Optimization problem: missing m_hat parameters

[GustavoMourao]

Hi, how is it going?
@VSainteuf @loicland

In equation (6), which is apply to extract the centerness map, I would like to ask what is the estimated parameters $\hat{I}{p}$ and $\hat{J}{p}$.

I'm asking since I have implemented this optimization problem and I didn't got those parameters:

def loss(params):
    i_measured, j_measured, sigma_h, sigma_w = params
    term_i = np.power((i_measured), 2) / np.power((2*sigma_h), 2)
    term_j = np.power((j_measured), 2) / np.power((2*sigma_w), 2)

    return np.exp(-(term_i + term_j))

Thank you so much!

[VSainteuf]

Hi @GustavoMourao !
So Eq. 6 shows how to obtain the centerness ground truth, and in this formula $\hat{i}{p}$ and $\hat{j}{p}$ denote the ground truth position of a given parcel $p$. Hence, a parcel in a given patch will result in a Gaussian kernel centred on $ (\hat{i}{p} , \hat{j}{p}) $ in the centerness ground truth.
Does that answer your question ?

[GustavoMourao]

I've got it!

However, have you used the original CenterMask implementation in order to get the heatmap, and the centerness ground truth, as well?

Besides of that, I haven't fully understood how you obtained the Zones? Was that extracted from centerness ground truth?

Thank you very much!

[VSainteuf]

Great!
We didn't use the CenterMask implementation we computed the centerness ground truth as described in Eq.6.
I think that in CenterMask the kernels are homoscedastic whereas we use heteroscedastic kernels that depend on the parcel's two dimensions.

For the Zones see this issue : #6

[GustavoMourao]

I see.

However, how have you calculated the ground truth heatmap, used as target that feed the loss function? In this case, the target heatmap used into Class PaPsLoss?

[VSainteuf]

that's what I mean (centerness ground truth = ground truth heatmap), so Eq. 6

[GustavoMourao]

Haven't you implemented Equation 6 in Class PaPs? If so, those results above represents the target heatmap and the calculated value from forwar method (class PaPs).

If not, have you implemented Eq.6?

Cheers

[VSainteuf]

The left figure is the result of our implementation of Eq. 6.
But the implementation is not contained in PaPs, the ground truth heatmap was computed once and for all and stored in the annotations of the dataset.

[GustavoMourao]

Great, I see.

So, could you share the methodology used to obtain the ground truth heatmap? It seems that isn't just the argmax of each parcel..

Thanks a lot!

[VSainteuf]

Well the ground truth heatmap is obtained with Eq. 6 ! ^^

[VSainteuf]

Maybe you are thinking of the mapping pixel->parcel (the "zones" tensor) ?

[GustavoMourao]

I see.

But look, do you use the Eq. 6 as parameter of your loss function, right (PaPsLoss)? And, considering this, do you use the same estimation (Eq.6) during the inference?

[VSainteuf]

This is the target signal for PaPsLoss, and specifically for the centerness regression head.
It is used as target signal during training.
You don't need this at inference time.

[GustavoMourao]

I've got.

I think that I misunderstanding the optimization loss func. ;)

Thank you for the support

[alexanderDuenas]

Hi Dears!

Is it possible to upload or share the code implementation for the eq 6 for generating the ground-truth heatmaps?

[VSainteuf]

Hi @alexanderDuenas ,
I pushed the implementation for the generation of the ground truth heatmaps, where you will also see how the zones tensor is obtained.
I pushed it in the dataset repository.