numpy实现卷积两种方法

暂时针对二维卷积

方法1 按定义计算

def numpy_conv(inputs, myfilter):
    h_ori, w_ori = inputs.shape
    h_k, w_k= myfilter.shape
    
    h_new, w_new = h_ori-h_k+1,w_ori-w_k+1
    result = np.zeros((h_new, w_new))
    
    for row in range(0, h_new, 1):
        for col in range(0, w_new, 1):
            # 池化大小的输入区域
            cur_input = inputs[row:row+h_k, col:col+w_k]
            #和核进行乘法计算
            cur_output = cur_input * myfilter
            #再把所有值求和
            conv_sum = np.sum(cur_output)
            #当前点输出值
            result[row, col] = conv_sum
    return result         

方法2 img2col

def my_img2col(img, filter_shape, padding='valid', strides=1):
   
    row, col = img.shape[:2]
    tp_row, tp_col = filter_shape[:2]
    
    if padding == 'valid':
        transfer_shape = np.array([(row - tp_row + 1), (col - tp_col + 1)])
        img_new = img 
        
    if padding == 'same':
        '''padding只补充卷积核带来的尺寸减少，不补充strides '''
        transfer_shape = np.array([row , col])
        padding_num_row = tp_row - 1
        padding_num_col = tp_col - 1
        
        flip_left = padding_num_row // 2
        flip_top = padding_num_col // 2
     
        
        img_new = np.zeros((row+tp_row-1, col+tp_col-1))
        img_new[flip_left:flip_left+row, flip_top:flip_top+col] = img 
        
    
    im2col = np.zeros((tp_row*tp_col, (transfer_shape[0]//strides) * (transfer_shape[1]//strides)))
    
    count = 0

    for y in range(0, transfer_shape[0], strides):
        for x in range(0, transfer_shape[1], strides):
    
            cur_item = img_new[y:y+tp_row, x:x+tp_col].reshape(-1)

            im2col[:, count] = cur_item 
            count += 1
    return im2col, transfer_shape // strides




def myconv(img, template, padding="valid", strides=1):
    
    im2col, transfer_shape = my_img2col(img, template.shape, padding=padding, strides=strides)
    filter_flatten = template.reshape(1, -1)
    conv_out = np.matmul(filter_flatten, im2col)
    
        
    return conv_out.reshape(transfer_shape[0],transfer_shape[1])

test

import time
import cv2
img = np.random.rand(100, 100)
template = np.ones((3,3))

start1 = time.perf_counter()
conv_out1 = numpy_conv(img, template)
end1 = time.perf_counter()
time_consume1 = (end1-start1)*1000
print('methold 1 %.4f ms'%time_consume1)

start2 = time.perf_counter()
conv_out2= myconv(img, template, padding='valid', strides=1)
end2 = time.perf_counter()
time_consume2 = (end2-start2)*1000


print('methold 2 %.4f ms'%time_consume2)

start2 = time.perf_counter()

conv_out3= cv2.filter2D(img,-1, template) #调用cv2的卷积
end2 = time.perf_counter()
time_consume3 = (end2-start2)*1000
print('methold 3 %.4f ms'%time_consume3)

结果如下：可见img2col比常规卷积快3倍。但相较底层为C的速度还是慢了近200倍！python的循环计算还是很低效。

methold 1 62.4741 ms
methold 2 19.9291 ms
methold 3 0.1726 ms