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  • 课程四(Convolutional Neural Networks),第三 周(Object detection) —— 2.Programming assignments:Car detection with YOLOv2

    Autonomous driving - Car detection

    Welcome to your week 3 programming assignment. You will learn about object detection using the very powerful YOLO model. Many of the ideas in this notebook are described in the two YOLO papers: Redmon et al., 2016 (https://arxiv.org/abs/1506.02640) and Redmon and Farhadi, 2016 (https://arxiv.org/abs/1612.08242).

    You will learn to:

    • Use object detection on a car detection dataset
    • Deal with bounding boxes

    Run the following cell to load the packages and dependencies that are going to be useful for your journey!

    【code】

    import argparse
    import os
    import matplotlib.pyplot as plt
    from matplotlib.pyplot import imshow
    import scipy.io
    import scipy.misc
    import numpy as np
    import pandas as pd
    import PIL
    import tensorflow as tf
    from keras import backend as K
    from keras.layers import Input, Lambda, Conv2D
    from keras.models import load_model, Model
    from yolo_utils import read_classes, read_anchors, generate_colors, preprocess_image, draw_boxes, scale_boxes
    from yad2k.models.keras_yolo import yolo_head, yolo_boxes_to_corners, preprocess_true_boxes, yolo_loss, yolo_body
    
    %matplotlib inline
    

    Important Note: As you can see, we import Keras's backend as K. This means that to use a Keras function in this notebook, you will need to write: K.function(...).

    1 - Problem Statement

    You are working on a self-driving car. As a critical (重要的)component of this project, you'd like to first build a car detection system. To collect data, you've mounted a camera to the hood (meaning the front) of the car, which takes pictures of the road ahead every few seconds while you drive around.

      【注释】原网页此处是视频

    We would like to especially thank drive.ai for providing this dataset! Drive.ai is a company building the brains of self-driving vehicles.

                                     

     You've gathered all these images into a folder and have labelled them by drawing bounding boxes around every car you found. Here's an example of what your bounding boxes look like.

    If you have 80 classes that you want YOLO to recognize, you can represent the class label cc either as an integer from 1 to 80, or as an 80-dimensional vector (with 80 numbers) one component of which is 1 and the rest of which are 0. The video lectures had used the latter representation; in this notebook, we will use both representations, depending on which is more convenient for a particular step.

    In this exercise, you will learn how YOLO works, then apply it to car detection. Because the YOLO model is very computationally expensive to train, we will load pre-trained weights for you to use.

    2 - YOLO

    YOLO ("you only look once") is a popular algoritm because it achieves high accuracy while also being able to run in real-time. This algorithm "only looks once" at the image in the sense that it requires only one forward propagation pass through the network to make predictions. After non-max suppression, it then outputs recognized objects together with the bounding boxes.

    2.1 - Model details

    First things to know:

    • The input is a batch of images of shape (m, 608, 608, 3)
    • The output is a list of bounding boxes along with the recognized classes. Each bounding box is represented by 6 numbers (pc,bx,by,bh,bw,c) as explained above. If you expand c into an 80-dimensional vector, each bounding box is then represented by 85 numbers.

    We will use 5 anchor boxes. So you can think of the YOLO architecture as the following: IMAGE (m, 608, 608, 3) -> DEEP CNN -> ENCODING (m, 19, 19, 5, 85). 

     Lets look in greater detail at what this encoding represents.

     

                          Figure2: Encoding architecture for YOLO (YOLO 编码体系结构

    If the center/midpoint of an object falls into a grid cell, that grid cell is responsible for detecting that object.

    Since we are using 5 anchor boxes, each of the 19 x19 cells thus encodes information about 5 boxes. Anchor boxes are defined only by their width and height.

    For simplicity, we will flatten the last two last dimensions of the shape (19, 19, 5, 85) encoding. So the output of the Deep CNN is (19, 19, 425).

     

    Figure 3 Flattening the last two last dimensions

    Now, for each box (of each cell) we will compute the following elementwise product and extract a probability that the box contains a certain class. 

     

    Figure 4 Find the class detected by each box

    Here's one way to visualize what YOLO is predicting on an image:

    • For each of the 19x19 grid cells, find the maximum of the probability scores (taking a max across both the 5 anchor boxes and across different classes).
    • Color that grid cell according to what object that grid cell considers the most likely.

     【中文翻译】

    这里一种方法可以直观显示 YOLO 图像预测:
    • 对于每个19x19 网格单元, 找出概率分数的最大值 (在5anchor boxes和不同的类的基础上找 max)。
    • 根据网格单元格认为最有可能的对象来对网格单元格进行着色。

    Doing this results in this picture:

    Note that this visualization isn't a core part of the YOLO algorithm itself for making predictions; it's just a nice way of visualizing an intermediate result of the algorithm.

     Another way to visualize YOLO's output is to plot the bounding boxes that it outputs. Doing that results in a visualization like this:

    Figure 6 : Each cell gives you 5 boxes. In total, the model predicts: 19x19x5 = 1805 boxes just by looking once at the image (one forward pass through the network)! Different colors denote different classes. 

    In the figure above, we plotted only boxes that the model had assigned a high probability to, but this is still too many boxes. You'd like to filter the algorithm's output down to a much smaller number of detected objects. To do so, you'll use non-max suppression. Specifically, you'll carry out these steps:

    • Get rid of boxes with a low score (meaning, the box is not very confident about detecting a class)
    • Select only one box when several boxes overlap with each other and detect the same object.

    【中文翻译】

    在上面的图中, 我们只绘制了被模型分配了高概率的框, 但这仍然是太多的框。您希望将算法的输出过滤到更小的检测对象数量。为此, 您将使用非最大抑制。具体来说, 执行以下步骤:
    • 去掉的boxes(意思, 这个boxes检测一个不是信心)
    • 当多个boxes相互重叠并检测到同一对象时, 只选择一个box。

    2.2 - Filtering with a threshold on class scores

    You are going to apply a first filter by thresholding. You would like to get rid of any box for which the class "score" is less than a chosen threshold.

    The model gives you a total of 19x19x5x85 numbers, with each box described by 85 numbers. It'll be convenient to rearrange the (19,19,5,85) (or (19,19,425)) dimensional tensor into the following variables:

    • box_confidence: tensor of shape (19×19,5,1) containing pc (confidence probability that there's some object) for each of the 5 boxes predicted in each of the 19x19 cells.
    • boxes: tensor of shape (19×19,5,4) containing (bx,by,bh,bw)for each of the 5 boxes per cell.
    • box_class_probs: tensor of shape (19×19,5,80)containing the detection probabilities (c1,c2,...c80)for each of the 80 classes for each of the 5 boxes per cell.

