第16章 CNN基础与卷积操作

目标

掌握计算机视觉的核心工具。

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必学内容

卷积操作

# 滤波器在图像上滑动，提取局部特征
output[i,j] = ΣΣ filter[m,n] * input[i+m, j+n]

padding 与 stride

# Valid convolution: 不填充
# Same convolution: 填充使输出尺寸不变
# Stride: 步长，控制下采样速度

通道维度

# 彩色图像: (height, width, channels=3)
# 卷积核: (f, f, c_in, c_out)

池化层

# Max Pooling: 保留最显著特征
# Average Pooling: 保留整体信息

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必须真正理解

为什么卷积有效

参数共享：同一个滤波器扫完整张图
稀疏连接：每个输出只连局部输入
平移等变：物体移动，特征跟着移动

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Python Example

Included in the static site for reading. Run locally from the source repository when needed.

""" 第16章：CNN基础 — NumPy 实现卷积操作 Chapter 16: CNN Basics — Convolution from Scratch """ import numpy as np def conv_single_step(a_slice_prev, W, b): """单步卷积""" return np.sum(a_slice_prev * W) + float(b) def conv_forward(A_prev, W, b, hparameters): """ A_prev: (m, n_H_prev, n_W_prev, n_C_prev) W: (f, f, n_C_prev, n_C) b: (1, 1, 1, n_C) """ (m, n_H_prev, n_W_prev, n_C_prev) = A_prev.shape (f, f, n_C_prev, n_C) = W.shape stride = hparameters['stride'] pad = hparameters['pad'] n_H = int((n_H_prev + 2*pad - f) / stride) + 1 n_W = int((n_W_prev + 2*pad - f) / stride) + 1 A_prev_pad = np.pad(A_prev, ((0,0), (pad,pad), (pad,pad), (0,0)), mode='constant') Z = np.zeros((m, n_H, n_W, n_C)) for i in range(m): for h in range(n_H): for w in range(n_W): for c in range(n_C): v_start = h * stride v_end = v_start + f h_start = w * stride h_end = h_start + f a_slice = A_prev_pad[i, v_start:v_end, h_start:h_end, :] Z[i, h, w, c] = conv_single_step(a_slice, W[:,:,:,c], b[:,:,:,c]) return Z # 测试 np.random.seed(1) A_prev = np.random.randn(2, 5, 5, 3) # 2张5x5 RGB图 W = np.random.randn(3, 3, 3, 8) # 8个3x3滤波器 b = np.random.randn(1, 1, 1, 8) hparameters = {"stride": 1, "pad": 1} Z = conv_forward(A_prev, W, b, hparameters) print(f"输入: {A_prev.shape}") print(f"滤波器: {W.shape}") print(f"输出: {Z.shape}") print(f"\n输出高度计算: ({A_prev.shape[1]} + 2*{hparameters['pad']} - {W.shape[0]}) / {hparameters['stride']} + 1 = {Z.shape[1]}")