Kmeasure(spatstat)
Kmeasure()所属R语言包：spatstat
Reduced Second Moment Measure
减少二阶矩测量
译者：生物统计家园网 机器人LoveR
描述----------Description----------
Estimates the reduced second moment measure Kappa from a point pattern in a window of arbitrary shape.
估算减少二次矩措施Kappa从在一个窗口中的任意形状的点图案。
用法----------Usage----------
Kmeasure(X, sigma, edge=TRUE, ..., varcov=NULL)
参数----------Arguments----------
参数：X
The observed point pattern, from which an estimate of Kappa will be computed. An object of class "ppp", or data in any format acceptable to as.ppp().
观测点的模式，从一个估算的Kappa将被计算。对象的类"ppp"，或任何格式的数据中接受的as.ppp()。
参数：sigma
Standard deviation sigma of the Gaussian smoothing kernel. Incompatible with varcov.
标准偏差sigma高斯平滑内核。不相容的varcov。
参数：edge
logical value indicating whether an edge correction should be applied.
逻辑值，该值指示是否应适用于边缘校正。
参数：...
Ignored.
忽略。
参数：varcov
Variance-covariance matrix of the Gaussian smoothing kernel. Incompatible with sigma.
方差 - 协方差矩阵的高斯平滑内核。不相容的sigma。
Details
详细信息----------Details----------
Given a point pattern dataset, this command computes an estimate of the reduced second moment measure Kappa of the point process. The result is a pixel image whose pixel values are estimates of the density of the reduced second moment measure.
此命令中给出一个点的模式数据集，计算估计二阶矩措施减少Kappa点过程。其结果是一个像素的图像，其像素值是估计值的密度降低的第二时刻措施。
The reduced second moment measure Kappa can be regarded as a generalisation of the more familiar K-function. An estimate of Kappa derived from a spatial point pattern dataset can be useful in exploratory data analysis. Its advantage over the K-function is that it is also sensitive to anisotropy and directional effects.
减少的第二个时刻措施Kappa可以算是比较熟悉的K功能的泛化。的估计Kappa来自一个空间点格局数据集可以是有益的探索性数据分析。它的优点是，它是在K功能也敏感的各向异性和定向效应。
In a nutshell, the command Kmeasure computes a smoothed version of the Fry plot. As explained under fryplot, the Fry plot is a scatterplot of the vectors joining all pairs of points in the pattern. The reduced second moment measure is (essentially) defined as the average of the Fry plot over different realisations of the point process. The command Kmeasure effectively smooths the Fry plot of a dataset to obtain an estimate of the reduced second moment measure.
简单地说中，命令Kmeasure计算一个平滑的鱼苗图。正如上文fryplot，鱼苗的图是向量加盟模式中的所有点对的散点图。二阶矩措施减少（本质上）是定义的鱼苗平均积点过程在不同的实现。命令Kmeasure有效地平滑弗莱图的数据集获得的估计值减少二阶矩措施。
In formal terms, the reduced second moment measure Kappa of a stationary point process X is a measure defined on the two-dimensional plane such that, for a "typical" point x of the process, the expected number of other points y of the process such that the vector y - x lies in a region A, equals lambda * Kappa(A). Here lambda is the intensity of the process, i.e. the expected number of points of X per unit area.
在形式上，减少二次矩措施Kappa的一个固定点过程X是量度上定义的二维平面上，例如，对于“典型”点x的过程中，其他各点的预期数目的y等过程，矢量y - x在于在区域A等于lambda * Kappa(A)。这是lambda过程的强度，即点X每单位面积的预期。
The K-function is a special case. The function value K(t) is the value of the reduced second moment measure for the disc of radius t centred at the origin; that is, K(t) = Kappa(b(0,t)).
K功能是一种特殊情况。的函数值K(t)是对于光盘的半径的值降低的第二时刻措施t以原点为中心，也就是说，K(t) = Kappa(b(0,t))。
The command Kmeasure computes an estimate of Kappa from a point pattern dataset X, which is assumed to be a realisation of a stationary point process, observed inside a known, bounded window. Marks are ignored.
命令Kmeasure计算的估计Kappa从一个点模式数据集中X，这被认为是一个实现了一个固定的点过程中，观察到在一个已知的，有限的窗口。标志将被忽略。
The algorithm approximates the point pattern and its window by binary pixel images, introduces a Gaussian smoothing kernel and uses the Fast Fourier Transform fft to form a density estimate of Kappa. The calculation corresponds to the edge correction known as the “translation correction”.
由二进制象素的图像，该算法接近的点图案和其窗口，引入了一个高斯平滑内核，并使用快速傅立叶变换fftKappa以形成密度估计。计算对应于被称为“翻译校正”的边缘校正。
The Gaussian smoothing kernel may be specified by either of the arguments sigma or varcov. If sigma is a single number, this specifies an isotropic Gaussian kernel with standard deviation sigma on each coordinate axis. If sigma is a vector of two numbers, this specifies a Gaussian kernel with standard deviation sigma[1] on the x axis, standard deviation sigma[2] on the y axis, and zero correlation between the x and y axes. If varcov is given, this specifies the variance-covariance matrix of the Gaussian kernel. There do not seem to be any well-established rules for selecting the smoothing kernel in this context.