    【中文翻译】

    您将通过阈值来应用第一个过滤器。你把3任何的类 "分数" 小于一个选择阈值的box去掉。
    该模型为您提供了一个共19x19x5x85 的数字, 每个盒子由85数字描述。将 (19,19,585) ( (19,1,9425)) 尺寸张量以下变量方便:
    • box_confidence: tensor of shape (19×19,5,1) containing pc (confidence probability that there's some object) for each of the 5 boxes predicted in each of the 19x19 cells.
    • boxes: tensor of shape (19×19,5,4) containing (bx,by,bh,bw)for each of the 5 boxes per cell.
    • box_class_probs: tensor of shape (19×19,5,80)containing the detection probabilities (c1,c2,...c80for each of the 80 classes for each of the 5 boxes per cell.

    Exercise: Implement yolo_filter_boxes().

    1. Compute box scores by doing the elementwise product as described in Figure 4. The following code may help you choose the right operator:
      a = np.random.randn(19*19, 5, 1)
      b = np.random.randn(19*19, 5, 80)
      c = a * b # shape of c will be (19*19, 5, 80)
      
    2. For each box, find:
      • the index of the class with the maximum box score (Hint) (Be careful with what axis you choose; consider using axis=-1)
      • the corresponding box score (Hint) (Be careful with what axis you choose; consider using axis=-1)
    3. Create a mask by using a threshold. As a reminder: ([0.9, 0.3, 0.4, 0.5, 0.1] < 0.4) returns: [False, True, False, False, True]. The mask should be True for the boxes you want to keep.
    4. Use TensorFlow to apply the mask to box_class_scores, boxes and box_classes to filter out the boxes we don't want. You should be left with just the subset of boxes you want to keep. (Hint)

    Reminder: to call a Keras function, you should use K.function(...).

    【中文翻译】 

     练习:实现yolo_filter_boxes()

      1、按图4所述的元素乘积计算每个box的分数。下面代码可以帮助选择正确运算符:

      a = np.random.randn(19*19, 5, 1)
      b = np.random.randn(19*19, 5, 80)
      c = a * b # shape of c will be (19*19, 5, 80)

      2、 对于每个box, 查找:

    • 具有最大box得分 索引 (注意选择; 考虑使用 axis=-1)
    • 相应的box评分 (小心选择; 考虑使用 axis=-1)

        3、使用阈值创建掩码。提醒: ([0.9, 0.3, 0.4, 0.5, 0.1] <0.4) 返回: [假, 真, 假, 假, 真]。对于要保留的box, 该掩码应为真。

        4、使用 TensorFlow 将掩码应用于 box_class_scores、boxes和 box_classes, 以筛选出我们不需要的框。你应该只剩下你想要保留的盒子的子集。

    提醒: 要调用 Keras 函数, 应使用  K.function(...)

    【code】

    # GRADED FUNCTION: yolo_filter_boxes
    
    def yolo_filter_boxes(box_confidence, boxes, box_class_probs, threshold = .6):
        """Filters YOLO boxes by thresholding on object and class confidence.
        
        Arguments:
        box_confidence -- tensor of shape (19, 19, 5, 1)
        boxes -- tensor of shape (19, 19, 5, 4)
        box_class_probs -- tensor of shape (19, 19, 5, 80)
        threshold -- real value, if [ highest class probability score < threshold], then get rid of the corresponding box
        
        Returns:
        scores -- tensor of shape (None,), containing the class probability score for selected boxes
        boxes -- tensor of shape (None, 4), containing (b_x, b_y, b_h, b_w) coordinates of selected boxes
        classes -- tensor of shape (None,), containing the index of the class detected by the selected boxes
        
        Note: "None" is here because you don't know the exact number of selected boxes, as it depends on the threshold. 
        For example, the actual output size of scores would be (10,) if there are 10 boxes.
        """
        
        # Step 1: Compute box scores
        ### START CODE HERE ### (≈ 1 line)
        box_scores = box_confidence * box_class_probs   #  (19, 19, 5, 80)
        ### END CODE HERE ###
        
        # Step 2: Find the box_classes thanks to the max box_scores, keep track of the corresponding score
        ### START CODE HERE ### (≈ 2 lines)
        box_classes =K.argmax( box_scores, axis=-1)   #找最大分数所对应的类别,即分数对应的索引值 (19, 19, 5, 1) 
        box_class_scores = K.max(box_scores, axis=-1, keepdims=False)  # 找最大分数所对应的类别的分数值 (19, 19, 5, 1)
        ### END CODE HERE ###
        
        # Step 3: Create a filtering mask based on "box_class_scores" by using "threshold". The mask should have the
        # same dimension as box_class_scores, and be True for the boxes you want to keep (with probability >= threshold)
        ### START CODE HERE ### (≈ 1 line)
        filtering_mask = box_class_scores >= threshold      #(19, 19, 5, 1)
        ### END CODE HERE ###
        
        # Step 4: Apply the mask to scores, boxes and classes
        ### START CODE HERE ### (≈ 3 lines)
        scores = tf.boolean_mask(box_class_scores,  filtering_mask)  # (19, 19, 5, 1)中false对应的值都去掉
        boxes = tf.boolean_mask(boxes,  filtering_mask) # tensor of shape (19, 19, 5, 4) 中false对应的值都去掉
        classes = tf.boolean_mask( box_classes,  filtering_mask) #tensor of shape 中(19, 19, 5, 1) 中false对应的值都去掉
        ### END CODE HERE ###
        
        return scores, boxes, classes
    
    with tf.Session() as test_a:
        box_confidence = tf.random_normal([19, 19, 5, 1], mean=1, stddev=4, seed = 1)
        boxes = tf.random_normal([19, 19, 5, 4], mean=1, stddev=4, seed = 1)
        box_class_probs = tf.random_normal([19, 19, 5, 80], mean=1, stddev=4, seed = 1)
        scores, boxes, classes = yolo_filter_boxes(box_confidence, boxes, box_class_probs, threshold = 0.5)
        print("scores[2] = " + str(scores[2].eval()))  # .eval()将字符串str当成有效的表达式来求值并返回计算结果
        print("classes[2] = " + str(classes[2].eval()))
        print("scores.shape = " + str(scores.shape))
        print("boxes.shape = " + str(boxes.shape))
        print("classes.shape = " + str(classes.shape))
    

