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0215Manifolds

Image Manifolds Images as Vectors Importance of Alignment Text Synthesis [Shannon,’48] proposed a way to generate English-looking text using N-grams: Assume a generalized Markov model Use a large text to compute prob. distributions of each letter given N-1 previous letters Starting from a seed repeatedly sample this Markov chain to generate new letters Also works for whole words Mark V. Shaney (Bell Labs) Results (using alt.singles corpus): “As Ive commented before, really relating to someone involves standing next to impossible.” “One morning I shot an elephant in my arms and kissed him.” “I spent an interesting evening recently with a grain of salt” Video Textures Arno Sch?dl Richard Szeliski David Salesin Irfan Essa Microsoft Research, Georgia Tech Video textures Our approach How do we find good transitions? Finding good transitions Compute L2 distance Di, j between all frames Markov chain representation Transition costs Transition from i to j if successor of i is similar to j Cost function: Ci?j = Di+1, j Transition probabilities Probability for transition Pi?j inversely related to cost: Pi?j ~ exp ( – Ci?j / s2 ) Preserving dynamics Preserving dynamics Preserving dynamics Cost for transition i?j Ci?j = wk Di+k+1, j+k Preserving dynamics – effect Cost for transition i?j Ci?j = wk Di+k+1, j+k Video sprite extraction Video sprite control Augmented transition cost: Interactive fish If we knew all pairwise distances… MDS result in 2D Actual plot of cities Isomap for images Build a data graph G. Vertices: images (u,v) is an edge iff SSD(u,v) is small For any two images, we approximate the distance between them with the “shortest path” on G Leakage problem Hi, video textures is a work that I started last year at Microsoft Research with Richard and David and continued at Georgia Tech with Richard, David and Irfan, my advisor. In this paper, we want to analyze regular video clips and turn them into video

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