Part1：人脸识别

训练FaceNet很不现实，所以模型已经都训练好了，我们只是学习一下loss函数，然后调用模型来进行简单的识别而已。

先计算triplet_loss函数，分为4步：

# 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(anchor - positive),axis=-1)
    # 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(anchor - negative),axis=-1)
    # 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.))
    ### END CODE HERE ###
    
    return loss

进行单个人脸验证：

# 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

进行人脸识别：

# 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 database.items():
        
        # Compute L2 distance between the target "encoding" and the current "emb" from the database. (≈ 1 line)
        dist = np.linalg.norm(encoding-database[name])

        # 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

Part2：风格迁移

模型也都是训练好的了，用的是VGG-19的网络。这里只是体验一下cost function的实现罢了。

计算J_content(C,G)

$J_{content}(C,G) = \frac{1}{4 \times n_H \times n_W \times n_C}\sum _{ \text{all entries}} (a^{(C)} - a^{(G)})^2$

在这过程中需要把三维的矩阵先展开成2维的矩阵进行计算（虽然不展开也是可以计算的，但是风格损失函数需要计算）

DeepLearning.ai作业:(4-4)-- 特殊应用:人脸识别和神经风格转换


def compute_content_cost(a_C, a_G):
    """
    Computes the content cost
    
    Arguments:
    a_C -- tensor of dimension (1, n_H, n_W, n_C), hidden layer activations representing content of the image C 
    a_G -- tensor of dimension (1, n_H, n_W, n_C), hidden layer activations representing content of the image G
    
    Returns: 
    J_content -- scalar that you compute using equation 1 above.
    """
    
    ### START CODE HERE ###
    # Retrieve dimensions from a_G (≈1 line)
    m, n_H, n_W, n_C = a_G.get_shape().as_list()
    
    # Reshape a_C and a_G (≈2 lines)
    a_C_unrolled = tf.reshape(a_C,[n_H * n_W, n_C])
    a_G_unrolled = tf.reshape(a_G,[n_H * n_W, n_C])
    
    # compute the cost with tensorflow (≈1 line)
    J_content = tf.reduce_sum(tf.square(a_C_unrolled - a_G_unrolled)) / (n_H * n_W * n_C * 4)
    ### END CODE HERE ###
    
    return J_content

计算J_style(S,G)

需要把三维矩阵展开，然后转置，做矩阵乘法，才能得到相关系数矩阵

DeepLearning.ai作业:(4-4)-- 特殊应用:人脸识别和神经风格转换

# GRADED FUNCTION: gram_matrix

def gram_matrix(A):
    """
    Argument:
    A -- matrix of shape (n_C, n_H*n_W)
    
    Returns:
    GA -- Gram matrix of A, of shape (n_C, n_C)
    """
    
    ### START CODE HERE ### (≈1 line)
    GA = tf.matmul(A,tf.transpose(A))
    ### END CODE HERE ###
    
    return GA

$J_{style}^{[l]}(S,G) = \frac{1}{4 \times n_{C}^{2} \times (n_H \times n_W)^2} \sum_{i=1}^{n_C} \sum_{j=1}^{n_C} (G^{(S)}_{ij} - G^{(G)} _ {ij})^{2}$

# GRADED FUNCTION: compute_layer_style_cost

def compute_layer_style_cost(a_S, a_G):
    """
    Arguments:
    a_S -- tensor of dimension (1, n_H, n_W, n_C), hidden layer activations representing style of the image S 
    a_G -- tensor of dimension (1, n_H, n_W, n_C), hidden layer activations representing style of the image G
    
    Returns: 
    J_style_layer -- tensor representing a scalar value, style cost defined above by equation (2)
    """
    
    ### START CODE HERE ###
    # Retrieve dimensions from a_G (≈1 line)
    m, n_H, n_W, n_C = a_G.get_shape().as_list()
    
    # Reshape the images to have them of shape (n_C, n_H*n_W) (≈2 lines)
    a_S = tf.transpose(tf.reshape(a_S,[n_H*n_W, n_C]))
    a_G = tf.transpose(tf.reshape(a_G,[n_H*n_W, n_C]))

    # Computing gram_matrices for both images S and G (≈2 lines)
    GS = gram_matrix(a_S)
    GG = gram_matrix(a_G)

    # Computing the loss (≈1 line)
    J_style_layer = 1 / (4 * (n_C*n_W*n_H)**2) * tf.reduce_sum(tf.square(tf.subtract(GS,GG)))
    
    ### END CODE HERE ###
    
    return J_style_layer

# GRADED FUNCTION: total_cost

def total_cost(J_content, J_style, alpha = 10, beta = 40):
    """
    Computes the total cost function
    
    Arguments:
    J_content -- content cost coded above
    J_style -- style cost coded above
    alpha -- hyperparameter weighting the importance of the content cost
    beta -- hyperparameter weighting the importance of the style cost
    
    Returns:
    J -- total cost as defined by the formula above.
    """
    
    ### START CODE HERE ### (≈1 line)
    J = alpha * J_content + beta * J_style
    ### END CODE HERE ###
    
    return J

### START CODE HERE ### (1 line)
J = total_cost(J_content, J_style, alpha = 10, beta = 40)
### END CODE HERE ###

def model_nn(sess, input_image, num_iterations = 200):
    
    # Initialize global variables (you need to run the session on the initializer)
    ### START CODE HERE ### (1 line)
    sess.run(tf.global_variables_initializer())
    ### END CODE HERE ###
    
    # Run the noisy input image (initial generated image) through the model. Use assign().
    ### START CODE HERE ### (1 line)
    generated_image = sess.run(model['input'].assign(input_image))
    ### END CODE HERE ###
    
    for i in range(num_iterations):
    
        # Run the session on the train_step to minimize the total cost
        ### START CODE HERE ### (1 line)
        sess.run(train_step)
        ### END CODE HERE ###
        
        # Compute the generated image by running the session on the current model['input']
        ### START CODE HERE ### (1 line)
        generated_image = sess.run(model['input'])
        ### END CODE HERE ###

        # Print every 20 iteration.
        if i%20 == 0:
            Jt, Jc, Js = sess.run([J, J_content, J_style])
            print("Iteration " + str(i) + " :")
            print("total cost = " + str(Jt))
            print("content cost = " + str(Jc))
            print("style cost = " + str(Js))
            
            # save current generated image in the "/output" directory
            save_image("output/" + str(i) + ".png", generated_image)
    
    # save last generated image
    save_image('output/generated_image.jpg', generated_image)
    
    return generated_image

DeepLearning.ai作业:(4-4)-- 特殊应用:人脸识别和神经风格转换

Part1：人脸识别

Part2：风格迁移

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