumi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Image Processing
An image is a visual representation of something. It can be two-dimensional, three-dimensional, or somehow otherwise feed into the visual system to convey information. An image can be an artifact, such as a photograph or other two-dimensional picture, that resembles a subject. In the context of signal processing, an image is a distributed amplitude of color(s). In optics, the term “image” may refer specifically to a 2D image. An image does not have to use the entire visual system to be a visual representation. A popular example of this is of a greyscale image, which uses the visual system's sensitivity to brightness across all wavelengths, without taking into account different colors. A black and white visual representation of something is still an image, even though it does not make full use of the visual system's capabilities. Images are typically still, but in some cases can be moving or animated. Characteristics Images may be two or three-dimensional, such as a pho ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
