CORNELL CS 664 - Lecture #13: EM algorithm, slanted surfaces, mutual information

Unformatted text preview:

CS664 Lecture #13: EM algorithm, slanted surfaces, mutual informationAnnouncementsRecapAnother SIGGRAPH exampleAnother PVT demoMore MR examplesStrongest evidence to date2-fold accelerationBack to vision!A simple problem – Line fitting“Chicken-egg problem”Chicken-egg problemExpectation-Maximization (EM)Example:Example:Example:Example:Example:Multiway Cut for Stereo and Motion with Slanted SurfacesMotivationSolutionAlgorithmStereo resultsBeyond simple stereoCS664 Lecture #13: EM algorithm, slanted surfaces, mutual informationSome material taken from:Ranjith Unnikrishnan & Marc Zinck, CMUhttp://www.cs.cmu.edu/~ranjith/Stan Birchfield, Clemsonhttp://www.ces.clemson.edu/~stb/research/stereo_multiwaycut/Steve Seitz, University of Washingtonhttp://www.cs.washington.edu/homes/seitz/Aseem Agarwala, University of Washingtonhttp://www.cs.washington.edu/homes/aseem2Announcements PS 1 due tonight– Probably not graded for a while Next quiz in one week (Thursday 10/13) Who in 664 is working on the CU-UAV (submarine) project?3Recap Many cool applications of pixel labeling problems– In graphics • Such as graph cut textures, photomontage, etc.– In medical imaging• Faster MR reconstruction– In vision• Stereo (regular, multicamera, sloped surfaces)4Another SIGGRAPH exampleInput OutputPanoramic video textures(Agarwala et al., SIGGRAPH05)Another PVT demo7More MR examples8Strongest evidence to dateUnaccelerated image Accelerated X3,SENSE reconstructionAccelerated X3,Graph cuts reconstructionUnacceleratedAccelerated X3, SENSE reconstructionAccelerated X3,Graph cuts reconstructionUnaccelerated132-fold accelerationGraph cutsUnaccelerated14Back to vision! How can we handle situations in stereo like slanted surfaces?– Extremely large number of possible planes– We can’t make each one a label What about curved surfaces?– Even harder to handle! There’s an easy way to use graph cuts Rely on a powerful technique for vision:– Expectation-Maximization (EM) method15A simple problem – Line fitting Goal: To group a bunch of points into two “best-fit” line segments16“Chicken-egg problem” If we knew which line each point belonged to, we could compute the best-fit lines.17Chicken-egg problem If we knew what the two best-fit lines were, we could find out which line each point belonged to.18Expectation-Maximization (EM) Initialize: Make random guess for lines Repeat:– Find the line closest to each point and group into two sets. (Expectation Step)– Find the best-fit lines to the two sets (Maximization Step)– Iterate until convergenceThe algorithm is guaranteed to converge to some local optima19Example:20Example:21Example:22Example:23Example:Converged!24Multiway Cut for Stereo and Motion with Slanted SurfacesStan Birchfield and Carlo TomasiICCV 199925Motivation Why does it look so bad?an image from a stereo pair disparity map from graph cuts26Solution Think of this as a segmentation– Fit plane to each region to give more accurate results– Once you have these planes, reassign pixels to get better fitan image from a stereo pair disparity map from graph cuts27Algorithm1. Initialize a set of pixel labels– Run graph cuts with integer disparities2. Fit a plane to each region (connected component)– They solve for an affine transformation that best aligns region in left image to corresponding region in right image3. Assign labels (planes) to pixels– Use graph cuts, of course!4. Repeat Steps 2 & 3 until convergence This style of algorithm should look familiar...2829Stereo results30Beyond simple stereo Graph cuts work incredibly well for stereo– Original successful example We write the energy function as What assumptions are we making?– Frontoparallel lambertian


View Full Document
Download Lecture #13: EM algorithm, slanted surfaces, mutual information
Our administrator received your request to download this document. We will send you the file to your email shortly.
Loading Unlocking...
Login

Join to view Lecture #13: EM algorithm, slanted surfaces, mutual information and access 3M+ class-specific study document.

or
We will never post anything without your permission.
Don't have an account?
Sign Up

Join to view Lecture #13: EM algorithm, slanted surfaces, mutual information 2 2 and access 3M+ class-specific study document.

or

By creating an account you agree to our Privacy Policy and Terms Of Use

Already a member?