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Difference Of Gaussians
In imaging science, difference of Gaussians (DoG) is a feature enhancement algorithm that involves the subtraction of one Gaussian blurred version of an original image from another, less blurred version of the original. In the simple case of grayscale images, the blurred images are obtained by convolving the original grayscale images with Gaussian kernels having differing width (standard deviations). Blurring an image using a Gaussian kernel suppresses only high-frequency spatial information. Subtracting one image from the other preserves spatial information that lies between the range of frequencies that are preserved in the two blurred images. Thus, the DoG is a spatial band-pass filter that attenuates frequencies in the original grayscale image that are far from the band center. \sigma_1. In one dimension, \Gamma is defined as: :\Gamma_(x) = I*\frac \, e^-I*\frac \, e^. and for the centered two-dimensional case: :\Gamma_(x,y) = I*\frac e^ - I*\frac e^ which is formally e ...
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Imaging Science
Imaging is the representation or reproduction of an object's form; especially a visual representation (i.e., the formation of an image). Imaging technology is the application of materials and methods to create, preserve, or duplicate images. Imaging science is a multidisciplinary field concerned with the generation, collection, duplication, analysis, modification, and visualization of images,Joseph P. Hornak, ''Encyclopedia of Imaging Science and Technology'' (John Wiley & Sons, 2002) including imaging things that the human eye cannot detect. As an evolving field it includes research and researchers from physics, mathematics, electrical engineering, computer vision, computer science, and perceptual psychology. ''Imager'' are imaging sensors. Imaging chain The foundation of imaging science as a discipline is the "imaging chain" – a conceptual model describing all of the factors which must be considered when developing a system for creating visual renderings (images). In ...
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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 ill ...
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Scale-invariant Feature Transform
The scale-invariant feature transform (SIFT) is a computer vision algorithm to detect, describe, and match local ''features'' in images, invented by David Lowe in 1999. Applications include object recognition, robotic mapping and navigation, image stitching, 3D modeling, gesture recognition, video tracking, individual identification of wildlife and match moving. SIFT keypoints of objects are first extracted from a set of reference images and stored in a database. An object is recognized in a new image by individually comparing each feature from the new image to this database and finding candidate matching features based on Euclidean distance of their feature vectors. From the full set of matches, subsets of keypoints that agree on the object and its location, scale, and orientation in the new image are identified to filter out good matches. The determination of consistent clusters is performed rapidly by using an efficient hash table implementation of the generalised Hough trans ...
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Scale Space
Scale-space theory is a framework for multi-scale signal representation developed by the computer vision, image processing and signal processing communities with complementary motivations from physics and biological vision. It is a formal theory for handling image structures at different scales, by representing an image as a one-parameter family of smoothed images, the scale-space representation, parametrized by the size of the smoothing kernel used for suppressing fine-scale structures.Ijima, T. "Basic theory on normalization of pattern (in case of typical one-dimensional pattern)". Bull. Electrotech. Lab. 26, 368– 388, 1962. (in Japanese) The parameter t in this family is referred to as the ''scale parameter'', with the interpretation that image structures of spatial size smaller than about \sqrt have largely been smoothed away in the scale-space level at scale t. The main type of scale space is the ''linear (Gaussian) scale space'', which has wide applicability as well as ...
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Gaussian Pyramid
Pyramid, or pyramid representation, is a type of multi-scale signal representation developed by the computer vision, image processing and signal processing communities, in which a signal or an image is subject to repeated smoothing and subsampling. Pyramid representation is a predecessor to scale-space representation and multiresolution analysis. Pyramid generation There are two main types of pyramids: lowpass and bandpass. A lowpass pyramid is made by smoothing the image with an appropriate smoothing filter and then subsampling the smoothed image, usually by a factor of 2 along each coordinate direction. The resulting image is then subjected to the same procedure, and the cycle is repeated multiple times. Each cycle of this process results in a smaller image with increased smoothing, but with decreased spatial sampling density (that is, decreased image resolution). If illustrated graphically, the entire multi-scale representation will look like a pyramid, with the original ...
