第四周第三课-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

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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.

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 $(p_c, b_x, b_y, b_h, b_w, c)$ 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.

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.

Doing this results in this picture:

**Figure 5** : Each of the 19x19 grid cells colored according to which class has the largest predicted probability in that cell.

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.

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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 $(19 \times 19, 5, 1)$ containing $p_c$ (confidence probability that there’s some object) for each of the 5 boxes predicted in each of the 19x19 cells.
• boxes: tensor of shape $(19 \times 19, 5, 4)$ containing $(b_x, b_y, b_h, b_w)$ for each of the 5 boxes per cell.
• box_class_probs: tensor of shape $(19 \times 19, 5, 80)$ containing the detection probabilities $(c_1, c_2, … c_{80})$ for 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(...).

# 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
    ### 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)
    box_class_scores = K.max(box_scores,axis=-1)
    ### END CODE HERE ###
   # print(box_class_scores)
    # 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)
    ### END CODE HERE ###
   # print(filtering_mask)
    # Step 4: Apply the mask to scores, boxes and classes
    ### START CODE HERE ### (≈ 3 lines)
    scores = tf.boolean_mask(box_class_scores,filtering_mask)
    boxes = tf.boolean_mask(boxes,filtering_mask)
    classes = tf.boolean_mask(box_classes,filtering_mask)
    ### END CODE HERE ###
    
    return scores, boxes, classes

---

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.

**Figure 8** : Definition of "Intersection over Union".

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.

# 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 = box1[0] > box2[0] and box1[0] or box2[0]
    yi1 = box1[1] > box2[1] and box1[1] or box2[1]
    xi2 = box1[2] < box2[2] and box1[2] or box2[2]
    yi2 = box1[3] < box2[3] and box1[3] or 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

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.

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):

• tf.image.non_max_suppression()
• K.gather()

# 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=boxes,scores=scores,max_output_size=max_boxes,iou_threshold=iou_threshold)
    ### END CODE HERE ###
    
    # Use K.gather() to select only nms_indices from scores, boxes and classes
    ### 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

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.

# 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=box_confidence,boxes=boxes,box_class_probs=box_class_probs,threshold=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=scores,boxes=boxes,classes=classes,max_boxes=max_boxes,iou_threshold=iou_threshold)
    
    ### END CODE HERE ###
    
    return scores, boxes, classes

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 $(p_c, b_x, b_y, b_h, b_w)$ 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.