1 - Task
- Implement the triplet loss function
- Use a pretrained model to map face images into 128-dimensional encodings
- Use these encodings to perform face verification and face recognition
2 - Import Packages
from keras.models import Sequential from keras.layers import Conv2D, ZeroPadding2D, Activation, Input, concatenate from keras.models import Model from keras.layers.normalization import BatchNormalization from keras.layers.pooling import MaxPooling2D, AveragePooling2D from keras.layers.merge import Concatenate from keras.layers.core import Lambda, Flatten, Dense from keras.initializers import glorot_uniform from keras.engine.topology import Layer from keras import backend as K K.set_image_data_format('channels_first') import cv2 import os import numpy as np from numpy import genfromtxt import pandas as pd import tensorflow as tf from fr_utils import * from inception_blocks_v2 import * %matplotlib inline %load_ext autoreload %autoreload 2 np.set_printoptions(threshold=np.nan)
3 - Naive Face Verification
在人脸验证任务中，我们需要判断两张图片中的人脸是否为同一个人。最简单的做法是逐个像素点比较，如果总共的距离低于给定的某一个阈值，则判断为同一个人。这种方法效果会很差。所以我们可以通过学习一个模型，可以将人脸图片提取出特征向量，再比较特征向量的距离来判断是否为同一个人。
4 - Encoding face images into a 128-dimensional vector
4.1 - Using an ConvNet to compute encodings
注意到
- 这个网络的输入的批次图像维度为$(m,3,96,96)$
- 网络的输出为$(m,128)$的编码，网络是对每一个输入编码成一个128维度向量的输出
FRmodel = faceRecoModel(input_shape=(3, 96, 96))
print("Total Params:", FRmodel.count_params())
Result:
Total Params: 3743280
好的编码应该具有如下性质：
- 同一个人的两张图片的编码应该尽可能的相似
- 不同人的两张图片的编码要非常不同
$triplet loss$损失函数便是描述上述性质的，并且尽量使得同一个人的两张图片的编码更加相似，不同人的两张图片的编码更具有区分性。
4.2 - The Triplet Loss
训练用于编码的神经网络（对应上面f映射），需要三元组图片$(A,P,N)$：
- A is an "Anchor" image--a picture of a person.
- P is a "Positive" image--a picture of the same person as the Anchor image.
- N is a "Negative" image--a picture of a different person than the Anchor image.
它们之间具有下式所示关系：
$$\mid \mid f(A^{(i)}) - f(P^{(i)}) \mid \mid_2^2 + \alpha < \mid \mid f(A^{(i)}) - f(N^{(i)}) \mid \mid_2^2$$
所以我们要最小化的"$triplet cost$"如下：
$$\mathcal{J} = \sum^{m}_{i=1} \large[ \small \underbrace{\mid \mid f(A^{(i)}) - f(P^{(i)}) \mid \mid_2^2}_\text{(1)} - \underbrace{\mid \mid f(A^{(i)}) - f(N^{(i)}) \mid \mid_2^2}_\text{(2)} + \alpha \large ] \small_+ \tag{3}$$
这里我们使用 "$[z]_+$"来表示$max(z,0)$。其中第一项描述的是$A$和$P$的距离，我们希望它尽可能的小，第二项描述的是$A$和$N$的距离，我们希望它尽可能的大（因此加上了负号）。
实现$triplet loss$需要如下四个步骤：
- Compute the distance between the encodings of "anchor" and "positive": $\begin{Vmatrix} f(A^{(i)}) - f(P^{(i)}) \end{Vmatrix}_2^2$
- Compute the distance between the encodings of "anchor" and "negative": $\begin{Vmatrix} f(A^{(i)}) - f(N^{(i)}) \end{Vmatrix}_2^2$
- Compute the formula per training example: $\begin{Vmatrix} f(A^{(i)}) - f(P^{(i)}) \end{Vmatrix} - \begin{Vmatrix} f(A^{(i)}) - f(N^{(i)}) \end{Vmatrix}_2^2 + \alpha$
- Compute the full formula by taking the max with zero and summing over the training examples:$$\mathcal{J} = \sum^{m}_{i=1} \large[ \small \mid \mid f(A^{(i)}) - f(P^{(i)}) \mid \mid_2^2 - \mid \mid f(A^{(i)}) - f(N^{(i)}) \mid \mid_2^2+ \alpha \large ] \small_+ \tag{3}$$
