Image Pyramids and BlendingImage PyramidsPowerPoint PresentationSlide 4Gaussian pyramidImage sub-samplingSlide 7SamplingGaussian pre-filteringSubsampling with Gaussian pre-filteringCompare with...What does blurring take away?Slide 13High-Pass filterSlide 15Slide 16Image BlendingFeatheringAffect of Window SizeSlide 20Good Window SizeWhat is the Optimal Window?Pyramid BlendingSlide 24Slide 25Laplacian Pyramid: BlendingBlending RegionsHorror PhotoSimplification: Two-band Blending2-band BlendingLinear BlendingSlide 32Gradient DomainGradient Domain blending (1D)Gradient Domain Blending (2D)Comparisons: Levin et al, 2004Perez et al., 2003Perez et al, 2003Don’t blend, CUT!Davis, 1998Efros & Freeman, 2001Minimal error boundaryKwatra et al, 2003Lazy Snapping (Li el al., 2004)Image Pyramids and BlendingSlides Modified from Alexei Efros, CMU, © Kenneth KwanImage PyramidsKnown as a Gaussian Pyramid [Burt and Adelson, 1983]•In computer graphics, a mip map [Williams, 1983]•A precursor to wavelet transformA bar in the big images is a hair on the zebra’s nose; in smaller images, a stripe; in the smallest, the animal’s noseFigure from David ForsythGaussian Pyramid for encoding1) Prediction using weighted local Gaussian average2) Encode the difference as the Laplacian3) Both Laplacian and the Averaged image is easy to encode[Burt & Adelson, 1983]Gaussian pyramidImage sub-samplingThrow away every other row and column to create a 1/2 size image- called image sub-sampling1/41/8Image sub-sampling1/4 (2x zoom) 1/8 (4x zoom)Why does this look so bad?1/2SamplingGood sampling:•Sample often or,•Sample wiselyBad sampling:•see aliasing in action!Gaussian pre-filteringG 1/4G 1/8Gaussian 1/2Solution: filter the image, then subsample•Filter size should double for each ½ size reduction. Why?Subsampling with Gaussian pre-filteringG 1/4 G 1/8Gaussian 1/2Solution: filter the image, then subsample•Filter size should double for each ½ size reduction. Why?•How can we speed this up?Compare with...1/4 (2x zoom) 1/8 (4x zoom)1/2What does blurring take away?originalWhat does blurring take away?smoothed (5x5 Gaussian)High-Pass filtersmoothed – originalGaussian pyramid is smooth=> can be subsampled Laplacian pyramid has narrow band of frequency=> compressedImage BlendingFeathering0101+=Encoding transparencyI(x,y) = (R, G, B, ) Iblend = Ileft + IrightAffect of Window Size01leftright01Affect of Window Size0101Good Window Size01“Optimal” Window: smooth but not ghostedWhat is the Optimal Window?To avoid seams•window >= size of largest prominent featureTo avoid ghosting•window <= 2*size of smallest prominent featurePyramid Blending010101Left pyramid Right pyramidblendPyramid Blendinglaplacianlevel4laplacianlevel2laplacianlevel0left pyramid right pyramid blended pyramidLaplacian Pyramid: BlendingGeneral Approach:1. Build Laplacian pyramids LA and LB from images A and B2. Build a Gaussian pyramid GR from selected region R3. Form a combined pyramid LS from LA and LB using nodes of GR as weights:•LS(i,j) = GR(I,j,)*LA(I,j) + (1-GR(I,j))*LB(I,j)4. Collapse the LS pyramid to get the final blended imageBlending RegionsHorror Photo© prof. dmartinSimplification: Two-band BlendingBrown & Lowe, 2003•Only use two bands: high freq. and low freq.•Blends low freq. smoothly•Blend high freq. with no smoothing: use binary maskLow frequency ( > 2 pixels)High frequency ( < 2 pixels)2-band BlendingLinear Blending2-band BlendingGradient DomainIn Pyramid Blending, we decomposed our image into 2nd derivatives (Laplacian) and a low-res imageLet us now look at 1st derivatives (gradients):•No need for low-res image –captures everything (up to a constant)•Idea: –Differentiate–Blend–ReintegrateGradient Domain blending (1D)TwosignalsRegularblendingBlendingderivativesbrightdarkGradient Domain Blending (2D)Trickier in 2D:•Take partial derivatives dx and dy (the gradient field)•Fidle around with them (smooth, blend, feather, etc)•Reintegrate–But now integral(dx) might not equal integral(dy)•Find the most agreeable solution–Equivalent to solving Poisson equation–Can use FFT, deconvolution, multigrid solvers, etc.Comparisons: Levin et al, 2004Perez et al., 2003Perez et al, 2003Limitations:•Can’t do contrast reversal (gray on black -> gray on white)•Colored backgrounds “bleed through”•Images need to be very well alignededitingDon’t blend, CUT!So far we only tried to blend between two images. What about finding an optimal seam?Moving objects become ghostsDavis, 1998Segment the mosaic•Single source image per segment•Avoid artifacts along boundries–Dijkstra’s algorithmInput textureB1 B2Random placement of blocks blockB1B2Neighboring blocksconstrained by overlapB1 B2Minimal errorboundary cutEfros & Freeman, 2001min. error boundaryMinimal error boundaryoverlapping blocks vertical boundary__==22overlap errorKwatra et al, 2003Actually, for this example, DP will work just as well…Lazy Snapping (Li el al., 2004)Interactive segmentation using