more-fundamentals.slides.printing

# Function between samples very well studied area in

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function between samples Very well-studied area in mathematics Common forms of interpolation Nearest-neighbor (0th order) Linear: draw a line between two known values Quadratic: fit a quadratic function to three points Cubic: fit a cubic function to four points Harmonic: fit using periodic functions (useful if you know the data is periodic)

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Interpolation Interpolating two-dimensional data: Bilinear, bicubic, etc.: Interpolate in one dimension, then the other (order doesn’t matter) More sophisticated multidimensional techniques (“data dependent” simplices, radial basis functions, etc.) Interpolating three-dimensional data: Trilinear, tricubic, etc.
Nearest-Neighbor Interpolation Simplest to implement Round off x and y values Result is not continuous (blocky)

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Interpolate vertically Interpolate vertically Interpolate horizontally Bilinear Interpolation Linearly interpolate vertically Linearly interpolate horizontally
Higher-Order Interpolation Higher-degree polynomials e.g., bicubic (cubic interpolation vertically followed by cubic interpolation horizontally) Sometimes other interpolating functions Requires a larger neighborhood e.g., bicubic requires a 4x4 neighborhood

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“Playing on the Pixel Grid” Many of the things we’ll do involve using “neighboring” samples “Who is my neighbor?” Common approaches: 4-connected (N, S, E, W) 8-connected (add NE, SE, SW, NW) Distance? Euclidean (as the crow flies) 4-connected (“city block”, “Manhattan”) 8-connected (“chessboard”)
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• Winter '08
• Morse,B

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