      

    【result】

    scores[2] = 10.7506
    boxes[2] = [ 8.42653275  3.27136683 -0.5313437  -4.94137383]
    classes[2] = 7
    scores.shape = (?,)
    boxes.shape = (?, 4)
    classes.shape = (?,)
    scores[2] = Tensor("strided_slice_15:0", shape=(), dtype=float32)
    

    Expected Output:

    scores[2]	10.7506
    boxes[2]	[ 8.42653275 3.27136683 -0.5313437 -4.94137383]
    classes[2]	7
    scores.shape	(?,)
    boxes.shape	(?, 4)
    classes.shape	(?,)
    

    2.3 - Non-max suppression

    Even after filtering by thresholding over the classes scores, you still end up a lot of overlapping boxes. A second filter for selecting the right boxes is called non-maximum suppression (NMS).

    Figure 7 : In this example, the model has predicted 3 cars, but it's actually 3 predictions of the same car. Running non-max suppression (NMS) will select only the most accurate (highest probabiliy) one of the 3 boxes. 

    Non-max suppression uses the very important function called "Intersection over Union", or IoU. 

    【中文翻译】

    即使在通过对类分数进行阈值筛选后, 仍然会出现许多重叠的box。用于选择正确的box的第二个筛选器称为非最大值抑制 (non-maximum suppression,NMS)。

     

    图 7: 在这个例子中, 模型预测了3辆汽车, 但实际上3预测都是同一辆车。运行非最大值抑制 (NMS) 将只选择最准确的 (最高 probabiliy) 3 个box之一。

    非最大值抑制使用非常重要的函数, 称为 "交并比", 或Intersection over Union, IoU。

    图 8 : "Intersection over Union"的定义

    Exercise: Implement iou(). Some hints:

    • In this exercise only, we define a box using its two corners (upper left and lower right): (x1, y1, x2, y2) rather than the midpoint and height/width.
    • To calculate the area of a rectangle you need to multiply its height (y2 - y1) by its width (x2 - x1)
    • You'll also need to find the coordinates (xi1, yi1, xi2, yi2) of the intersection of two boxes. Remember that:
      • xi1 = maximum of the x1 coordinates of the two boxes
      • yi1 = maximum of the y1 coordinates of the two boxes
      • xi2 = minimum of the x2 coordinates of the two boxes
      • yi2 = minimum of the y2 coordinates of the two boxes

    In this code, we use the convention that (0,0) is the top-left corner of an image, (1,0) is the upper-right corner, and (1,1) the lower-right corner.

     【code】

    # GRADED FUNCTION: iou
    
    def iou(box1, box2):
        """Implement the intersection over union (IoU) between box1 and box2
        
        Arguments:
        box1 -- first box, list object with coordinates (x1, y1, x2, y2)
        box2 -- second box, list object with coordinates (x1, y1, x2, y2)
        """
    
        # Calculate the (y1, x1, y2, x2) coordinates of the intersection of box1 and box2. Calculate its Area.
        ### START CODE HERE ### (≈ 5 lines)
        xi1 = np.maximum( box1, box2)[0]     # 或者  max(box1[0],box2[0])
        yi1 =  np.maximum( box1, box2)[1]
        xi2 = np.minimum( box1, box2)[2]
        yi2 = np.minimum( box1, box2)[3]
        inter_area = (yi2-yi1)*(xi2-xi1)
        ### END CODE HERE ###    
    
        # Calculate the Union area by using Formula: Union(A,B) = A + B - Inter(A,B)
        ### START CODE HERE ### (≈ 3 lines)
        box1_area = (box1[3]-box1[1])* (box1[2]-box1[0])
        box2_area =  (box2[3]-box2[1])* (box2[2]-box2[0])
        union_area = box1_area + box2_area - inter_area
        ### END CODE HERE ###
        
        # compute the IoU
        ### START CODE HERE ### (≈ 1 line)
        iou =inter_area /  union_area
        ### END CODE HERE ###
    
        return iou
    
    box1 = (2, 1, 4, 3)
    box2 = (1, 2, 3, 4) 
    print("iou = " + str(iou(box1, box2)))
    

    【result】

    iou = 0.142857142857
    

    Expected Output:

    iou =	0.14285714285714285
    

      

    You are now ready to implement non-max suppression. The key steps are:

    1. Select the box that has the highest score.
    2. Compute its overlap with all other boxes, and remove boxes that overlap it more than iou_threshold.
    3. Go back to step 1 and iterate until there's no more boxes with a lower score than the current selected box.

    This will remove all boxes that have a large overlap with the selected boxes. Only the "best" boxes remain.

      

    【中文翻译】  

    您现在可以实现非最大值抑制。关键步骤如下:
    1. 选择具有最高分数的box。
    2. 计算其与所有其他box的重叠, 并移除比 iou_threshold 值大的重叠的框。
    3. 返回到步骤1并进行迭代, 直到没有比当前选定box更低的分数的box。
    这将删除与所选box有很大重叠的所有box。只有 "最好" 的box依然存在。

      

    Exercise: Implement yolo_non_max_suppression() using TensorFlow. TensorFlow has two built-in functions that are used to implement non-max suppression (so you don't actually need to use your iou() implementation):

     【code】

    # GRADED FUNCTION: yolo_non_max_suppression
    
    def yolo_non_max_suppression(scores, boxes, classes, max_boxes = 10, iou_threshold = 0.5):
        """
        Applies Non-max suppression (NMS) to set of boxes
        
        Arguments:
        scores -- tensor of shape (None,), output of yolo_filter_boxes()
        boxes -- tensor of shape (None, 4), output of yolo_filter_boxes() that have been scaled to the image size (see later)
        classes -- tensor of shape (None,), output of yolo_filter_boxes()
        max_boxes -- integer, maximum number of predicted boxes you'd like
        iou_threshold -- real value, "intersection over union" threshold used for NMS filtering
        
        Returns:
        scores -- tensor of shape (, None), predicted score for each box
        boxes -- tensor of shape (4, None), predicted box coordinates
        classes -- tensor of shape (, None), predicted class for each box
        
