1	Announcements Project 1 artifact voting Project 2 out today (help session at end of class)
2	Mosaics Today’s Readings Szeliski and Shum paper (sections 1 and 2, skim the rest) http://www.acm.org/pubs/citations/proceedings/graph/258734/p251-szeliski/
3	Image Mosaics + + … + =
4	How to do it? Basic Procedure Take a sequence of images from the same position Rotate the camera about its optical center Compute transformation between second image and first Lucas & Kanade registration Shift the second image to overlap with the first Blend the two together to create a mosaic If there are more images, repeat
5	Aligning images How to account for warping? Translations are not enough to align the images Photoshop demo
6	Image reprojection The mosaic has a natural interpretation in 3D The images are reprojected onto a common plane The mosaic is formed on this plane
7	Image reprojection Basic question How to relate two images from the same camera center? how to map a pixel from PP1 to PP2
8	Image reprojection Observation Rather than thinking of this as a 3D reprojection, think of it as a 2D image warp from one image to another
9	Homographies Perspective projection of a plane Lots of names for this: homography, texture-map, colineation, planar projective map Modeled as a 2D warp using homogeneous coordinates
10	Image warping with homographies
11	Panoramas What if you want a 360° field of view?
12	Cylindrical projection Map 3D point (X,Y,Z) onto cylinder
13	Cylindrical reprojection How to map from a cylinder to a planar image?
14	Cylindrical reprojection Map image to cylindrical coordinates need to know the focal length
15	Cylindrical panoramas Steps Reproject each image onto a cylinder Blend Output the resulting mosaic
16	Cylindrical image stitching What if you don’t know the camera rotation? Solve for the camera rotations Note that a rotation of the camera is a translation of the cylinder! Use Lukas-Kanade to solve for translations of cylindrically-warped images
17	Full-view Panorama
18	Different projections are possible
19	Project 2 (out today) Take pictures on a tripod (or handheld) Warp to cylindrical coordinates Automatically compute pair-wise alignments Correct for drift Blend the images together Crop the result and import into a viewer
20	Image Blending
21	Feathering
22	Effect of window size
23	Effect of window size
24	Good window size
25	Pyramid blending
26	Image warping Given a coordinate transform (x’,y’) = h(x,y) and a source image f(x,y), how do we compute a transformed image g(x’,y’) = f(h(x,y))?
27	Forward warping Send each pixel f(x,y) to its corresponding location (x’,y’) = h(x,y) in the second image
28	Forward warping Send each pixel f(x,y) to its corresponding location (x’,y’) = h(x,y) in the second image
29	Inverse warping Get each pixel g(x’,y’) from its corresponding location (x,y) = h^-1(x’,y’) in the first image
30	Inverse warping Get each pixel g(x’,y’) from its corresponding location (x,y) = h^-1(x’,y’) in the first image
31	Forward vs. inverse warping Q: which is better? A: usually inverse—eliminates holes however, it requires an invertible warp function—not always possible...
32	Other types of mosaics Can mosaic onto any surface if you know the geometry See NASA’s Visible Earth project for some stunning earth mosaics http://earthobservatory.nasa.gov/Newsroom/BlueMarble/
33	Summary Things to take home from this lecture Image alignment Image reprojection homographies cylindrical projection Radial distortion Creating cylindrical panoramas Image blending Image warping forward warping inverse warping bilinear interpolation