基于Python的PCA人脸识别算法的原理及实现代码详解.zip

# coding:utf-8 import os from numpy import * import numpy as np import cv2 import matplotlib.pyplot as plt from pylab import mpl mpl.rcParams['font.sans-serif'] = ['SimHei'] # 图片矢量化 def img2vector(image): img = cv2.imread(image, 0) # 读取图片 rows, cols = img.shape imgVector = np.zeros((1, rows * cols)) imgVector = np.reshape(img, (1, rows * cols)) return imgVector orlpath = "E:/face_recongize/ORL" # 读入人脸库,每个人随机选择k张作为训练集,其余构成测试集 def load_orl(k): ''' 对训练数据集进行数组初始化，用0填充，每张图片尺寸都定为112*92, 现在共有40个人，每个人都选择k张，则整个训练集大小为40*k,112*92 ''' train_face = np.zeros((40 * k, 112 * 92)) train_label = np.zeros(40 * k) # [0,0,.....0](共40*k个0) test_face = np.zeros((40 * (10 - k), 112 * 92)) test_label = np.zeros(40 * (10 - k)) # sample=random.sample(range(10),k)#每个人都有的10张照片中，随机选取k张作为训练样本(10个里面随机选取K个成为一个列表) sample = random.permutation(10) + 1 # 随机排序1-10 (0-9）+1 for i in range(40): # 共有40个人 people_num = i + 1 for j in range(10): # 每个人都有10张照片 image = orlpath + '/s' + str(people_num) + '/' + str(sample[j]) + '.jpg' # 读取图片并进行矢量化 img = img2vector(image) if j < k: # 构成训练集 train_face[i * k + j, :] = img train_label[i * k + j] = people_num else: # 构成测试集 test_face[i * (10 - k) + (j - k), :] = img test_label[i * (10 - k) + (j - k)] = people_num return train_face, train_label, test_face, test_label # 定义PCA算法 def PCA(data, r): data = np.float32(np.mat(data)) rows, cols = np.shape(data) data_mean = np.mean(data, 0) # 对列求平均值 A = data - np.tile(data_mean, (rows, 1)) # 将所有样例减去对应均值得到A C = A * A.T # 得到协方差矩阵 D, V = np.linalg.eig(C) # 求协方差矩阵的特征值和特征向量 V_r = V[:, 0:r] # 按列取前r个特征向量 V_r = A.T * V_r # 小矩阵特征向量向大矩阵特征向量过渡 for i in range(r): V_r[:, i] = V_r[:, i] / np.linalg.norm(V_r[:, i]) # 特征向量归一化 final_data = A * V_r return final_data, data_mean, V_r # 人脸识别 def face_rec(): # k=int(input("每个人选择几张照片进行训练：")) # x_value=[] # y_value=[] for r in range(10, 41, 10): # 最多降到40维,即选取前40个主成分（因为当k=1时，只有40维) print("当降维到%d时" % (r)) x_value = [] y_value = [] for k in range(1, 10): train_face, train_label, test_face, test_label = load_orl(k) # 得到数据集 # 利用PCA算法进行训练 data_train_new, data_mean, V_r = PCA(train_face, r) num_train = data_train_new.shape[0] # 训练脸总数 num_test = test_face.shape[0] # 测试脸总数 temp_face = test_face - np.tile(data_mean, (num_test, 1)) data_test_new = temp_face * V_r # 得到测试脸在特征向量下的数据 data_test_new = np.array(data_test_new) # mat change to array data_train_new = np.array(data_train_new) # 测试准确度 true_num = 0 for i in range(num_test): testFace = data_test_new[i, :] diffMat = data_train_new - np.tile(testFace, (num_train, 1)) # 训练数据与测试脸之间距离 sqDiffMat = diffMat ** 2 sqDistances = sqDiffMat.sum(axis=1) # 按行求和 sortedDistIndicies = sqDistances.argsort() # 对向量从小到大排序，使用的是索引值,得到一个向量 indexMin = sortedDistIndicies[0] # 距离最近的索引 if train_label[indexMin] == test_label[i]: true_num += 1 else: pass accuracy = float(true_num) / num_test x_value.append(k) y_value.append(round(accuracy, 2)) print('当每个人选择%d张照片进行训练时，The classify accuracy is: %.2f%%' % (k, accuracy * 100)) # 绘图 if r == 10: y1_value = y_value plt.plot(x_value, y_value, marker="o", markerfacecolor="red") for a, b in zip(x_value, y_value): plt.text(a, b, (a, b), ha='center', va='bottom', fontsize=10) plt.title("降到10维时识别准确率", fontsize=14) plt.xlabel("K值", fontsize=14) plt.ylabel("准确率", fontsize=14) plt.show() # print ('y1_value',y1_value) if r == 20: y2_value = y_value plt.plot(x_value, y2_value, marker="o", markerfacecolor="red") for a, b in zip(x_value, y_value): plt.text(a, b, (a, b), ha='center', va='bottom', fontsize=10) plt.title("降到20维时识别准确率", fontsize=14) plt.xlabel("K值", fontsize=14) plt.ylabel("准确率", fontsize=14) plt.show() # print ('y2_value',y2_value) if r == 30: y3_value = y_value plt.plot(x_value, y3_value, marker="o", markerfacecolor="red") for a, b in zip(x_value, y_value): plt.text(a, b, (a, b), ha='center', va='bottom', fontsize=10) plt.title("降到30维时识别准确率", fontsize=14) plt.xlabel("K值", fontsize=14) plt.ylabel("准确率", fontsize=14) plt.show() # print ('y3_value',y3_value) if r == 40: y4_value = y_value plt.plot(x_value, y4_value, marker="o", markerfacecolor="red") for a, b in zip(x_value, y_value): plt.text(a, b, (a, b), ha='center', va='bottom', fontsize=10) plt.title("降到40维时识别准确率", fontsize=14) plt.xlabel("K值", fontsize=14) plt.ylabel("准确率", fontsize=14) plt.show() # print ('y4_value',y4_value) # 各维度下准确度比较 L1, = plt.plot(x_value, y1_value, marker="o", markerfacecolor="red") L2, = plt.plot(x_value, y2_value, marker="o", markerfacecolor="red") L3, = plt.plot(x_value, y3_value, marker="o", markerfacecolor="red") L4, = plt.plot(x_value, y4_value, marker="o", markerfacecolor="red") # for a, b in zip(x_value, y1_value): # plt.text(a,b,(a,b),ha='center', va='bottom', fontsize=10) plt.legend([L1, L2, L3, L4], ["降到10维", "降到20维", "降到30维", "降到40维"], loc=4) plt.title("各维度识别准确率比较", fontsize=14) plt.xlabel("K值", fontsize=14) plt.ylabel("准确率", fontsize=14) plt.show() if __name__ == '__main__': face_rec()