        Note: The "None" dimension of the output tensors has obviously to be less than max_boxes. Note also that this
        function will transpose the shapes of scores, boxes, classes. This is made for convenience.
        """
        
        max_boxes_tensor = K.variable(max_boxes, dtype='int32')     # tensor to be used in tf.image.non_max_suppression()
        K.get_session().run(tf.variables_initializer([max_boxes_tensor])) # initialize variable max_boxes_tensor
        
        # Use tf.image.non_max_suppression() to get the list of indices corresponding to boxes you keep
        ### START CODE HERE ### (≈ 1 line)
        nms_indices = tf.image.non_max_suppression(boxes,scores, max_boxes_tensor,iou_threshold)
        ### END CODE HERE ###
        
        # Use K.gather() to select only nms_indices from scores, boxes and classes  使用 K.gather() 从 scores, boxes and classes只选择 nms_indices
        ### START CODE HERE ### (≈ 3 lines)
        scores =  K.gather(scores,nms_indices)
        boxes = K.gather(boxes,nms_indices)
        classes = K.gather(classes,nms_indices)
        ### END CODE HERE ###
        
        return scores, boxes, classes
    
    with tf.Session() as test_b:
        scores = tf.random_normal([54,], mean=1, stddev=4, seed = 1)
        boxes = tf.random_normal([54, 4], mean=1, stddev=4, seed = 1)
        classes = tf.random_normal([54,], mean=1, stddev=4, seed = 1)
        scores, boxes, classes = yolo_non_max_suppression(scores, boxes, classes)
        print("scores[2] = " + str(scores[2].eval()))
        print("boxes[2] = " + str(boxes[2].eval()))
        print("classes[2] = " + str(classes[2].eval()))
        print("scores.shape = " + str(scores.eval().shape))
        print("boxes.shape = " + str(boxes.eval().shape))
        print("classes.shape = " + str(classes.eval().shape))
    

    【result】  

    scores[2] = 6.9384
    boxes[2] = [-5.299932    3.13798141  4.45036697  0.95942086]
    classes[2] = -2.24527
    scores.shape = (10,)
    boxes.shape = (10, 4)
    classes.shape = (10,)
    

    Expected Output:

    scores[2] 6.9384
    boxes[2] [-5.299932 3.13798141 4.45036697 0.95942086]
    classes[2] -2.24527
    scores.shape (10,)
    boxes.shape (10, 4)
    classes.shape (10,)

      

    2.4 Wrapping up the filtering

    It's time to implement a function taking the output of the deep CNN (the 19x19x5x85 dimensional encoding) and filtering through all the boxes using the functions you've just implemented.

    Exercise: Implement yolo_eval() which takes the output of the YOLO encoding and filters the boxes using score threshold and NMS. There's just one last implementational detail you have to know. There're a few ways of representing boxes, such as via their corners or via their midpoint and height/width. YOLO converts between a few such formats at different times, using the following functions (which we have provided):

    boxes = yolo_boxes_to_corners(box_xy, box_wh)
    

    which converts the yolo box coordinates (x,y,w,h) to box corners' coordinates (x1, y1, x2, y2) to fit the input of yolo_filter_boxes

    boxes = scale_boxes(boxes, image_shape)

    YOLO's network was trained to run on 608x608 images. If you are testing this data on a different size image--for example, the car detection dataset had 720x1280 images--this step rescales the boxes so that they can be plotted on top of the original 720x1280 image.

    Don't worry about these two functions; we'll show you where they need to be called.

    【中文翻译】  

    2.4 Wrapping up the filtering

    现在是时候来实现一个函数,该函数把深度 CNN (19x19x5x85 维编码)的输出用你刚刚实现函数来过滤筛选。

    练习: 实现 yolo_eval (), 它采用 yolo 编码的输出, 并使用分数阈值和 NMS 过滤这些box。这有你要知道的最后一个实施细节。有几种方式来表示框, 如通过其角或通过其中心点和高度/宽度。YOLO 使用以下函数 (我们提供的) 在不同的时候转换几个这样的格式:

    boxes = yolo_boxes_to_corners(box_xy, box_wh)

    它将 yolo box坐标 (x、y、w、h) 转换为box角坐标 (x1、y1、x2、y2) 以适合 yolo_filter_boxes 的输入

    boxes = scale_boxes(boxes, image_shape)

    YOLO 的网络被训练在608x608 图像上运行。如果您在不同大小的图像上测试此数据 (例如, 汽车检测数据集有720x1280 图像), 则此步骤缩放这些box, 以便可以在原始720x1280 图像的顶部绘制它们。

    不要担心两个函数;我们告诉他们需要召唤地方

    【code】

    # GRADED FUNCTION: yolo_eval
    
    def yolo_eval(yolo_outputs, image_shape = (720., 1280.), max_boxes=10, score_threshold=.6, iou_threshold=.5):
        """
        Converts the output of YOLO encoding (a lot of boxes) to your predicted boxes along with their scores, box coordinates and classes.
        
        Arguments:
        yolo_outputs -- output of the encoding model (for image_shape of (608, 608, 3)), contains 4 tensors:
                        box_confidence: tensor of shape (None, 19, 19, 5, 1)
                        box_xy: tensor of shape (None, 19, 19, 5, 2)
                        box_wh: tensor of shape (None, 19, 19, 5, 2)
                        box_class_probs: tensor of shape (None, 19, 19, 5, 80)
        image_shape -- tensor of shape (2,) containing the input shape, in this notebook we use (608., 608.) (has to be float32 dtype)
        max_boxes -- integer, maximum number of predicted boxes you'd like
        score_threshold -- real value, if [ highest class probability score < threshold], then get rid of the corresponding box
        iou_threshold -- real value, "intersection over union" threshold used for NMS filtering
        
        Returns:
        scores -- tensor of shape (None, ), predicted score for each box
        boxes -- tensor of shape (None, 4), predicted box coordinates
        classes -- tensor of shape (None,), predicted class for each box
        """
        
        ### START CODE HERE ### 
        
        # Retrieve outputs of the YOLO model (≈1 line)
        box_confidence, box_xy, box_wh, box_class_probs = yolo_outputs
    
        # Convert boxes to be ready for filtering functions 
        boxes = yolo_boxes_to_corners(box_xy, box_wh)
    
        # Use one of the functions you've implemented to perform Score-filtering with a threshold of score_threshold (≈1 line)
        scores, boxes, classes = yolo_filter_boxes(box_confidence, boxes, box_class_probs, score_threshold)
        
