从R中的二进制矩阵中提取子矩阵 [英] Extract sub-matrices from binary matrix in R

问题描述

说出二进制矩阵m:

      # [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9]
 # [1,]    0    0    0    0    0    0    0    0    0
 # [2,]    0    0    0    0    0    0    0    0    0
 # [3,]    0    0    0    1    1    1    1    0    0
 # [4,]    0    0    0    1    1    1    1    0    0
 # [5,]    0    0    0    1    1    1    1    0    0
 # [6,]    0    0    0    0    0    0    0    0    0
 # [7,]    0    1    1    0    0    0    0    1    1
 # [8,]    0    1    1    0    1    1    0    1    1
 # [9,]    0    0    0    0    1    1    0    1    1
# [10,]    0    0    0    0    1    1    0    0    0

m <- structure(c(0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 
1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 
0, 0, 0, 0, 1, 1, 1, 0, 0, 1, 1, 1, 0, 0, 1, 1, 1, 0, 0, 1, 1, 
1, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 
0, 0, 0, 0, 0, 0, 1, 1, 1, 0), .Dim = c(10L, 9L))

我们如何提取那些1值的子矩阵?例如

How we can extract those 1-valued sub-matrices? e.g.

m[7:9,8:9]

#     [,1] [,2]
#[1,]    1    1
#[2,]    1    1
#[3,]    1    1

重点是我想从算法上提取它们，而不是像m[7:9,8:9]那样显式索引它们.

The point is that I want to extract them algorithmtically not indexing them explicitly like m[7:9,8:9].

• 输入是二进制矩阵
• 作为输出的子矩阵列表(所以是昏暗的3*4，2*2，3*2和3*2的四个矩阵的列表)
• 子矩阵是1值的矩形
• 子矩阵的边界用零固定.

• The input is a binary matrix
• List of sub-matrices as output (so list of four matrices of dim 3*4, 2*2, 3*2 and 3*2)
• Sub-matrices are 1-valued rectangular
• The border of the sub-matrices are secured with zeros.

推荐答案

我将其视为空间问题，在该问题中您有栅格并想要检测连接的像元区域.

I'd treat it as a spatial problem where you have a raster and want to detect regions of connected cells.

library(raster)
r <- raster(m)

library(igraph)
rc <- clump(r)

plot(rc, col = rainbow(rc@data@max))

m1 <- as.matrix(rc)

lapply(seq_len(rc@data@max), function(x) {
  inds <- which(m1 == x, arr.ind = TRUE)
  nrow <- diff(range(inds[, "row"])) + 1
  ncol <- diff(range(inds[, "col"])) + 1
  matrix(1, ncol = ncol, nrow = nrow)
})
#[[1]]
#     [,1] [,2] [,3] [,4]
#[1,]    1    1    1    1
#[2,]    1    1    1    1
#[3,]    1    1    1    1
#
#[[2]]
#     [,1] [,2]
#[1,]    1    1
#[2,]    1    1
#
#[[3]]
#     [,1] [,2]
#[1,]    1    1
#[2,]    1    1
#[3,]    1    1
#
#[[4]]
#     [,1] [,2]
#[1,]    1    1
#[2,]    1    1
#[3,]    1    1

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