Nearest Neighbor and Linear Interpolation

Figure 18 shows the result of this experiment when using the two most commonly found interpolants: nearest-neighbor and linear. Clearly, nearest-neighbor interpolation results in a lot of data shuffling; as a curiosity, we mention that perfect unshuffling is sometimes possible under special circumstances, such that reversing the order of operations restores the initial data without error [43]. No other interpolation methods proposed here is reversible. For example, linear interpolation results in strong attenuation of high frequencies, as can be inferred from the visual comparison of Fig. 17 with Fig. 18. This loss cannot be compensated. It corresponds to the prediction made in Fig. io, according to which linear interpolation, or ¿S1, performs poorly when compared to other cases.

FIGURE 18 Some visual results. (Left) Nearest-neighbor interpolation. (Right) Linear interpolation.
FIGURE 19 Some visual results. (Left) Keys. (Center) Cubic spline. (Right) Cubic o-Moms.
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