        # Scale boxes back to original image shape.
        boxes = scale_boxes(boxes, image_shape)
    
        # Use one of the functions you've implemented to perform Non-max suppression with a threshold of iou_threshold (≈1 line)
        scores, boxes, classes = yolo_non_max_suppression(scores, boxes, classes, max_boxes, iou_threshold)
        
        ### END CODE HERE ###
        
        return scores, boxes, classes
    
    with tf.Session() as test_b:
        yolo_outputs = (tf.random_normal([19, 19, 5, 1], mean=1, stddev=4, seed = 1),
                        tf.random_normal([19, 19, 5, 2], mean=1, stddev=4, seed = 1),
                        tf.random_normal([19, 19, 5, 2], mean=1, stddev=4, seed = 1),
                        tf.random_normal([19, 19, 5, 80], mean=1, stddev=4, seed = 1))
        scores, boxes, classes = yolo_eval(yolo_outputs)
        print("scores[2] = " + str(scores[2].eval()))
        print("boxes[2] = " + str(boxes[2].eval()))
        print("classes[2] = " + str(classes[2].eval()))
        print("scores.shape = " + str(scores.eval().shape))
        print("boxes.shape = " + str(boxes.eval().shape))
        print("classes.shape = " + str(classes.eval().shape))
    

    【result】  

    scores[2] = 138.791
    boxes[2] = [ 1292.32971191  -278.52166748  3876.98925781  -835.56494141]
    classes[2] = 54
    scores.shape = (10,)
    boxes.shape = (10, 4)
    classes.shape = (10,)
    

    Expected Output:

    scores[2] 138.791
    boxes[2] [ 1292.32971191 -278.52166748 3876.98925781 -835.56494141]
    classes[2] 54
    scores.shape (10,)
    boxes.shape (10, 4)
    classes.shape (10,)

      

    Summary for YOLO:

    • Input image (608, 608, 3)
    • The input image goes through a CNN, resulting in a (19,19,5,85) dimensional output.
    • After flattening the last two dimensions, the output is a volume of shape (19, 19, 425):
      • Each cell in a 19x19 grid over the input image gives 425 numbers.
      • 425 = 5 x 85 because each cell contains predictions for 5 boxes, corresponding to 5 anchor boxes, as seen in lecture.
      • 85 = 5 + 80 where 5 is because (pc,bx,by,bh,bw)has 5 numbers, and and 80 is the number of classes we'd like to detect
    • You then select only few boxes based on:
      • Score-thresholding: throw away boxes that have detected a class with a score less than the threshold
      • Non-max suppression: Compute the Intersection over Union and avoid selecting overlapping boxes
    • This gives you YOLO's final output.  

    【中文翻译】

    YOLO 总结:
    • 输入图像 (6086083)
    • 输入图像通过 CNN, 导致 (19195, 85) 维度输出。
    • 拼合最后两个维度之后, 输出维度 (1919425):
        在输入图像上的19x19 网格中的每个网格提供425数字。
        425 = 5 x 85, 因为每个网格包含5个box的预测, 对应于5 个anchor boxes, 如在讲座中所见。
        85 = 5 + 80其中5因为(pc,bx,by,bh,bw)5数字, 80我们检测数量
    • 然后根据以下内容选择几个boxes:
        分数阈值: 丢弃检测分数小于阈值的box
        非最大抑制: 计算并比,避免选择重叠的box
    • 这给你 YOLO 的最终输出。

    3 - Test YOLO pretrained model on images

     In this part, you are going to use a pretrained model and test it on the car detection dataset. As usual, you start by creating a session to start your graph. Run the following cell.

     【code】

    sess = K.get_session()
    

    3.1 - Defining classes, anchors and image shape.

    Recall that we are trying to detect 80 classes, and are using 5 anchor boxes. We have gathered the information about the 80 classes and 5 boxes in two files "coco_classes.txt" and "yolo_anchors.txt". Let's load these quantities into the model by running the next cell.

    The car detection dataset has 720x1280 images, which we've pre-processed into 608x608 images.

    【code】  

    class_names = read_classes("model_data/coco_classes.txt")
    anchors = read_anchors("model_data/yolo_anchors.txt")
    image_shape = (720., 1280.)    
    

      

    3.2 - Loading a pretrained model

    Training a YOLO model takes a very long time and requires a fairly large dataset of labelled bounding boxes for a large range of target classes. You are going to load an existing pretrained Keras YOLO model stored in "yolo.h5". (These weights come from the official YOLO website, and were converted using a function written by Allan Zelener. References are at the end of this notebook. Technically, these are the parameters from the "YOLOv2" model, but we will more simply refer to it as "YOLO" in this notebook.) Run the cell below to load the model from this file.

     【code】

    yolo_model = load_model("model_data/yolo.h5")
    

      

    This loads the weights of a trained YOLO model. Here's a summary of the layers your model contains. 

    【code】

    yolo_model.summary()
    