# GRADED FUNCTION: triplet_loss def triplet_loss(y_true, y_pred, alpha = 0.2): """ Implementation of the triplet loss as defined by formula (3) Arguments: y_true -- true labels, required when you define a loss in Keras, you don't need it in this function. y_pred -- python list containing three objects: anchor -- the encodings for the anchor images, of shape (None, 128) positive -- the encodings for the positive images, of shape (None, 128) negative -- the encodings for the negative images, of shape (None, 128) Returns: loss -- real number, value of the loss """ anchor, positive, negative = y_pred[0], y_pred[1], y_pred[2] ### START CODE HERE ### (≈ 4 lines) # Step 1: Compute the (encoding) distance between the anchor and the positive, you will need to sum over axis=-1 pos_dist = tf.reduce_sum(tf.square(tf.subtract(anchor, positive))) # Step 2: Compute the (encoding) distance between the anchor and the negative, you will need to sum over axis=-1 neg_dist = tf.reduce_sum(tf.square(tf.subtract(anchor, negative))) # Step 3: subtract the two previous distances and add alpha. basic_loss = tf.add(tf.subtract(pos_dist, neg_dist), alpha) # Step 4: Take the maximum of basic_loss and 0.0. Sum over the training examples. loss = tf.reduce_sum(tf.maximum(basic_loss, 0.0)) ### END CODE HERE ### return loss
with tf.Session() as test: tf.set_random_seed(1) y_true = (None, None, None) y_pred = (tf.random_normal([3, 128], mean=6, stddev=0.1, seed = 1), tf.random_normal([3, 128], mean=1, stddev=1, seed = 1), tf.random_normal([3, 128], mean=3, stddev=4, seed = 1)) loss = triplet_loss(y_true, y_pred) print("loss = " + str(loss.eval()))
Result: //和答案不一样，但我找到别人能出正确答案的代码也跟我一样，所以我认为应该是随机种子的问题
loss = 350.027
5 - Loading the trained model
因为训练FaceNet需要大量的数据和计算，因此此作业不打算训练该模型，而是直接加载已经训练好的模型。
FRmodel.compile(optimizer = 'adam', loss = triplet_loss, metrics = ['accuracy']) load_weights_from_FaceNet(FRmodel)
6 - Applying the model
6.1 - Face Verification
使用方法$img_to_encoding(image_path, model)$建立一个人脸特征库，只有识别到其中的人脸才能通过验证。
database = {} database["danielle"] = img_to_encoding("images/danielle.png", FRmodel) database["younes"] = img_to_encoding("images/younes.jpg", FRmodel) database["tian"] = img_to_encoding("images/tian.jpg", FRmodel) database["andrew"] = img_to_encoding("images/andrew.jpg", FRmodel) database["kian"] = img_to_encoding("images/kian.jpg", FRmodel) database["dan"] = img_to_encoding("images/dan.jpg", FRmodel) database["sebastiano"] = img_to_encoding("images/sebastiano.jpg", FRmodel) database["bertrand"] = img_to_encoding("images/bertrand.jpg", FRmodel) database["kevin"] = img_to_encoding("images/kevin.jpg", FRmodel) database["felix"] = img_to_encoding("images/felix.jpg", FRmodel) database["benoit"] = img_to_encoding("images/benoit.jpg", FRmodel) database["arnaud"] = img_to_encoding("images/arnaud.jpg", FRmodel)
实现$verify()$方法去识别这个人是否能够通过验证，有如下几步：
- Compute the encoding of the image from image_path
- Compute the distance about this encoding and the encoding of the identity image stored in the database
- Open the door if the distance is less than 0.7, else do not open.
