# What is the "bilinear interpolation kernel" in personlab paper?

What is this bilinear interpolation kernel in the paper PersonLab: Person Pose Estimation and Instance Segmentation with a Bottom-Up, Part-Based, Geometric Embedding Model page 6 equation (1)?

Here it is: $$h_k(x) = \frac{1}{\pi R^2}\sum_{i=1:N}p_k(x_i)B(x_i+S_k(x_i)-x)$$ where:

• $$x$$, $$x_i$$ are image coordinates (2-D vectors).
• $$h_k \colon \mathbb{R}^2 \mapsto \mathbb{R}$$ localized heatmaps obtained by a sort of Hough voting.
• $$S_k \colon \mathbb{R}^2 \mapsto \mathbb{R}$$ offest vectors
• $$p_k \colon \mathbb{R}^2 \mapsto \mathbb{R}^2$$ heatmaps
• $$B(.)$$ denotes the bilinear interpolation kernel.

This is a form of Hough voting: each point i in the image crop grid casts a vote with its estimate for the position of every keypoint, with the vote being weighted by the probability that it is in the disk of influence of the corresponding keypoint

I guess bilinear interpolation kernel is a class of function and not an actual one (I may be wrong).

But if it is bilinear why does it only take one argument in the equation?

Maybe this is bilinear 1D interpolation, interpolating between the coordinates of 2-D vector?

Otherwise this formula doesn't make sense.

• i.postimg.cc/kXn8GJxS/Bilinear-interpolation-kernel.png Mar 10, 2020 at 17:58
• Can I have a little more details? This does not help me understanding the formula in the paper, nor why the bilinear interpolation kernel only have one parameter in the formula despite being called bilinear. Mar 11, 2020 at 10:34
• researchgate.net/publication/… Mar 11, 2020 at 20:26