    【result】

    Layer (type)                     Output Shape          Param #     Connected to                     
    ====================================================================================================
    input_1 (InputLayer)             (None, 608, 608, 3)   0                                            
    ____________________________________________________________________________________________________
    conv2d_1 (Conv2D)                (None, 608, 608, 32)  864         input_1[0][0]                    
    ____________________________________________________________________________________________________
    batch_normalization_1 (BatchNorm (None, 608, 608, 32)  128         conv2d_1[0][0]                   
    ____________________________________________________________________________________________________
    leaky_re_lu_1 (LeakyReLU)        (None, 608, 608, 32)  0           batch_normalization_1[0][0]      
    ____________________________________________________________________________________________________
    max_pooling2d_1 (MaxPooling2D)   (None, 304, 304, 32)  0           leaky_re_lu_1[0][0]              
    ____________________________________________________________________________________________________
    conv2d_2 (Conv2D)                (None, 304, 304, 64)  18432       max_pooling2d_1[0][0]            
    ____________________________________________________________________________________________________
    batch_normalization_2 (BatchNorm (None, 304, 304, 64)  256         conv2d_2[0][0]                   
    ____________________________________________________________________________________________________
    leaky_re_lu_2 (LeakyReLU)        (None, 304, 304, 64)  0           batch_normalization_2[0][0]      
    ____________________________________________________________________________________________________
    max_pooling2d_2 (MaxPooling2D)   (None, 152, 152, 64)  0           leaky_re_lu_2[0][0]              
    ____________________________________________________________________________________________________
    conv2d_3 (Conv2D)                (None, 152, 152, 128) 73728       max_pooling2d_2[0][0]            
    ____________________________________________________________________________________________________
    batch_normalization_3 (BatchNorm (None, 152, 152, 128) 512         conv2d_3[0][0]                   
    ____________________________________________________________________________________________________
    leaky_re_lu_3 (LeakyReLU)        (None, 152, 152, 128) 0           batch_normalization_3[0][0]      
    ____________________________________________________________________________________________________
    conv2d_4 (Conv2D)                (None, 152, 152, 64)  8192        leaky_re_lu_3[0][0]              
    ____________________________________________________________________________________________________
    batch_normalization_4 (BatchNorm (None, 152, 152, 64)  256         conv2d_4[0][0]                   
    ____________________________________________________________________________________________________
    leaky_re_lu_4 (LeakyReLU)        (None, 152, 152, 64)  0           batch_normalization_4[0][0]      
    ____________________________________________________________________________________________________
    conv2d_5 (Conv2D)                (None, 152, 152, 128) 73728       leaky_re_lu_4[0][0]              
    ____________________________________________________________________________________________________
    batch_normalization_5 (BatchNorm (None, 152, 152, 128) 512         conv2d_5[0][0]                   
    ____________________________________________________________________________________________________
    leaky_re_lu_5 (LeakyReLU)        (None, 152, 152, 128) 0           batch_normalization_5[0][0]      
    ____________________________________________________________________________________________________
    max_pooling2d_3 (MaxPooling2D)   (None, 76, 76, 128)   0           leaky_re_lu_5[0][0]              
    ____________________________________________________________________________________________________
    conv2d_6 (Conv2D)                (None, 76, 76, 256)   294912      max_pooling2d_3[0][0]            
    ____________________________________________________________________________________________________
    batch_normalization_6 (BatchNorm (None, 76, 76, 256)   1024        conv2d_6[0][0]                   
    ____________________________________________________________________________________________________
    leaky_re_lu_6 (LeakyReLU)        (None, 76, 76, 256)   0           batch_normalization_6[0][0]      
    ____________________________________________________________________________________________________
    conv2d_7 (Conv2D)                (None, 76, 76, 128)   32768       leaky_re_lu_6[0][0]              
    ____________________________________________________________________________________________________
    batch_normalization_7 (BatchNorm (None, 76, 76, 128)   512         conv2d_7[0][0]                   
    ____________________________________________________________________________________________________
    leaky_re_lu_7 (LeakyReLU)        (None, 76, 76, 128)   0           batch_normalization_7[0][0]      
    ____________________________________________________________________________________________________
    conv2d_8 (Conv2D)                (None, 76, 76, 256)   294912      leaky_re_lu_7[0][0]              
    ____________________________________________________________________________________________________
    batch_normalization_8 (BatchNorm (None, 76, 76, 256)   1024        conv2d_8[0][0]                   
    ____________________________________________________________________________________________________
    leaky_re_lu_8 (LeakyReLU)        (None, 76, 76, 256)   0           batch_normalization_8[0][0]      
    ____________________________________________________________________________________________________
    max_pooling2d_4 (MaxPooling2D)   (None, 38, 38, 256)   0           leaky_re_lu_8[0][0]              
    ____________________________________________________________________________________________________
    conv2d_9 (Conv2D)                (None, 38, 38, 512)   1179648     max_pooling2d_4[0][0]            
    ____________________________________________________________________________________________________
    batch_normalization_9 (BatchNorm (None, 38, 38, 512)   2048        conv2d_9[0][0]                   
    ____________________________________________________________________________________________________
    leaky_re_lu_9 (LeakyReLU)        (None, 38, 38, 512)   0           batch_normalization_9[0][0]      
    ____________________________________________________________________________________________________
    conv2d_10 (Conv2D)               (None, 38, 38, 256)   131072      leaky_re_lu_9[0][0]              
    ____________________________________________________________________________________________________
    batch_normalization_10 (BatchNor (None, 38, 38, 256)   1024        conv2d_10[0][0]                  
    ____________________________________________________________________________________________________
    leaky_re_lu_10 (LeakyReLU)       (None, 38, 38, 256)   0           batch_normalization_10[0][0]     
    ____________________________________________________________________________________________________
    conv2d_11 (Conv2D)               (None, 38, 38, 512)   1179648     leaky_re_lu_10[0][0]             
    ____________________________________________________________________________________________________
    batch_normalization_11 (BatchNor (None, 38, 38, 512)   2048        conv2d_11[0][0]                  
    ____________________________________________________________________________________________________
    leaky_re_lu_11 (LeakyReLU)       (None, 38, 38, 512)   0           batch_normalization_11[0][0]     
    ____________________________________________________________________________________________________
    conv2d_12 (Conv2D)               (None, 38, 38, 256)   131072      leaky_re_lu_11[0][0]             
    ____________________________________________________________________________________________________
    batch_normalization_12 (BatchNor (None, 38, 38, 256)   1024        conv2d_12[0][0]                  
    ____________________________________________________________________________________________________
    leaky_re_lu_12 (LeakyReLU)       (None, 38, 38, 256)   0           batch_normalization_12[0][0]     
    ____________________________________________________________________________________________________
    conv2d_13 (Conv2D)               (None, 38, 38, 512)   1179648     leaky_re_lu_12[0][0]             
    ____________________________________________________________________________________________________
    batch_normalization_13 (BatchNor (None, 38, 38, 512)   2048        conv2d_13[0][0]                  
    ____________________________________________________________________________________________________
    leaky_re_lu_13 (LeakyReLU)       (None, 38, 38, 512)   0           batch_normalization_13[0][0]     
    ____________________________________________________________________________________________________
    max_pooling2d_5 (MaxPooling2D)   (None, 19, 19, 512)   0           leaky_re_lu_13[0][0]             
    ____________________________________________________________________________________________________
    conv2d_14 (Conv2D)               (None, 19, 19, 1024)  4718592     max_pooling2d_5[0][0]            
    ____________________________________________________________________________________________________
    batch_normalization_14 (BatchNor (None, 19, 19, 1024)  4096        conv2d_14[0][0]                  
    ____________________________________________________________________________________________________
    leaky_re_lu_14 (LeakyReLU)       (None, 19, 19, 1024)  0           batch_normalization_14[0][0]     
    ____________________________________________________________________________________________________
    conv2d_15 (Conv2D)               (None, 19, 19, 512)   524288      leaky_re_lu_14[0][0]             
    ____________________________________________________________________________________________________
    batch_normalization_15 (BatchNor (None, 19, 19, 512)   2048        conv2d_15[0][0]                  
    ____________________________________________________________________________________________________
    leaky_re_lu_15 (LeakyReLU)       (None, 19, 19, 512)   0           batch_normalization_15[0][0]     
    ____________________________________________________________________________________________________
    conv2d_16 (Conv2D)               (None, 19, 19, 1024)  4718592     leaky_re_lu_15[0][0]             
    ____________________________________________________________________________________________________
    batch_normalization_16 (BatchNor (None, 19, 19, 1024)  4096        conv2d_16[0][0]                  
    ____________________________________________________________________________________________________
    leaky_re_lu_16 (LeakyReLU)       (None, 19, 19, 1024)  0           batch_normalization_16[0][0]     
    ____________________________________________________________________________________________________
    conv2d_17 (Conv2D)               (None, 19, 19, 512)   524288      leaky_re_lu_16[0][0]             
    ____________________________________________________________________________________________________
    batch_normalization_17 (BatchNor (None, 19, 19, 512)   2048        conv2d_17[0][0]                  
    ____________________________________________________________________________________________________
    leaky_re_lu_17 (LeakyReLU)       (None, 19, 19, 512)   0           batch_normalization_17[0][0]     
    ____________________________________________________________________________________________________
    conv2d_18 (Conv2D)               (None, 19, 19, 1024)  4718592     leaky_re_lu_17[0][0]             
    ____________________________________________________________________________________________________
    batch_normalization_18 (BatchNor (None, 19, 19, 1024)  4096        conv2d_18[0][0]                  
    ____________________________________________________________________________________________________
    leaky_re_lu_18 (LeakyReLU)       (None, 19, 19, 1024)  0           batch_normalization_18[0][0]     
    ____________________________________________________________________________________________________
    conv2d_19 (Conv2D)               (None, 19, 19, 1024)  9437184     leaky_re_lu_18[0][0]             
    ____________________________________________________________________________________________________
    batch_normalization_19 (BatchNor (None, 19, 19, 1024)  4096        conv2d_19[0][0]                  
    ____________________________________________________________________________________________________
    conv2d_21 (Conv2D)               (None, 38, 38, 64)    32768       leaky_re_lu_13[0][0]             
    ____________________________________________________________________________________________________
    leaky_re_lu_19 (LeakyReLU)       (None, 19, 19, 1024)  0           batch_normalization_19[0][0]     
    ____________________________________________________________________________________________________
    batch_normalization_21 (BatchNor (None, 38, 38, 64)    256         conv2d_21[0][0]                  
    ____________________________________________________________________________________________________
    conv2d_20 (Conv2D)               (None, 19, 19, 1024)  9437184     leaky_re_lu_19[0][0]             
    ____________________________________________________________________________________________________
    leaky_re_lu_21 (LeakyReLU)       (None, 38, 38, 64)    0           batch_normalization_21[0][0]     
    ____________________________________________________________________________________________________
    batch_normalization_20 (BatchNor (None, 19, 19, 1024)  4096        conv2d_20[0][0]                  
    ____________________________________________________________________________________________________
    space_to_depth_x2 (Lambda)       (None, 19, 19, 256)   0           leaky_re_lu_21[0][0]             
    ____________________________________________________________________________________________________
    leaky_re_lu_20 (LeakyReLU)       (None, 19, 19, 1024)  0           batch_normalization_20[0][0]     
    ____________________________________________________________________________________________________
    concatenate_1 (Concatenate)      (None, 19, 19, 1280)  0           space_to_depth_x2[0][0]          
                                                                       leaky_re_lu_20[0][0]             
    ____________________________________________________________________________________________________
    conv2d_22 (Conv2D)               (None, 19, 19, 1024)  11796480    concatenate_1[0][0]              
    ____________________________________________________________________________________________________
    batch_normalization_22 (BatchNor (None, 19, 19, 1024)  4096        conv2d_22[0][0]                  
    ____________________________________________________________________________________________________
    leaky_re_lu_22 (LeakyReLU)       (None, 19, 19, 1024)  0           batch_normalization_22[0][0]     
    ____________________________________________________________________________________________________
    conv2d_23 (Conv2D)               (None, 19, 19, 425)   435625      leaky_re_lu_22[0][0]             
    ====================================================================================================
    Total params: 50,983,561
    Trainable params: 50,962,889
    Non-trainable params: 20,672
    