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Retina
The retina (from la, rete "net") is the innermost, light-sensitive layer of tissue of the eye of most vertebrates and some molluscs. The optics of the eye create a focused two-dimensional image of the visual world on the retina, which then processes that image within the retina and sends nerve impulses along the optic nerve to the visual cortex to create visual perception. The retina serves a function which is in many ways analogous to that of the film or image sensor in a camera. The neural retina consists of several layers of neurons interconnected by synapses and is supported by an outer layer of pigmented epithelial cells. The primary light-sensing cells in the retina are the photoreceptor cells, which are of two types: rods and cones. Rods function mainly in dim light and provide monochromatic vision. Cones function in well-lit conditions and are responsible for the perception of colour through the use of a range of opsins, as well as high-acuity vision used fo ...
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Multivariate Normal Distribution
In probability theory and statistics, the multivariate normal distribution, multivariate Gaussian distribution, or joint normal distribution is a generalization of the one-dimensional ( univariate) normal distribution to higher dimensions. One definition is that a random vector is said to be ''k''-variate normally distributed if every linear combination of its ''k'' components has a univariate normal distribution. Its importance derives mainly from the multivariate central limit theorem. The multivariate normal distribution is often used to describe, at least approximately, any set of (possibly) correlated real-valued random variables each of which clusters around a mean value. Definitions Notation and parameterization The multivariate normal distribution of a ''k''-dimensional random vector \mathbf = (X_1,\ldots,X_k)^ can be written in the following notation: : \mathbf\ \sim\ \mathcal(\boldsymbol\mu,\, \boldsymbol\Sigma), or to make it explicitly known that ''X'' ...
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Scale-invariant Feature Transform
The scale-invariant feature transform (SIFT) is a computer vision algorithm to detect, describe, and match local ''features'' in images, invented by David Lowe in 1999. Applications include object recognition, robotic mapping and navigation, image stitching, 3D modeling, gesture recognition, video tracking, individual identification of wildlife and match moving. SIFT keypoints of objects are first extracted from a set of reference images and stored in a database. An object is recognized in a new image by individually comparing each feature from the new image to this database and finding candidate matching features based on Euclidean distance of their feature vectors. From the full set of matches, subsets of keypoints that agree on the object and its location, scale, and orientation in the new image are identified to filter out good matches. The determination of consistent clusters is performed rapidly by using an efficient hash table implementation of the generalised Hough trans ...
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Blob Detection
In computer vision, blob detection methods are aimed at detecting regions in a digital image that differ in properties, such as brightness or color, compared to surrounding regions. Informally, a blob is a region of an image in which some properties are constant or approximately constant; all the points in a blob can be considered in some sense to be similar to each other. The most common method for blob detection is convolution. Given some property of interest expressed as a function of position on the image, there are two main classes of blob detectors: (i) '' differential methods'', which are based on derivatives of the function with respect to position, and (ii) ''methods based on local extrema'', which are based on finding the local maxima and minima of the function. With the more recent terminology used in the field, these detectors can also be referred to as ''interest point operators'', or alternatively interest region operators (see also interest point detec ...
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Blob Detection
In computer vision, blob detection methods are aimed at detecting regions in a digital image that differ in properties, such as brightness or color, compared to surrounding regions. Informally, a blob is a region of an image in which some properties are constant or approximately constant; all the points in a blob can be considered in some sense to be similar to each other. The most common method for blob detection is convolution. Given some property of interest expressed as a function of position on the image, there are two main classes of blob detectors: (i) '' differential methods'', which are based on derivatives of the function with respect to position, and (ii) ''methods based on local extrema'', which are based on finding the local maxima and minima of the function. With the more recent terminology used in the field, these detectors can also be referred to as ''interest point operators'', or alternatively interest region operators (see also interest point detec ...
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Laplacian Of Gaussian
In computer vision, blob detection methods are aimed at detecting regions in a digital image that differ in properties, such as brightness or color, compared to surrounding regions. Informally, a blob is a region of an image in which some properties are constant or approximately constant; all the points in a blob can be considered in some sense to be similar to each other. The most common method for blob detection is convolution. Given some property of interest expressed as a function of position on the image, there are two main classes of blob detectors: (i) '' differential methods'', which are based on derivatives of the function with respect to position, and (ii) ''methods based on local extrema'', which are based on finding the local maxima and minima of the function. With the more recent terminology used in the field, these detectors can also be referred to as ''interest point operators'', or alternatively interest region operators (see also interest point detecti ...
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