Summary of target tracking related knowledge

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feather map

stay cnn Every convolution layer of , All data exist in three-dimensional form . It can be seen as many two-dimensional pictures stacked together , Each of them is called a feature map.

1. In the input layer , If it is a grayscale picture , Then there is only one feature map; If it's a color picture , It is commonly 3 individual feature map（ Red, green and blue ）.

2. On other layers , There are several convolution kernels between layers （kernel）, Each on the upper floor feature map Convolute with each convolution kernel , Will produce a next layer feature map, Yes N Convolution kernels , The lower layer will produce N individual feather map.

Convolution kernel （filter）

Each convolution kernel has three dimensions of length, width and depth ; The depth of convolution kernel is the same as that of the current image （feather map Number of sheets ） identical . The number of convolution kernels and the number of convolution kernels required for the next layer feather map identical . stay CNN In a convolution layer of ： The length of convolution kernel 、 The width is artificially specified , Long X The width is also known as the size of the convolution kernel , The commonly used size is 3X3,5X5 etc. ; for example , In the original image layer （ Input layer ）, If the image is a grayscale image , Its feather map The number of 1, Then the depth of the convolution kernel is 1; If the image is grb Images , Its feather map The number of 3, Then the depth of the convolution kernel is 3.

Training data

• batchsize： Batch size . In deep learning , It is generally used SGD Training , That is to say, each training session takes batchsize Sample training ;
• iteration：1 individual iteration Equal to using batchsize One sample training ;
• epoch：1 individual epoch It is equal to training once with all the samples in the training set , Generally speaking epoch The value of is how many times the entire dataset is rotated .

for example 300 One sample training ,epoch=1,batchsize = 10 ,iteration=30.

BN（Batch Normalization） layer

BN Layer is batch-norm layer , It is generally used to accelerate the training speed and a method in deep learning , It is usually placed in the convolution layer （conv layer ） Or after the full connection layer , The data are normalized and the training fitting speed is accelerated .

Common location ：conv→bn→relu

If the network uses sigmod Activation function , When the error passes forward , after sigmod unit , Need to take sigmod Gradient of , and sigmod The maximum gradient of is 0.25, So the more forward it goes , The smaller the error , This is gradient dissipation , But what is a gradient explosion ？ Note the error when passing through the full connection or convolution layer , Also multiply by the weight w, If w They're all bigger , greater than sigmod The resulting reduction , In this way, the error will become larger and larger as we move forward , Produce a gradient explosion .

BN The calculation diagram of the layer is shown below ,x It's input data , To xhat The mean variance is normalized , Back xhat To y In fact, it is an ordinary linear transformation , Similar to full connection but no crossover . without BN layer ,x Enter the following network directly , During training x The transformation of the distribution will inevitably lead to the later network to adjust to the learning x The mean and variance of , Into BN layer ,xhat Is a normalized data , The cost is an additional linear layer in the network y, But the former brings more performance , So it accelerates .

AUC（Area Under Curve）

A good example , A negative example , The probability that the prediction is positive is more likely than the probability that the prediction is negative . So by definition ： We have two most intuitive calculations AUC Methods ：

1： draw ROC curve ,ROC The area under the curve is AUC Value

2： Suppose there are （m+n） Samples , Among them, positive samples m individual , Negative sample n individual , All in all mn A sample is right , Count , The probability value of positive sample predicted as positive sample is greater than that of negative sample predicted as positive sample, which is recorded as 1, Add up the count , Then divide by （mn） Namely AUC Value .

AUC As a numerical value, we can evaluate the classifier directly , The higher the value, the better .

Mean average accuracy MAP(Mean Average Precision)

We use loU And threshold to determine whether it is the target . Calculate the... Of each detection frame obtained from the model loU value , Use the calculated loU Value and setting loU Threshold comparison , The correct detection times of each class in each image can be calculated (A). For each image , We all have ground truth The data of , Therefore, the actual target of a given category in the image is also known (B) The number of . We also calculated the number of correct predictions (A)（True possitive）. So we can use this formula to calculate the accuracy of this kind of model (A/B)

That is, given the category of an image C Of Precision= The number of correctly predicted images is divided by the total number of targets in the category of images . Suppose you now have a given class , The validation set has 100 Images , And we know that every image has all of its classes ( be based on ground truth). So we can get 100 A precision value , Calculate this 100 Average of precision values , The result is the average precision of this class .

That is, a C Average precision of class = All images on the validation set are for the class C The sum of the precision values of / Some kind C The number of all images for this target . Now add to our entire collection 20 Classes , For each category , We all calculate first loU, Next, calculate the accuracy , Then calculate the average accuracy . All we have now 20 Different average precision values . Use these average precision values , We can easily judge the performance of any given category of models .

But the problem is using 20 Different average accuracies make it difficult to measure the whole model , So we can choose a single number to represent the performance of a model ( A metric to unify them ), We can take the average of the average precision values of all classes , namely MAP( Mean average accuracy ).

MAP= The average precision sum of all categories is divided by all categories . That is, the average of the average precision of all classes in the dataset .

EAO Expected average coverage

EAO The purpose of this paper is to hope that a good tracker can have good accuracy at the same time A And robustness R, If you use it directly A and R The weighted sum of two numbers is unfair , So we need to redefine .

Suppose there is A video with a frame length , So one with The coverage accuracy of the tracker in this video （Overlay accuracy）op For each frame op The average of ,op Namely bonding box And ground truth Cross and compare Φ Express , namely ：

So an ideal EAO Is to put from 1 To an expected maximum Find an average , Is the expected average coverage , Just like its name , Equivalent to the area under the curve in the figure below ：

shortcut connection

ResNet The structure uses a connection method , namely “ Detour ” It means .

Bottleneck（ The bottleneck layer ）

This means that the input and output dimensions differ greatly , Like a bottleneck , Narrow at the top and wide at the bottom, or wide at the top and narrow at the bottom .1x1 filters Can play a role in changing the output dimension （channels） The role of . You can see , On the right 1x1 filters Put dimension （channels） It's going up , The difference between input and output dimensions is large .

Feel the field ：

In convolutional neural networks CNN in , Determine the area size of the input layer corresponding to an element in the output result of a certain layer , It's called the receptive field receptive field. Using mathematical language is to feel the wild is CNN An element of the output result of a layer in corresponds to a mapping of the input layer .

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