IMAGE MOSAICING

INTRODUCTION

Many problems require finding the coordinate transformation between two images of the same scene or object. One of them is Image Mosaicing. It is important to have a precise description of the coordinate transformation between a pair of images. Image mosaics are collection of overlapping images together with coordinate transformations that relate the different image coordinate systems. By applying the appropriate transformations via a warping operation and merging the overlapping regions of a warped images, it is possible to construct a single image covering the entire visible area of the scene. This merged single image is the motivation for the term ``mosaic''. 

Image mosaics allow one to compensate for differences in viewing geometry. Thus they can be used to simplify version tasks by simulating the condition in which the scene is viewed from a fixed position with single camera. Mosaic are therefore quite useful in tasks involving motion or change detection or determining the relative pose of the new images that are acquired. They can be used to determine what parts of the scene visible from that point have been observed. There are lots of paper about motion parameter estimation about which can be used in image mosaicing.

A coordinate transformation maps the image coordinatesx=[x,y]T,  to new set of coordinatesx'=[x',y']T . 

The most common assumption especially in motion estimation for coding and optical flow, is that the coordinate transformation between frames is only translation. Although it is easy to implement, it is very poor to handle large changes due to camera rotation, panning and tilting. The other technique is Affine Model which contains translation, rotation and scale. However, the affine model can not capture camera pan and tilt and therefore cannot accurately express the seen that we see in the world. 8-parameter projective model gives the exact eight desired parameters to account for all the possible camera motions. 

However, its parameters have traditionally mathematically and computationally too hard to find. Going from first order to second order, gives the 12-parameter biquadratic model. Increasing the order and number of parameters doesn't help us too much, because the physical camera model fits exactly 8-parameter projective model. Therefore, biquadratic model is not suitable for our purposes. The 8-parameter bilinear model is the most widely-used in the field of image processing.