高斯平滑的核心可以指定任一参数sigma或varcov。如果sigma是单数，指定一个各向同性的高斯核与标准差sigma了各坐标轴。 sigma如果是一个向量的两个数字，指定高斯内核与标准差sigma[1]x轴，标准差sigma[2]y轴和零x和y轴之间的相关性。 varcov如果，这指定的方差 - 协方差矩阵的高斯内核。似乎没有在这种情况下选择平滑的内核是任何既定规则。
The density estimate of Kappa is returned in the form of a real-valued pixel image. Pixel values are estimates of the normalised second moment density at the centre of the pixel. (The uniform Poisson process would have values identically equal to 1.) The image x and y coordinates are on the same scale as vector displacements in the original point pattern window. The point x=0, y=0 corresponds to the "typical point". A peak in the image near (0,0) suggests clustering; a dip in the image near (0,0) suggests inhibition; peaks or dips at other positions suggest possible periodicity.
Kappa的密度估计的实值的像素图像的形式返回。像素值是估计值的归一化的二次矩密度的像素的中心处。 （统一的泊松过程将有值恒等于1。）的图像x和y坐标是同等规模的矢量位移在原来的点模式窗口。点x=0, y=0对应的“特征点”。中的峰值附近的图像(0,0)建议聚类;浸在附近的形象(0,0)表明抑制的峰值或在其他位置上建议逢低可能的周期性。
If desired, the value of Kappa(A) for a region A can be estimated by computing the integral of the pixel image over the domain A, i.e.\ summing the pixel values and multiplying by pixel area, using integral.im. One possible application is to compute anisotropic counterparts of the K-function (in which the disc of radius t is replaced by another shape). See Examples.
如果需要的话，的值Kappa(A)区域A可以通过计算在域的像素图像的积分来估计A，即\求和的像素值，并乘以像素区域使用integral.im。一种可能的应用是计算各向异性同行K-功能（在其中的光盘的半径t被替换另一个形状）。请参阅示例。
值----------Value----------
A real-valued pixel image (an object of class "im", see im.object) whose pixel values are estimates of the density of the reduced second moment measure at each location.
一个真正的值的像素的图像（类的一个对象"im"，请参阅im.object），其像素值是估计值，在每个位置的密度的降低的第二时刻措施。
警告----------Warning----------
Some writers use the term reduced second moment measure when they mean the K-function. This has caused confusion.
有些作家使用的术语，减少二阶矩措施时，他们指的是K功能。这已经引起了混乱。
As originally defined, the reduced second moment measure is a measure, obtained by modifying the second moment measure, while the K-function is a function obtained by evaluating this measure for discs of increasing radius. In spatstat, the K-function is computed by Kest and the reduced second moment measure is computed by Kmeasure.
原本的定义，减少二次矩量度属于一个量度，通过修改所述第二时刻措施而获得的，而K-函数是一个函数，通过评价这一措施的光盘的半径增加而获得。在spatstat，K的计算方法是Kest和二阶矩措施减少的计算方法是Kmeasure功能。
（作者）----------Author(s)----------
Adrian Baddeley
<a href="mailto:Adrian.Baddeley@csiro.au">Adrian.Baddeley@csiro.au</a>
<a href="http://www.maths.uwa.edu.au/~adrian/">http://www.maths.uwa.edu.au/~adrian/</a>
and Rolf Turner
<a href="mailto:r.turner@auckland.ac.nz">r.turner@auckland.ac.nz</a>
参考文献----------References----------
Stochastic geometry and its applications. 2nd edition. Springer Verlag.
Fractals, random shapes and point fields: methods of geometrical statistics. John Wiley and Sons.
参见----------See Also----------
Kest, fryplot, spatstat.options, integral.im, im.object
Kest，fryplot，spatstat.options，integral.im，im.object
实例----------Examples----------
data(cells)
plot(Kmeasure(cells, 0.05))
# shows pronounced dip around origin consistent with strong inhibition[周围原产地相一致，具有较强的抑制表现出明显的浸]
data(redwood)
plot(Kmeasure(redwood, 0.03), col=grey(seq(1,0,length=32)))
# shows peaks at several places, reflecting clustering and ?periodicity[峰在几个地方，反映聚类和周期性]
M <- Kmeasure(cells, 0.05)
# evaluate measure on a sector[评估一个部门的措施]
W <- as.owin(M)
ang <- as.im(atan2, W)
rad <- as.im(function(x,y){sqrt(x^2+y^2)}, W)
sector <- solutionset(ang > 0 & ang < 1 & rad < 0.6)
integral.im(M[sector, drop=FALSE])
转载请注明:出自 生物统计家园网(http://www.biostatistic.net)。
注：
注1：为了方便大家学习，本文档为生物统计家园网机器人LoveR翻译而成，仅供个人R语言学习参考使用，生物统计家园保留版权。
注2：由于是机器人自动翻译，难免有不准确之处，使用时仔细对照中、英文内容进行反复理解，可以帮助R语言的学习。
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发表于 2012-9-30 13:40:00
