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Exact(5)

where S i is the cluster i, X j is coordinate of sensor node j and m i is the coordinate of mean of point.

When the classification of all nodes is done, the new mean of point is created which is calculated by m i ( t + 1 ) = 1 S i ( t ) ∑ X j ∈ S i ( t ) X j, (10).

The cluster head is a sensor node which is closer to the final mean of point and the residual energy of the sensor node is higher than the average residual energy in each cluster.

We use the k-means algorithm to partition the n sensor nodes into k clusters in which each sensor node belongs to the cluster with the nearest mean of point.

According to C and R, the locations of initial mean of point m i ( m i x, m i y ) for the cluster i is calculated by m i x = R × cos ( 360 k × ( i - 1 ) × π 180 ) + C x m i y = R × sin ( 360 k × ( i - 1 ) × π 180 ) + C y, (6).

Similar(55)

where μ i is the mean of points in S i, is minimized [49,50].

Where μ i is the mean of points in S i and k = 2.

The non-local mean filter takes the mean of points whose Gaussian neighborhood resembles the neighborhood of a given pixel [4, 5].

An elementary mean of points x 1, …, x n ∈ I is the arithmetic mean 1 n ∑ i = 1 n x i ∈ I.

The points are divided into k clusters by iteratively calculating the mean of points (or centroid of points) as the new temporary center point within a given radius of the current temporal center point until the center point converges.

Spatial structure was investigated by means of Point Pattern Analysis and LISA (Local Indices of Spatial Autocorrelation).

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