Image Processing Reference
In-Depth Information
Fig. 9.2. The
top row
illustrates the reconstruction of a 1D function (as in Fig. 9.1) and its
up-sampling by the factor 2. The
bottom row
illustrates the data used that achieves this: the
original discrete signal and the sampled filter
volving the two discrete signals at the bottom and deleting every second. The
deleted samples do not need to be computed if efficiency is cared for in the im-
plementation.
Example 9.2. In this example, Fig. 9.2, we illustrate the up-sampling of a 1D signal
with the factor 2. The goal is to keep the same descriptive power in the resulting
samples,becausewewilldoublethenumberofthesamplescomparedtotheoriginal
sampling.
1. The top, left graph illustrates the same sampled discrete signal (green stems)
alongwiththeoriginal(greensolid)asshowninFig.9.1.However,thistimethe
dashed magenta curves show that the interpolation functions that are narrower
(magenta curve) are able to reproduce the original signal more faithfully. We
wish to sample the original at a smaller step size than the distance between the
given samples, and we should therefore not lose the existing richness of the
variations.
2. On the top, right of the same figure we show with magenta samples the desired
values, which represent the samples of the reconstructed signal using twice as
small discretization step as the one shown on top, left.
3. On the bottom we show how this up-sampling can be implemented by process-
ingonlydiscretesignalsamples.Ontheleftweshow aslightlydifferentversion
of the discrete signal to be up-sampled. The difference consists in that midway
betweentheoriginalsignalsamplepositionswehaveinsertedzeros.Ontheright