    Note: On some computers, you may see a warning message from Keras. Don't worry about it if you do--it is fine.  

    Reminder: this model converts a preprocessed batch of input images (shape: (m, 608, 608, 3)) into a tensor of shape (m, 19, 19, 5, 85) as explained in Figure (2).  

    3.3 - Convert output of the model to usable bounding box tensors

    The output of yolo_model is a (m, 19, 19, 5, 85) tensor that needs to pass through non-trivial processing and conversion. The following cell does that for you.

     【中文翻译】

    3.3-模型输出转换可用边界
    yolo_model 的输出是一个 (m, 19, 19, 5, 85) 张量, 需要通过处理和转换。下面的单元格为您提供。

    【code】

    yolo_outputs = yolo_head(yolo_model.output, anchors, len(class_names))
    

    You added yolo_outputs to your graph. This set of 4 tensors is ready to be used as input by your yolo_eval function.  

    3.4 - Filtering boxes

    yolo_outputs gave you all the predicted boxes of yolo_model in the correct format. You're now ready to perform filtering and select only the best boxes. Lets now call yolo_eval, which you had previously implemented, to do this.

     【code】

    scores, boxes, classes = yolo_eval(yolo_outputs, image_shape)
    

      

    3.5 - Run the graph on an image

    Let the fun begin. You have created a (sess) graph that can be summarized as follows:

    1. yolo_model.input is given to yolo_model. The model is used to compute the output yolo_model.output
    2. yolo_model.output is processed by yolo_head. It gives you yolo_outputs
    3. yolo_outputs goes through a filtering function, yolo_eval. It outputs your predictions: scores, boxes, classes

    Exercise: Implement predict() which runs the graph to test YOLO on an image. You will need to run a TensorFlow session, to have it compute scores, boxes, classes.

    The code below also uses the following function:

    image, image_data = preprocess_image("images/" + image_file, model_image_size = (608, 608))
    

    which outputs:

    • image: a python (PIL) representation of your image used for drawing boxes. You won't need to use it.
    • image_data: a numpy-array representing the image. This will be the input to the CNN.

