Marc LevoyComputer Science DepartmentStanford UniversityCS 178, Spring 2011Panoramas! Marc LevoyWhat is a panorama?!a wider-angle image than a normal camera can capture!any image stitched from overlapping photographs!an extreme aspect ratio on a normal shot2! Marc LevoyOutline!capturing panoramas!stitching together a panorama!perspective versus cylindrical projection3! Marc LevoyPanoramic cameras4swing-lens panoramic cameraflatback panoramic camera! Marc LevoySwing-lens panoramic images5San Francisco in ruins, 1906101 Ranch, Oklahoma, circa 1920! Marc LevoyPanoramic cameras6swing-lens panoramic cameraflatback panoramic cameraSLR on panning clampmotorized pan-tilt headto avoid parallax errors,rotate around center of perspective! Marc LevoyParallax errors7Photoshop aligned on the background, so only foreground objects exhibit severe parallax errorsLee Frost, Val D’Orcia, Tuscany, ItalyFuji GX 617Lee Frost, Volubilis, MoroccoLee Frost,Vertical Panoramas,SantoriniMatthew Scott, Cuernos del Paine, Chilegigapan.org, Scanning Electron Micrograph (SEM) of barnaclegigapan.org, Scanning Electron Micrograph (SEM) of barnacle! Marc LevoyStitching images together to make a mosaic14! Marc LevoyWhat kind of transformation do we need?15translation?rotation?rotation?perspective!! Marc LevoyQuick review of perspective projection!these three image formation methods will produce the same perspective view on the p.p. (except for the size of the view)•all that matters is position of c.p. and orientation of p.p.16==pinhole cameraphotographic cameraAlbrecht Dürer’s drawing glassp.p.p.p.p.p.= center of perspective (c.p.)= projection of feature in scene onto picture plane (p.p)! Marc LevoyReprojecting an image ontoa different picture plane!the view on any picture plane can be projected onto any other plane in 3D without changing its appearance as seen from a common center of projection17the sidewalk art of Julian Beever! Marc LevoyReprojecting panoramic imagesto a common picture plane!the common picture plane of the mosaic replaces having had a wide-angle (non-fish-eye) camera in the first place18common p.p.of the mosaic! Marc LevoyHomography!perspective mapping between two p.p.’s using the same center of projection is called a homography•input and output x,y positions are related by a 3!3 matrix19p.p. #2p.p. #1! Marc LevoyStitching images together to make a mosaic!step 1: find corresponding features in a pair of image!step 2: compute perspective from 2nd to 1st image!step 3: warp 2nd image so it overlays 1st image!step 4: blend images where they overlap one another!repeat for 3rd image and mosaic of first two, etc.20! Marc Levoy!step 1: find corresponding features in a pair of image!step 2: compute perspective from 2nd to 1st image!step 3: warp 2nd image so it overlays 1st image!step 4: blend images where they overlap one another!repeat for 3rd image and mosaic of first two, etc.Stitching images together to make a mosaic21Take CS 148:Introduction to Computer Graphics (Aut)Take CS 223B:Computer Vision (Win)Also CS 448A:Computational Photography (Win)! Marc LevoyExample: the Matterhorn22perspective projectioncommon picture plane of mosaicimage! Marc LevoyUsing 4 shots instead of 323perspective projection! Marc LevoyCylindrical panoramas!even works for 360° panorama!project each image onto a cylinder!a cylindrical image can be stored as a rectangular image24mosaic imagexy! Marc LevoyCylindrical panoramas!even works for 360° panorama!project each image onto a cylinder!a cylindrical image can be stored as a rectangular image!to view without distortion, reproject part of the cylinder onto a picture plane representing the display screen•if your FOV is narrow, this view won’t be too distorted25mosaic imagexy(Flash demo)http://graphics.stanford.edu/courses/cs178/applets/projection.html! Marc Levoycylindrical projectionBack to the Matterhorn26surface of cylinder! Marc LevoyblendedBack to the Matterhorn27surface of cylinder! Marc LevoyExample28perspective reprojection onto a planeAs mentioned in class, Photoshop does not perform the perspective reprojection shown here. Instead, it leaves you with the raw cylindrical image shown in the previous slide. On this image, straight lines are not straight, and the edges of the original photographs appear as curves. This is not a correct linear perspective. However, some panorama viewing software does perform this perspective reprojection, e.g. Microsoft’s HDView (Google for it).! Marc LevoyExample29cropped to avoid distortionAs I mentioned in class, the sequence of (1) projecting one or more images to a cylindrical surface, and (2) reprojecting that cylindrical image back to a planar surface, produces an image with no distortion, i.e. it is a correct linear perspective. However, it might be rather wide-angle, as shown in the previous slide. Unless you view this image with your face close to the display, which would be the correct viewpoint for such a wide-angle perspective, it will seem distorted. We covered this issue in the first lecture of the course. To reduce the requirement that you must place yourself so close to the display, you should crop the reprojected panorama, as is done in this slide. The resulting image is not so wide-angle, and can be viewed from a normal viewing distance without seeming distorted.! Marc LevoySpherical panoramas!projections are to a sphere instead of a cylinder!can’t store as rectangular image without distortion30++++! Marc LevoyRecap!panoramas can be captured by a camera with a wide planar back, a cylindrical back and a moving slit, or a rotating camera•rotate around the center of perspective to avoid parallax errors!to assemble panoramas from a rotating camera, use corresponding features to compute a perspective warp that projects the images to a common picture plane, then blend them together!for very wide angle or 360° panoramas, project the images to a common cylindrical surface, which can be stored as an ordinary (wide) rectangular image•reproject them to a picture plane for display!spherical panoramas are possible, but cannot be stored as rectangular images without distortion31Questions?! Marc LevoySlide credits!Fredo Durand!Alyosha Efros!Steve Seitz!Rick Szeliski!Frost, Lee, Panoramic Photography, F+W Publications,