IDL im2col和col2im函数示例

本人在卷积神经网络的卷积层、池化层的im2col和反向传播的col2im方法上有所启发，考虑到IDL本身并没有im2col和col2im函数，于是编写了相关的IDL函数。话不多说，直接上代码！

1. im2col

;input_data: 由(高, 长)的2维数组构成的输入数据
;filter_h: 滤波器的高
;filter_w: 滤波器的长
;stride=stride: 步幅
;pad=pad: 填充的个数(默认填充值为0)
;return 二维数组

FUNCTION fun_im2col, input_data, filter_h, filter_w, stride=stride, pad=pad
  param_number = N_PARAMS() ;返回非关键字参数的个数（即位置参数的个数）

  IF param_number EQ 3 THEN BEGIN
    arr_info = SIZE( input_data )
    w = arr_info[1] ;w和h为矩阵的长（列）和高（行）
    h = arr_info[2]
    ;out_h和out_w分别为输出矩阵的长和高
    out_h = FLOOR( (h + 2*pad - filter_h) / stride ) + 1 
    out_w = FLOOR( (w + 2*pad - filter_w) / stride ) + 1

    img = REPLICATE(0.0, w + 2 * pad, h + 2 * pad)
    end_w = w - 1 + pad
    end_h = h - 1 + pad
    img[pad:end_w, pad:end_h] = input_data
    column = FLTARR(filter_w, filter_h, out_w, out_h)

    FOR x = 0, filter_w-1 DO BEGIN
      x_max = x + stride*out_w
      FOR y = 0, filter_h-1 DO BEGIN
        y_max = y + stride*out_h
        ;        if y_max ge h + 2 * pad or x_max ge w + 2 * pad then break
        ;        print, x, x_max, y, y_max
        column[x, y, *, *] = img[x:x_max-1:stride, y:y_max-1:stride]
      ENDFOR
    ENDFOR
    column = TRANSPOSE(column, [2, 3, 0, 1])
    column = REFORM(column, [out_h*out_w, filter_w*filter_h])
    RETURN, column
  ENDIF ELSE BEGIN
    PRINT, "Function params is not enough!"
    RETURN, 0
  ENDELSE

END

2. col2im

;input_shape : 输入数据的形状（例：[28, 28]）
;filter_h: 滤波器的高
;filter_w: 滤波器的长
;stride: 步幅
;pad: 填充的个数(默认填充值为0)
FUNCTION fun_col2im, column, input_shape, filter_h, filter_w, stride=stride, pad=pad
  param_number = N_PARAMS()
  IF param_number EQ 4 THEN BEGIN
    w= input_shape[0]
    h = input_shape[1]

    out_h = FLOOR( (h + 2*pad - filter_h) / stride ) + 1
    out_w = FLOOR( (w + 2*pad - filter_w) / stride ) + 1
    column = REFORM(column, [out_w, out_h, filter_w, filter_h])
    ;  column = TRANSPOSE(column, [2, 3, 0, 1])

    img = FLTARR(w + 2*pad + stride - 1, h + 2*pad + stride - 1)
    FOR x = 0, filter_w-1 DO BEGIN
      x_max = x + stride*out_w
      FOR y = 0, filter_h-1 DO BEGIN
        y_max = y + stride*out_h
        ;      print, x, x_max, y, y_max
        img[x:x_max-1:stride, y:y_max-1:stride] = column[*, *, x, y]
      ENDFOR
    ENDFOR
    end_w = w - 1 + pad
    end_h = h - 1 + pad
    RETURN, img[pad:end_w, pad:end_h]
  ENDIF ELSE BEGIN
    PRINT, "Function params is not enough!"
    RETURN, 0
  ENDELSE
END

3. 运行结果

首先来看一下im2col的运行结果

pro test
;输入数据为4*4的二维数组，滤波器大小为3*3
  input_data = findGEN(4, 4)
  filter_h = 3
  filter_w = 3
  column = fun_im2col(input_data, filter_h, filter_w, stride=1, pad=0)
  PRINT, "输入数据",input_data
  PRINT, "输出数据", column
end

结果如下，输出的每一列对应一组滤波器的数据

输入数据
     0.000000      1.00000      2.00000      3.00000
      4.00000      5.00000      6.00000      7.00000
      8.00000      9.00000      10.0000      11.0000
      12.0000      13.0000      14.0000      15.0000
输出数据
     0.000000      1.00000      4.00000      5.00000
      1.00000      2.00000      5.00000      6.00000
      2.00000      3.00000      6.00000      7.00000
      4.00000      5.00000      8.00000      9.00000
      5.00000      6.00000      9.00000      10.0000
      6.00000      7.00000      10.0000      11.0000
      8.00000      9.00000      12.0000      13.0000
      9.00000      10.0000      13.0000      14.0000
      10.0000      11.0000      14.0000      15.0000

在来看一下col2im的运行结果，将im2col的结果还原回去

pro test
  input_data = FINDGEN(4, 4)
  filter_h = 3
  filter_w = 3
  column = fun_im2col(input_data, filter_h, filter_w, stride=1, pad=0)
  PRINT, input_data
  PRINT, column
  b = fun_col2im(column, [4, 4], filter_h, filter_w, stride=1, pad=0)
  PRINT, b
 end

结果如下，可以看到完美的将矩阵还原了回去

;im2col得到的column
      0.000000      1.00000      4.00000      5.00000
      1.00000      2.00000      5.00000      6.00000
      2.00000      3.00000      6.00000      7.00000
      4.00000      5.00000      8.00000      9.00000
      5.00000      6.00000      9.00000      10.0000
      6.00000      7.00000      10.0000      11.0000
      8.00000      9.00000      12.0000      13.0000
      9.00000      10.0000      13.0000      14.0000
      10.0000      11.0000      14.0000      15.0000
;col2im得到的input_data
      0.000000      1.00000      2.00000      3.00000
      4.00000      5.00000      6.00000      7.00000
      8.00000      9.00000      10.0000      11.0000
      12.0000      13.0000      14.0000      15.0000

最后看一下如果有填充值的话是什么样的结果

;原始输入矩阵
     0.000000      1.00000      2.00000
      3.00000      4.00000      5.00000
      6.00000      7.00000      8.00000
;填充后的矩阵，填充一个数值
     0.000000     0.000000     0.000000     0.000000     0.000000
     0.000000     0.000000      1.00000      2.00000     0.000000
     0.000000      3.00000      4.00000      5.00000     0.000000
     0.000000      6.00000      7.00000      8.00000     0.000000
     0.000000     0.000000     0.000000     0.000000     0.000000
;输出的col矩阵
     0.000000     0.000000     0.000000     0.000000     0.000000      1.00000     0.000000      3.00000      4.00000
     0.000000     0.000000     0.000000     0.000000      1.00000      2.00000      3.00000      4.00000      5.00000
     0.000000     0.000000     0.000000      1.00000      2.00000     0.000000      4.00000      5.00000     0.000000
     0.000000     0.000000      1.00000     0.000000      3.00000      4.00000     0.000000      6.00000      7.00000
     0.000000      1.00000      2.00000      3.00000      4.00000      5.00000      6.00000      7.00000      8.00000
      1.00000      2.00000     0.000000      4.00000      5.00000     0.000000      7.00000      8.00000     0.000000
     0.000000      3.00000      4.00000     0.000000      6.00000      7.00000     0.000000     0.000000     0.000000
      3.00000      4.00000      5.00000      6.00000      7.00000      8.00000     0.000000     0.000000     0.000000
      4.00000      5.00000     0.000000      7.00000      8.00000     0.000000     0.000000     0.000000     0.000000

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