# GRADED FUNCTION: verify def verify(image_path, identity, database, model): """ Function that verifies if the person on the "image_path" image is "identity". Arguments: image_path -- path to an image identity -- string, name of the person you'd like to verify the identity. Has to be a resident of the Happy house. database -- python dictionary mapping names of allowed people's names (strings) to their encodings (vectors). model -- your Inception model instance in Keras Returns: dist -- distance between the image_path and the image of "identity" in the database. door_open -- True, if the door should open. False otherwise. """ ### START CODE HERE ### # Step 1: Compute the encoding for the image. Use img_to_encoding() see example above. (≈ 1 line) encoding = img_to_encoding(image_path, model) # Step 2: Compute distance with identity's image (≈ 1 line) dist = np.linalg.norm(encoding-database[identity]) # Step 3: Open the door if dist < 0.7, else don't open (≈ 3 lines) if dist<0.7: print("It's " + str(identity) + ", welcome home!") door_open = True else: print("It's not " + str(identity) + ", please go away") door_open = False ### END CODE HERE ### return dist, door_open
verify("images/camera_0.jpg", "younes", database, FRmodel)
verify("images/camera_2.jpg", "kian", database, FRmodel)
6.2 - Face Recognition
实现$who\_is\_it()$方法需要以下几步：
- Compute the target encoding of the image from image_path
- Find the encoding from the database that has smallest distance with the target encoding.
- Initialize the
min_distvariable to a large enough number (100). It will help you keep track of what is the closest encoding to the input's encoding. - Loop over the database dictionary's names and encodings. To loop use
for (name, db_enc) in database.items().- Compute L2 distance between the target "encoding" and the current "encoding" from the database.
- If this distance is less than the min_dist, then set min_dist to dist, and identity to name.
- Initialize the
# GRADED FUNCTION: who_is_it def who_is_it(image_path, database, model): """ Implements face recognition for the happy house by finding who is the person on the image_path image. Arguments: image_path -- path to an image database -- database containing image encodings along with the name of the person on the image model -- your Inception model instance in Keras Returns: min_dist -- the minimum distance between image_path encoding and the encodings from the database identity -- string, the name prediction for the person on image_path """ ### START CODE HERE ### ## Step 1: Compute the target "encoding" for the image. Use img_to_encoding() see example above. ## (≈ 1 line) encoding = img_to_encoding(image_path, model) ## Step 2: Find the closest encoding ## # Initialize "min_dist" to a large value, say 100 (≈1 line) min_dist = 100 # Loop over the database dictionary's names and encodings. for (name, db_enc) in dataset: # Compute L2 distance between the target "encoding" and the current "emb" from the database. (≈ 1 line) dist = np.linalg.norm(encoding-db_enc) # If this distance is less than the min_dist, then set min_dist to dist, and identity to name. (≈ 3 lines) if dist < min_dist: min_dist = dist identity = name ### END CODE HERE ### if min_dist > 0.7: print("Not in the database.") else: print ("it's " + str(identity) + ", the distance is " + str(min_dist)) return min_dist, identity
who_is_it("images/camera_0.jpg", database, FRmodel)
7 - Summary
虽然我们没有实现和训练神经网络，但是可以通过下面两种方法来提高算法的准确性：
- Put more images of each person (under different lighting conditions, taken on different days, etc.) into the database. Then given a new image, compare the new face to multiple pictures of the person. This would increae accuracy.（增加数据集）
- Crop the images to just contain the face, and less of the "border" region around the face. This preprocessing removes some of the irrelevant pixels around the face, and also makes the algorithm more robust.（降低噪声）