Paper details

Hi authors, Congratulations on the acceptance! I am trying to reproduce the paper. I have the following questions regarding the details of the paper in order to implement it.

1. What exactly are the parameters of a stroke? I thought it should be 3 control points (6 params) + RGB (3 params) + width (1 param) but in the paper you mentioned you used 12 params in total. In Figure 12, you said that d is used, but isn’t it redundant given p2?
2. Do you use tanh or sigmoid to control the locations and colors of strokes into [0,1]?
3. In Algorithm 1, is the formula of M_strokes right? Since the values of the 2-norm are positive, the mask then should be in [.5,1] (or [0, .5] if the temperature is negative), which is not in the full range [0,1] as it should.
4. In Algorithm 1, is A=softmax(- t.D_strokes, axis=3), the negative logit instead of positive as in the paper?
5. What is the learning rate did you use? Did you use any lr scheduler?

THanks in advance!

[justanhduc]

Hey @justanhduc, thanks for your interest in our work.

1. Two more parameters are brushstroke center coordinates. 3 control points are given relative to the brushstrokes center. The direction (or orientation) vector `d` is used to control the orientation of strokes, see Sec. B and C. This vector is indeed redundant but it's convenient to use it for explanation purposes.

2. At each optimization step we clip the location to be in the range [0; 1]. No need to clip the color values - but it rather depends on particular implementation. We did not see any benefit applying activation functions.

3. There was a typo in the paper. The correcti expression is  M_{strokes} = max(sigm(t * ( w_{strokes} - D_{strokes} ) , axis=4) .

4. Yes, minus sign is missing there. Actually, you can use not `t` but a different large constant.

5. We use no learning rate scheduler. Default learning rate for adam is 0.1 but you may have to change it depending on how you prefer your images stylized.

Hi @dimakot55! Thanks a lot for your reply. Many things have been cleared up. I still have some questions regarding your answer.

1. In Algorithm 1, D_{strokes} has shape hxwxn and w_{strokes} has shape 1x1xn, then there can’t be max across axis 4 can it? Or I guess it should be D (shape hxwxnxs) rather than D_{strokes} if there is a max across axis 4.
2. What are the temperature values did you use for sigmoid and softmax?

[TZYSJTU]

Hey @justanhduc, thanks for your interest in our work.

1. Two more parameters are brushstroke center coordinates. 3 control points are given relative to the brushstrokes center. The direction (or orientation) vector `d` is used to control the orientation of strokes, see Sec. B and C. This vector is indeed redundant but it's convenient to use it for explanation purposes.

2. At each optimization step we clip the location to be in the range [0; 1]. No need to clip the color values - but it rather depends on particular implementation. We did not see any benefit applying activation functions.

3. There was a typo in the paper. The correcti expression is  M_{strokes} = max(sigm(t * ( w_{strokes} - D_{strokes} ) , axis=4) .

4. Yes, minus sign is missing there. Actually, you can use not `t` but a different large constant.

5. We use no learning rate scheduler. Default learning rate for adam is 0.1 but you may have to change it depending on how you prefer your images stylized.

Hi @dimakot55! Thanks a lot for your reply. Many things have been cleared up. I still have some questions regarding your answer.

1. In Algorithm 1, D_{strokes} has shape hxwxn and w_{strokes} has shape 1x1xn, then there can’t be max across axis 4 can it? Or I guess it should be D (shape hxwxnxs) rather than D_{strokes} if there is a max across axis 4.
2. What are the temperature values did you use for sigmoid and softmax? Is Q3 solved?