3 of 3 deleted 576 characters in body

# Bilinear interpolation implemented by convolution

I read the paper Deep Feature Flow for Video Recognition https://arxiv.org/abs/1611.07715.

In Sec.3, the author implements bilinear interpolation like this:

$$f_i^c(p)=\sum\limits_{q}G(q,p+\delta p)f_k^c(q) \tag{1}$$

Where $$q$$ is the point from the source image, and $$p$$ is the points on the target image. $$\delta p$$ is the distance the point moved each point $$p$$ (not $$\delta \bullet p$$). $$G$$ is defined as

$$G(q,p+\delta p)=g(q_x,p_x+\delta p_x)g(q_y,p_y+\delta p_y)\tag{2}$$

And the bilinear interpolation is defined in wiki as:

$$f(x,y)\approx {\frac {y_{2}-y}{y_{2}-y_{1}}}f(x,y_{1})+{\frac {y-y_{1}}{y_{2}-y_{1}}}f(x,y_{2})\tag{3}$$

I think the operation $$(1)$$ and $$(3)$$ is equivalent. How can I derive the filter $$(1)$$ from $$(3)$$?