    Important note: when a model uses BatchNorm (as is the case in YOLO), you will need to pass an additional placeholder in the feed_dict {K.learning_phase(): 0}.

    【中文翻译】

    练习: 执行predict(), 它运行 graph,在一张图像上来测试YOLO。您将需要运行一个 TensorFlow 的 session, 让它计算scores, boxes, classes
    下面代码使用以下函数:
    image, image_data = preprocess_image("images/" + image_file, model_image_size = (608, 608))
    该函数输出:
    • image: 用于绘制boxes的图像的 python (PIL) 表示。你不需要使用它。
    • image_data: 表示图像的 numpy 数组。这将是 CNN 的输入。
    重要提示: 当模型使用 BatchNorm (如 YOLO 中的情况) 时, 您需要在 feed_dict {K. learning_phase (): 0} 中传递一个额外的占位符。

    【code】

    def predict(sess, image_file):
        """
        Runs the graph stored in "sess" to predict boxes for "image_file". Prints and plots the preditions.
        
        Arguments:
        sess -- your tensorflow/Keras session containing the YOLO graph
        image_file -- name of an image stored in the "images" folder.
        
        Returns:
        out_scores -- tensor of shape (None, ), scores of the predicted boxes
        out_boxes -- tensor of shape (None, 4), coordinates of the predicted boxes
        out_classes -- tensor of shape (None, ), class index of the predicted boxes
        
        Note: "None" actually represents the number of predicted boxes, it varies between 0 and max_boxes. 
        """
    
        # Preprocess your image
        image, image_data = preprocess_image("images/" + image_file, model_image_size = (608, 608))
    
        # Run the session with the correct tensors and choose the correct placeholders in the feed_dict.
        # You'll need to use feed_dict={yolo_model.input: ... , K.learning_phase(): 0})
        ### START CODE HERE ### (≈ 1 line)
        out_scores, out_boxes, out_classes = sess.run([scores, boxes, classes],feed_dict={yolo_model.input:image_data , K.learning_phase(): 0})
        ### END CODE HERE ###
    
        # Print predictions info
        print('Found {} boxes for {}'.format(len(out_boxes), image_file))
        # Generate colors for drawing bounding boxes.
        colors = generate_colors(class_names)
        # Draw bounding boxes on the image file
        draw_boxes(image, out_scores, out_boxes, out_classes, class_names, colors)
        # Save the predicted bounding box on the image
        image.save(os.path.join("out", image_file), quality=90)
        # Display the results in the notebook
        output_image = scipy.misc.imread(os.path.join("out", image_file))
        imshow(output_image)
        
        return out_scores, out_boxes, out_classes
    

    Run the following cell on the "test.jpg" image to verify that your function is correct.  

    out_scores, out_boxes, out_classes = predict(sess, "test.jpg")
    

    【result】  

    Found 7 boxes for test.jpg
    car 0.60 (925, 285) (1045, 374)
    car 0.66 (706, 279) (786, 350)
    bus 0.67 (5, 266) (220, 407)
    car 0.70 (947, 324) (1280, 705)
    car 0.74 (159, 303) (346, 440)
    car 0.80 (761, 282) (942, 412)
    car 0.89 (367, 300) (745, 648)
    

    Expected Output:

    Found 7 boxes for test.jpg
    car 0.60 (925, 285) (1045, 374)
    car 0.66 (706, 279) (786, 350)
    bus 0.67 (5, 266) (220, 407)
    car 0.70 (947, 324) (1280, 705)
    car 0.74 (159, 303) (346, 440)
    car 0.80 (761, 282) (942, 412)
    car 0.89 (367, 300) (745, 648)

    The model you've just run is actually able to detect 80 different classes listed in "coco_classes.txt". To test the model on your own images:

    1. Click on "File" in the upper bar of this notebook, then click "Open" to go on your Coursera Hub.
    2. Add your image to this Jupyter Notebook's directory, in the "images" folder
    3. Write your image's name in the cell above code
    4. Run the code and see the output of the algorithm!

    If you were to run your session in a for loop over all your images. Here's what you would get:  

     【注释】原文是视频,此处是截图

     Predictions of the YOLO model on pictures taken from a camera while driving around the Silicon Valley 
                                         Thanks drive.ai for providing this dataset!

    What you should remember:

    • YOLO is a state-of-the-art object detection model that is fast and accurate
    • It runs an input image through a CNN which outputs a 19x19x5x85 dimensional volume.
    • The encoding can be seen as a grid where each of the 19x19 cells contains information about 5 boxes.
    • You filter through all the boxes using non-max suppression. Specifically:
      • Score thresholding on the probability of detecting a class to keep only accurate (high probability) boxes
      • Intersection over Union (IoU) thresholding to eliminate overlapping boxes
    • Because training a YOLO model from randomly initialized weights is non-trivial and requires a large dataset as well as lot of computation, we used previously trained model parameters in this exercise. If you wish, you can also try fine-tuning the YOLO model with your own dataset, though this would be a fairly non-trivial exercise.

    【中文翻译】

    应该记住:
    • YOLO 一种快速准确的 state-of-the-art对象检测模型
    • 它把一个图像输入 CNN, 输出一个19x19x5x85 维volume。
    • 编码可以被视为一个网格, 19x19 网格其中每个包含大约5个box的信息。
    • 您可以使用非最大值抑制来过滤所有的box。具体:
        分数阈值概率检测保持只有准确 (概率) 的box
        交并比阈值消除重叠的box
    • 因为从随机初始化的权重训练 YOLO 模型是不容易的, 并且需要大量的数据集以及大量的计算, 所以我们在本练习中使用了以前训练过的模型参数。如果您愿意, 还可以尝试用您自己的数据集微调 YOLO 模型, 尽管这将是一个相当不错的练习。

    References: The ideas presented in this notebook came primarily from the two YOLO papers. The implementation here also took significant inspiration and used many components from Allan Zelener's github repository. The pretrained weights used in this exercise came from the official YOLO website.

    Car detection dataset:

    The Drive.ai Sample Dataset (provided by drive.ai) is licensed under a Creative Commons Attribution 4.0 International License. We are especially grateful to Brody Huval, Chih Hu and Rahul Patel for collecting and providing this dataset.

    -----------------------------------------

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  • 原文地址:https://www.cnblogs.com/hezhiyao/p/8428511.html
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