Bilinear Interpolation on A Subsection Of An Image
Bilinear interpolation can be viewed as traditional sample rate conversion (insert 0s between existing samples, convolve with a triangular kernel in each dimension). Somewhat unusually, the size of the (continous-time) triangular filter kernel is not scaled relative to resampling ratio before it is sampled; each sample is always the result of 4 neighbouring input sample (unless it falls exactly on one of them). This makes it quirky seen with dsp goggles but maps very efficiently to compute hw.

When doing convolution you need overlap between separate chunks, or you will get some kind of discontinuity. For bilinear interpolation the overlap need only be one sample wide.