Image Mosaics
Xiang Lan Zhuo, R.J. Berger 

Abstract

Image mosiacs are created by "stitching" different individual images into one cohesive larger image. We have implemented a system that allows warping of images through projective (prospective) mapping in order to align the individual images. The original purpose of this project is to create a mosiac of the mural in Hick's Mural Room. 





Registering Images

Our program asks the user to input two images, then the user is prompt for 4 pairs registration points between these two images. 

Projective Mapping

It is known that the relationship between two points in 3D space can be expressed as the following homogeneous matrix notation:




Assuming i=1, we can solve for parameters a through h to obtain the projective transform matrix. In order to solve for the eight parameters, we needed four pairs of correlation points between two images, which result in eight linear equations:



where (u, v) are pixels of the reference image and (x, y) are pixels of the warped image. We implemented the Gaussian-Jordan elimination to solve the system of linear equations in our gauss-jordan.c. Since projective mapping is not one-to-one, the inverse of the transform matrix is used instead to find the corresponding pixel value at the original location for each transformed pixel. 

Blending

After two images are composited into one, it if often marked by distinctive edges due to differences in light intensity. To blend the two images together, we used a weighted factor that correlates to the location of the curr pixel in respect to the edge of the two images. For pixel locations that are overlay by the two images, the image where the current pixel is further from its own edge gets a heavier weight while the image where the current pixel is closer to the its own edge gets a lighter weight. The added weight increases and decreases linearly with respect to distance from edges.
(Note: edge blending was implemented in the horizontal direction only assuming the algorithm is primarily used for making panoramas) 



Results

(Pictures were taken without tripod, just walking around)

Click here to see each step and correlation points we used


           
Original images



Without edge blending.




With edge blending.



Trotter Hall On a Rainy Day
We had a hard time picking correlation points for this one. You can see that the projective transform severely warped the edge of the image due to the projected plane (z) not being very planar to the cartesian planes. we would probably get better results through brute force histogram matching for this one, although it might take a while. Or use cylindrical mapping ...

     
Original images 







FUTURE WORKS
1. Intensity/Chromaticity based automated registration through Lavenberg-Marquardt algorithm.
2. Feature based automated registration. 

REFERENCES
"Projective Mappings For Image Warping" by Paul Heckbert, Sept 13, 1999.