Transcription of Upsampling and Interpolation
1 CSC320: Introduction to Visual ComputingMichael GuerzhoyMany slides from Steve Marschner, Alexei Efros, Noah SnavelyUpsampling and InterpolationNearest-neighbor interpolationhq3x Interpolation (ZSNES) time: Non-Maximum SuppressionAt q, we have a maximum if the value is larger than those at both p and at r. Interpolate to get these : D. ForsythInterpolation See blackboardBilinear Interpolation : SummaryBilinear Interpolation Not actually linear If you fix xit s linear in y. If you fix y, it s linear in This image is too small for this screen: How can we make it 10 times as big? Simplest approach:repeat each rowand column 10 times ( Nearest neighborinterpolation )Image interpolationRecall how a digital image is formed It is a discrete point-sampling of a continuous function If we could somehow reconstruct the original function, any new image could be generated, at any resolution and scale 12345 Adapted from: S.
2 Seitzd = 1 in this exampleImage interpolation12345d = 1 in this exampleRecall how a digital image is formed It is a discrete point-sampling of a continuous function If we could somehow reconstruct the original function, any new image could be generated, at any resolution and scale Adapted from: S. SeitzImage Convert to a continuous function: Reconstruct by convolution with a reconstruction filter,h What if we don t know ? Guess an approximation: Can be done in a principled way: filteringd = 1 in this : this is linear Interpolation !Adapted from: S. SeitzImage Interpolation Ideal reconstructionNearest-neighbor interpolationLinear interpolationGaussian reconstructionSource: B. CurlessReconstruction filters What does the 2D version of this hat function look like?Better filters give better resampled images Bicubicis common choiceperforms linear Interpolation (tent function) performs bilinear interpolationCubic reconstruction filterUpsampling The empty pixels are initially set to 0 Convolve with a (Gaussian, or another) filter If the filter sums to 1, multiply the result by 4 of the new image was initially 0 Image interpolationNearest-neighbor interpolationBilinear interpolationBicubic interpolationOriginal image: x 10 Image interpolationAlso used for resampling
