title: Image downsampling and upsampling using bilinear interpolation
body: <p>I am trying to understand how exactly the upsampling and downsampling of a 2D image I have, would happen using Bilinear interpolation. Now I am aware of how bilinear interpolation works using a 2x2 neighbourhood values to interpolate the data point inside this 2x2 area using weights. But what I am not aware of, is asked below. My objectives and specific queries are - </p>
  
  <p>1.To start with I have a 2D image of values(size MxN). The width(M) and height(N) of this image is not fixed, but will change from case to case. This 2D image needs to be down-sampled using bilinear interpolation to a grid of size PxQ (P and Q are to be configured as input parameters) e.g. lets take PxQ is 8x8. And assume input 2D array image is of size 200x100. i.e 200 columns, 100 rows.</p>
  
  <p>Now how while performing downsampling using bilinear interpolation of this 200x100 image, should I first obtain a downsampled image of size 100x50 (downsampling by 2 in both dimensions using bilinear interpolation); then a 50x25 image(again by doing downsampling by 2 in both dimensions), then a 25x12 image, then a 12x12(this time doing downsampling by linear(not bilinear!) interpolation only along the rows, and finally drop some pixels to get 8x8.
  Any pointers to exact algorithm or different ways to achieve this, are appreciated.</p>
  
  <p>2.Above question raises another one - how to downsample using bilinear interpolation by a non-integer scale factor, e.g. how to go from a say 8x8 image array to a 6x2 image wherein resampling/scaling factors in both dimensions are not integers.</p>
  
  <p>3.Then when I get a 8x8 sized image I need to upsample it by bilinear interpolation to the same original size I started with- MxN. If I need to go from 8x8 to say 20x20. How would it interpolate in between points in a row and would it interpolate a full row by some means. Again in case of non-integer scale factors how would bilinear interpolation for upsampling happen. Exact steps.</p>
  
  <p>And finally I need to implement this in C.</p>
  
  <p>I tried visualizing these particular questions by taking different examples, but not got a clear picture of how this bilinear interpolation would happen while downsampling and upsampling. All I have is plenty of paper sheets having'dots and crossed' pictures on my desk, but still no clear solution! </p>
  
  <p>Any detailed reading material, books appreciated. </p>