How do you interpolate between points in an image (2D), e.g. using splines? I can understand just fine how to use 1-dimensional interpolation on data points where one coordinate is a function of the other: y = f(x). However, when we have an image, we generally have points in the image that are not given uniquely by such a function, e.g. two points (x1,y1) and (x1,y2), so how do we describe this in order to interpolate between points in the image?
There are various methods on 2d interpolation (this one, and this one). But most of them considered at least 4 points rather than 2. The simplest 2d interpolation is 3 1d interpolation, in which you interpolate the points between (x1-d1, y1-d2) and (x1+d1, y1-d2) as (x2,y2), then you interpolate the points between (x1-d3, y1+d4) and (x1+d3, y1+d4) as (x3,y3). Finally (x1,y1) is obtained by 1d interpolation of (x2,y2) and (x3,y3).