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Bilateral Upsample theory

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I have implemented bilateral upsample but I'm skeptical of it, because I couldn't understand it's concept especially where they describe the sampling part in the papers
For each pixel I get four samples of normal and four samples of depth from 1/2 buffer, and one sample of normal and depth from 1/1 texture, also four samples of color from 1/2 buffer to multiply by weights and calculate the final color.
My sampling kernel (for sampling 1/2 buffer) looks like this :

static const float2 kernel[4] = {
float2(-0.5f, -0.5f), // 0
float2(0.5, -0.5f), // 1
float2(-0.5f, 0.5f), // 2
float2(0.5f, 0.5f), // 3

But in mixed resolution rendering paper, it described it a little bit different and used billinear weights and seems like he does four samples for 1/1 buffer which I couldn't understand.
could someone make this more clear for me please ?


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