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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 scale space ： ウィキペディア英語版 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.〔〔〔〔〔〔〔 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 $\backslash sqrt$ 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 the attractive property of being possible to derive from a small set of ''scale-space axioms''. The corresponding scale-space framework encompasses a theory for Gaussian derivative operators, which can be used as a basis for expressing a large class of visual operations for computerized systems that process visual information. This framework also allows visual operations to be made ''scale invariant'', which is necessary for dealing with the size variations that may occur in image data, because real-world objects may be of different sizes and in addition the distance between the object and the camera may be unknown and may vary depending on the circumstances.〔〔 ==Definition== The notion of scale space applies to signals of arbitrary numbers of variables. The most common case in the literature applies to two-dimensional images, which is what is presented here. For a given image $f(x,\; y)$, its linear (Gaussian) ''scale-space representation'' is a family of derived signals $L(x,\; y;\; t)$ defined by the convolution of $f(x,\; y)$ with the two-dimensional Gaussian kernel :$g(x,\; y;\; t)\; =\; \backslash frac\; e^\backslash ,$ such that :$L(\backslash cdot,\; \backslash cdot\; ;\; t)\backslash \; =\; g(\backslash cdot,\; \backslash cdot\; ;\; t)$ * f(\cdot, \cdot) , where the semicolon in the argument of $L$ implies that the convolution is performed only over the variables $x,\; y$, while the scale parameter $t$ after the semicolon just indicates which scale level is being defined. This definition of $L$ works for a continuum of scales $t\; \backslash geq\; 0$, but typically only a finite discrete set of levels in the scale-space representation would be actually considered. The scale parameteter $t\; =\; \backslash sigma^2$ is the variance of the Gaussian filter and as a limit for $t\; =\; 0$ the filter $g$ becomes an impulse function such that $L(x,\; y;\; 0)\; =\; f(x,\; y),$ that is, the scale-space representation at scale level $t\; =\; 0$ is the image $f$ itself. As $t$ increases, $L$ is the result of smoothing $f$ with a larger and larger filter, thereby removing more and more of the details which the image contains. Since the standard deviation of the filter is $\backslash sigma\; =\; \backslash sqrt$, details which are significantly smaller than this value are to a large extent removed from the image at scale parameter $t$, see the following figure and 〔 for graphical illustrations. Image:Scalespace0.png|Scale-space representation $L(x,y;t)$ at scale $t=0$, corresponding to the original image $f$ Image:Scalespace1.png|Scale-space representation $L(x,y;t)$ at scale $t=1$ Image:Scalespace2.png|Scale-space representation $L(x,y;t)$ at scale $t=4$ Image:Scalespace3.png|Scale-space representation $L(x,y;t)$ at scale $t=16$ Image:Scalespace4.png|Scale-space representation $L(x,y;t)$ at scale $t=64$ Image:Scalespace5.png|Scale-space representation $L(x,y;t)$ at scale $t=256$ 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「scale space」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. All Rights Reserved.