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Backgrounds

I am working with a dataset, where compass-like images are labeled with their corresponding angles from horizontal line ($0$ degrees).

I am trying to make a CNN model to predict the correct label for each input observation. The following is my quick description of the data(train, with labels).

enter image description here

Note that labels have the coding scheme of describing the angle of the stick from the horizon as a real number between $0 \sim 179$ in degrees.

Since angles $\pm 180 n$ for $n=1,2,\cdots$ have exactly the same meanings, the range $0 \sim 179$ was taken in order to make one-to-one correspondence to the picture and angle. For example, the first observation above could have been labeled as $-90, 90, 270, \cdots$ but in order to evade redundancy the range $0 \sim 179$ was taken.

Try 1

I have made a vanilla CNN model using Keras, with the loss : mean_squared_error.

But I think this loss is very inappropriate, since it gives preference to angle $90$, whereas it gives disadvantages to angles $1$ or $179$. To support my argument, let me show you an example:

  • For angle $90$, the model's try of $88$ or $92$ are both "close tries".

  • For angle $179$, the model's try of $177$ are considered close, whereas $181$ is considered absurd. Therefore,

So I think this scheme should be evaded.

Try 2

I have defined the following sine loss

$$ l(y_{true},y_{pred}) = \sin\left((y_{true}-y_{pred}) \times \frac{\pi}{180}\right) $$

or in Python code using Keras, I have defined the following custom loss:

def sine_loss(y_true, y_pred):
    res = K.sin((y_true-y_pred)*np.pi/180.) 
    return(K.sum(res*res) )

I have trained the model using the above loss, and cross-validated using 180 angle samples. The result is as follows, where x axis is the ground-truth angle, and y axis is the predicted angle.

enter image description here

It was kind of frustrating to see that the range of predicted values, and I have tried to convert them into $0\sim 179$ space, using the above angle$\pm 180 n$ scheme, but there was a massive white noise.

What loss should I proceed in this situation?

kjetil b halvorsen
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moreblue
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    people typically parameterize the target as $\sin(\theta), \cos(\theta)$. – shimao Jul 12 '19 at 04:10
  • Hi @moreblue, I am currently to perform pretty much the same task but on experimental data (charge stability diagrams of quantum dots). My model works fine on binary image (0, 1) generated by hand, but struggles learning anything with experimental data (it returns a value that minimize the loss, but it's the same for all images). What network architecture did you use in your problem? Funnily enough I also calculated the angles like you did ;) – Chris Ze Third Jun 15 '23 at 12:32

2 Answers2

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This can probably be done in a hand crafted way. No reason to use CNNs. If you do then why don't you pass your second last fully connected layer in to decision tree.

Otherwise the problem you are facing is that linear functions are not bounded. So use sigmoid activation on fully connected layers till the last one. If you are facing issue around 180 degrees, i would oversample such cases in the train set so network learns this very strongly

Rahul Deora
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On a simple regression task with lines on binary image, the MSE is enough to obtain very accurate results:

enter image description here

But adding noises, by generating the patches with a normal distribution for the background, I found that the SmoothL1Loss was a much better choice. I used Pytorch for that but you might have the same for Keras. It's not as precised as binary images but it works fine for the moment, it's a matter of tweating hyper-parameters and network size.

enter image description here

The angles are sometimes not exact because of the anti alias used to generate the lines.

enter image description here

Chris Ze Third
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