Estou tentando entender a função de perda do Yolo v2:
Se alguém puder detalhar a função.
neural-networks
loss-functions
object-detection
yolo
Kamel BOUYACOUB
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Respostas:
Explanation of the different terms :
Note that I used two indexesi and j for each bbox predictions, this is not the case in the article because there is always a factor 1objij or 1noobjij so there is no ambigous interpretation : the j chosen is the one corresponding to the highest confidence score in that cell.
More general explanation of each term of the sum :
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B*(5+C)
? Atleast that's the case for YOLO v3.Doesn't the YOLOv2 Loss function looks scary? It's not actually! It is one of the boldest, smartest loss function around.
Let's first look at what the network actually predicts.
If we recap, YOLOv2 predicts detections on a 13x13 feature map, so in total, we have 169 maps/cells.
We have 5 anchor boxes. For each anchor box we need Objectness-Confidence Score (whether any object was found?), 4 Coordinates (tx,ty,tw, and th ) for the anchor box, and 20 top classes. This can crudely be seen as 20 coordinates, 5 confidence scores, and 100 class probabilities for all 5 anchor box predictions put together.
We have few things to worry about:
All losses are mean-squared errors, except classification loss, which uses cross-entropy function.
Now, let's break the code in the image.
We need to compute losses for each Anchor Box (5 in total)
We need to do this for each of the 13x13 cells where S = 12 (since we start index from 0)
var1 | var2 | (var1 - var2)^2 | (sqrtvar1 - sqrtvar2)^2
0.0300 | 0.020 | 9.99e-05 | 0.001
0.0330 | 0.022 | 0.00012 | 0.0011
0.0693 | 0.046 | 0.000533 | 0.00233
0.2148 | 0.143 | 0.00512 | 0.00723
0.3030 | 0.202 | 0.01 | 0.01
0.8808 | 0.587 | 0.0862 | 0.0296
4.4920 | 2.994 | 2.2421 | 0.1512
Not that scary, right!
Read HERE for further details.
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Your loss function is for YOLO v1 and not YOLO v2. I was also confused with the difference in the two loss functions and seems like many people are: https://groups.google.com/forum/#!topic/darknet/TJ4dN9R4iJk
YOLOv2 paper explains the difference in architecture from YOLOv1 as follows:
This means that the confidence probabilitypi(c) above should depend not only on i and c but also an anchor box index, say j . Therefore, the loss needs to be different from above. Unfortunately, YOLOv2 paper does not explicitly state its loss function.
I try to make a guess on the loss function of YOLOv2 and discuss it here: https://fairyonice.github.io/Part_4_Object_Detection_with_Yolo_using_VOC_2012_data_loss.html
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Here is my Study Note
Loss function: sum-squared error
a. Reason: Easy to optimize b. Problem: (1) Does not perfectly align with our goal of maximize average precision. (2) In every image, many grid cells do not contain any object. This pushes the confidence scores of those cells towards 0, often overpowering the gradient from cells that do contain an object. c. Solution: increase loss from bounding box coordinate predictions and decrease the loss from confidence predictions from boxes that don't contain objects. We use two parametersλcoord=5 and λnoobj = 0.5
d. Sum-squared error also equally weights errors in large boxes and small boxes
Only one bounding box should be responsible for each obejct. We assign one predictor to be responsible for predicting an object based on which prediction has the highest current IOU with the ground truth.
a. Loss from bound box coordinate (x, y) Note that the loss comes from one bounding box from one grid cell. Even if obj not in grid cell as ground truth.
b. Loss from width w and height h. Note that the loss comes from one bounding box from one grid cell, even if the object is not in the grid cell as ground truth.
c. Loss from the confidence in each bound box. Not that the loss comes from one bounding box from one grid cel, even if the object is not in the grid cell as ground truth.
Loss function only penalizes classification if obj is present in the grid cell. It also penalize bounding box coordinate if that box is responsible for the ground box (highest IOU)
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The loss formula you wrote is of the original YOLO paper loss, not the v2, or v3 loss.
There are some major differences between versions. I suggest reading the papers, or checking the code implementations. Papers: v2, v3.
Some major differences I noticed:
Class probability is calculated per bounding box (hence output is now S∗S∗B*(5+C) instead of SS(B*5 + C))
Bounding box coordinates now have a different representation
In v3 they use 3 boxes across 3 different "scales"
You can try getting into the nitty-gritty details of the loss, either by looking at the python/keras implementation v2, v3 (look for the function yolo_loss) or directly at the c implementation v3 (look for delta_yolo_box, and delta_yolo_class).
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