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Top2. Mean-Shift Method
Given the
samples
,
=1,
,
, in the d-dimensional space Rd, then the Mean-shift vector at the
is defined that:
(1)
is a district of high-dimensional spheroid with radius
, and satisfies the following relation of
in order of gather:
(2)
is the number of points in the
samples
, which falls into the
district. (
-
) is the deviation vector of the sample
. The Mean Shift vector
which is defined in Equation (1) is the average value of the deviation vectors of the
samples which fall into the
district opposite the
point. If the sample
is got from the sample of the probability density function
, non-zero probability density gradient points to the direction at which the probability density increases most. On average, the samples in the
district mostly fall at along the direction of probability density gradient, therefore the corresponding Mean-shift vector
points to the direction of the probability density gradient (Comaniciu & Meer, 2002). From Equation (1), as long as it is the sample which falls into
district, the contribution to
calculation is all similar no matter its distance from
, however, the sample which is near the
is more effective to the statistics characteristic that estimates
surroundings, therefore the concept of kernel function is introduced. As important values of all samples
are different, therefore a weighted coefficient is used for each sample. So the expand basic form of Mean-shift is:
![japuc.2013010104.m33](https://igiprodst.blob.core.windows.net:443/source-content/9781466631045_71301/japuc.2013010104.m33.png?sv=2015-12-11&sr=c&sig=%2BF5PCce%2BjKMBw7NBKaK7j4%2FlQAklmzvvOQwfz%2BWoDdM%3D&se=2019-12-21T14%3A57%3A29Z&sp=r)
(3) where: