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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Laplacian of Gaussian ： ウィキペディア英語版 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. 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 detection and corner detection). There are several motivations for studying and developing blob detectors. One main reason is to provide complementary information about regions, which is not obtained from edge detectors or corner detectors. In early work in the area, blob detection was used to obtain regions of interest for further processing. These regions could signal the presence of objects or parts of objects in the image domain with application to object recognition and/or object tracking. In other domains, such as histogram analysis, blob descriptors can also be used for peak detection with application to segmentation. Another common use of blob descriptors is as main primitives for texture analysis and texture recognition. In more recent work, blob descriptors have found increasingly popular use as interest points for wide baseline stereo matching and to signal the presence of informative image features for appearance-based object recognition based on local image statistics. There is also the related notion of ridge detection to signal the presence of elongated objects. ==The Laplacian of Gaussian== One of the first and also most common blob detectors is based on the Laplacian of the Gaussian (LoG). Given an input image $f(x,\; y)$, this image is convolved by a Gaussian kernel :$g(x,\; y,\; t)\; =\; \backslash frac\; e^\}$ at a certain scale $t$ to give a scale space representation $L(x,\; y;\; t)\backslash \; =\; g(x,\; y,\; t)$ * f(x, y). Then, the result of applying the Laplacian operator :$\backslash nabla^2\; L\; =L\_\; +\; L\_$ is computed, which usually results in strong positive responses for dark blobs of extent $\backslash sqrt$ and strong negative responses for bright blobs of similar size. A main problem when applying this operator at a single scale, however, is that the operator response is strongly dependent on the relationship between the size of the blob structures in the image domain and the size of the Gaussian kernel used for pre-smoothing. In order to automatically capture blobs of different (unknown) size in the image domain, a multi-scale approach is therefore necessary. A straightforward way to obtain a ''multi-scale blob detector with automatic scale selection'' is to consider the ''scale-normalized Laplacian operator'' :$\backslash nabla^2\_\; L(x,\; y;\; t)\; =\; t\; (L\_\; +\; L\_)$ and to detect ''scale-space maxima/minima'', that are points that are ''simultaneously local maxima/minima of $\backslash nabla^2\_\; L$ with respect to both space and scale'' (Lindeberg 1994, 1998). Thus, given a discrete two-dimensional input image $f(x,\; y)$ a three-dimensional discrete scale-space volume $L(x,\; y,\; t)$ is computed and a point is regarded as a bright (dark) blob if the value at this point is greater (smaller) than the value in all its 26 neighbours. Thus, simultaneous selection of interest points $(\backslash hat,\; \backslash hat)$ and scales $\backslash hat$ is performed according to :$(\backslash hat,\; \backslash hat;\; \backslash hat)\; =\; \backslash operatorname\_(\backslash nabla^2\_\; L(x,\; y;\; t))$. Note that this notion of blob provides a concise and mathematically precise operational definition of the notion of "blob", which directly leads to an efficient and robust algorithm for blob detection. Some basic properties of blobs defined from scale-space maxima of the normalized Laplacian operator are that the responses are covariant with translations, rotations and rescalings in the image domain. Thus, if a scale-space maximum is assumed at a point $(x\_0,\; y\_0;\; t\_0)$ then under a rescaling of the image by a scale factor $s$, there will be a scale-space maximum at $(s\; x\_0,\; s\; y\_0;\; s^2\; t\_0)$ in the rescaled image (Lindeberg 1998). This in practice highly useful property implies that besides the specific topic of Laplacian blob detection, ''local maxima/minima of the scale-normalized Laplacian are also used for scale selection in other contexts'', such as in corner detection, scale-adaptive feature tracking (Bretzner and Lindeberg 1998), in the scale-invariant feature transform (Lowe 2004) as well as other image descriptors for image matching and object recognition. The scale selection properties of the Laplacian operator and other closely scale-space interest point detectors are analyzed in detail in (Lindeberg 2013a).〔(Lindeberg, Tony (2013) "Scale Selection Properties of Generalized Scale-Space Interest Point Detectors", Journal of Mathematical Imaging and Vision, Volume 46, Issue 2, pages 177-210. )〕 In (Lindeberg 2013b, 2015)〔(Lindeberg (2013) "Image Matching Using Generalized Scale-Space Interest Points", Scale Space and Variational Methods in Computer Vision, Springer Lecture Notes in Computer Science Volume 7893, 2013, pp 355-367. )〕〔 it is shown that there exist other scale-space interest point detectors, such as the determinant of the Hessian operator, that perform better than Laplacian operator or its difference-of-Gaussians approximation for image-based matching using local SIFT-like image descriptors. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Blob detection」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. 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