im2col：更正版

學過CNN的都知道im2col是非常重要的函數之一，用於將輸入的四維數據轉化成二維數據方便進行卷積運算。

代碼雖就10來行不過要理解透徹還是相當不容易的，第一次寫涉及到如此高維的數據處理，有點難以適應...

im2col

def im2col(input_data, filter_h, filter_w, stride=1, pad=0):
    """

    Parameters
    ----------
    input_data : 由(數據量, 通道, 高, 長)的4維數組構成的輸入數據
    filter_h : 濾波器的高
    filter_w : 濾波器的長
    stride : 步幅
    pad : 填充

    Returns
    -------
    col : 2維數組
    """
    N, C, H, W = input_data.shape
    out_h = (H + 2*pad - filter_h)//stride + 1
    out_w = (W + 2*pad - filter_w)//stride + 1

    img = np.pad(input_data, [(0,0), (0,0), (pad, pad), (pad, pad)], 'constant')
    col = np.zeros((N, C, filter_h, filter_w, out_h, out_w))

    for y in range(filter_h):
        # 這一步是因爲y還可以往下走(out_h - 1)步，所以需要計算ymax，用y:y_max:stride的方式來表達每一次的跨步
        y_max = y + stride*out_h
        for x in range(filter_w):
            x_max = x + stride*out_w
            col[:, :, y, x, :, :] = img[:, :, y:y_max:stride, x:x_max:stride]

    col = col.transpose(0, 4, 5, 1, 2, 3).reshape(N*out_h*out_w, -1)
    return col

col2im

def col2im(col, input_shape, filter_h, filter_w, stride=1, pad=0):
    """

    Parameters
    ----------
    col :
    input_shape : 輸入數據的形狀（例：(10, 1, 28, 28)）
    filter_h :
    filter_w
    stride
    pad

    Returns
    -------

    """
    N, C, H, W = input_shape
    out_h = (H + 2*pad - filter_h)//stride + 1
    out_w = (W + 2*pad - filter_w)//stride + 1

    # 下面將變成(N, C, filter_h, filter_w, out_h, out_w)，是標準的col模式
    col = col.reshape(N, out_h, out_w, C, filter_h, filter_w).transpose(0, 3, 4, 5, 1, 2)

    # 下面這句話怎麼理解？
    # img = np.zeros((N, C, H + 2*pad + stride - 1, W + 2*pad + stride - 1))
    img = np.pad(np.zeros(input_shape), [(0, 0), (0, 0), (pad, pad), (pad, pad)], 'constant')
    cnt = np.pad(np.zeros(input_shape), [(0, 0), (0, 0), (pad, pad), (pad, pad)], 'constant')

    for y in range(filter_h):
        y_max = y + stride*out_h
        for x in range(filter_w):
            x_max = x + stride*out_w
            img[:, :, y:y_max:stride, x:x_max:stride] += col[:, :, y, x, :, :]
            cnt[:, :, y:y_max:stride, x:x_max:stride] = cnt[:, :, y:y_max:stride, x:x_max:stride] + 1
    res = img / cnt
    return res[:, :, pad:H + pad, pad:W + pad]

demo

import numpy as np 

def my_im2col(input_data, fh, fw, stride=1, pad=0):
    N, C, H, W = input_data.shape
    out_h = (H + 2 * pad - fh) // stride + 1
    out_w = (W + 2 * pad - fw) // stride + 1
    img = np.pad(input_data, [(0, 0), (0, 0), (pad, pad), (pad, pad)], 'constant')
 
    col = np.zeros((N, C, out_h, out_w, fh, fw))
 
    for y in range(out_h):
        for x in range(out_w):
            col[:, :, y, x, :, :] = img[:, :, y : y + fh : stride, x : x + fw : stride]
 
    col = col.transpose(0, 2, 3, 1, 4, 5).reshape(N * out_h * out_w, -1)
    return col

def im2col(input_data, filter_h, filter_w, stride=1, pad=0):
    """

    Parameters
    ----------
    input_data : 由(數據量, 通道, 高, 長)的4維數組構成的輸入數據
    filter_h : 濾波器的高
    filter_w : 濾波器的長
    stride : 步幅
    pad : 填充

    Returns
    -------
    col : 2維數組
    """
    N, C, H, W = input_data.shape
    out_h = (H + 2*pad - filter_h)//stride + 1
    out_w = (W + 2*pad - filter_w)//stride + 1

    img = np.pad(input_data, [(0,0), (0,0), (pad, pad), (pad, pad)], 'constant')
    col = np.zeros((N, C, filter_h, filter_w, out_h, out_w))

    for y in range(filter_h):
        # 這一步是因爲y還可以往下走(out_h - 1)步，所以需要計算ymax，用y:y_max:stride的方式來表達每一次的跨步
        y_max = y + stride*out_h
        for x in range(filter_w):
            x_max = x + stride*out_w
            col[:, :, y, x, :, :] = img[:, :, y:y_max:stride, x:x_max:stride]

    col = col.transpose(0, 4, 5, 1, 2, 3).reshape(N*out_h*out_w, -1)
    return col

def col2im(col, input_shape, filter_h, filter_w, stride=1, pad=0):
    """

    Parameters
    ----------
    col :
    input_shape : 輸入數據的形狀（例：(10, 1, 28, 28)）
    filter_h :
    filter_w
    stride
    pad

    Returns
    -------

    """
    N, C, H, W = input_shape
    out_h = (H + 2*pad - filter_h)//stride + 1
    out_w = (W + 2*pad - filter_w)//stride + 1

    # 下面將變成(N, C, filter_h, filter_w, out_h, out_w)，是標準的col模式
    col = col.reshape(N, out_h, out_w, C, filter_h, filter_w).transpose(0, 3, 4, 5, 1, 2)

    # 下面這句話怎麼理解？
    # img = np.zeros((N, C, H + 2*pad + stride - 1, W + 2*pad + stride - 1))
    img = np.pad(np.zeros(input_shape), [(0, 0), (0, 0), (pad, pad), (pad, pad)], 'constant')
    cnt = np.pad(np.zeros(input_shape), [(0, 0), (0, 0), (pad, pad), (pad, pad)], 'constant')

    for y in range(filter_h):
        y_max = y + stride*out_h
        for x in range(filter_w):
            x_max = x + stride*out_w
            img[:, :, y:y_max:stride, x:x_max:stride] += col[:, :, y, x, :, :]
            cnt[:, :, y:y_max:stride, x:x_max:stride] = cnt[:, :, y:y_max:stride, x:x_max:stride] + 1
    res = img / cnt
    return res[:, :, pad:H + pad, pad:W + pad]
    # return img

data = np.arange(1, 17).reshape((1, 1, 4, 4))
print(data)
col = im2col(data, 4, 4, stride = 2, pad = 1)
print(col)

img = col2im(col, data.shape, 4, 4, stride = 2, pad = 1)
print(img)