IMAGE MATCHING WITH PHASE SHIFT METHODS 
John Stokes 
Institutionen för Fotogrammetri 
Kungliga Tekniska Högskolan 
5-100 44 Stockholm, Sweden 
ABSTRACT 
Determination of approximate parallaxes has been performed on both 
synthetic and real image pairs using Fourier transform methods. In a 
first model it was found that the results were very sensitive to 
wrap-around effects. This model includes the intuitive method to 
consider the images as sine waves plus noise and then match using the 
phase shift between the sine waves. In a second model designed to 
repress wrap-around effects, parts not common to both images strongly 
degrade the results. Also, the results were very sensitive to 
radiometric differences. Matching was also tested using the phase 
correlation function. Although the results were promising for 
synthetic image pairs without noise, the method was found to break 
down when tested on real image pairs. Finally, promising results were 
obtained for synthetic images using maximum entropy methods. However, 
it is not yet known if the method works for real image pairs. 
INTRODUCTION 
Digital processing of images has become a routine procedure within a 
number of rather different applications. Examples are photogrammetry, 
remote sensing, vision problems within the robot industry, etc. A 
common problem for many applications is then to relate different 
digital images to each other. Given the fact that two images overlap, 
the problem is to locate the images in a common system of coordinates 
in such a way that the information duplicated in the two images is 
located in the same place. One strategy is to identify the information 
contained in the images and then use this information to locate the 
images (object matching). Another strategy, to which the methods 
discussed in this paper belong, is to consider the information as 
unknown and locate the images using statistical properties of the grey 
levels (grey level matching). 
When two overlapping images are to be matched, a reasonable method is 
to maximize their correlation or minimize the energy of their 
difference. These two methods together with variants of them are in 
fact the most common used. However, they do have a severe 
disadvantage: For the matching procedure to be effective, the function 
to be minimized must contain information as to where the minimum is 
located. In regions where paths to the minimum exist along which this 
function is decreasing, there exist effective procedures for finding 
this minimum. However, when the images are noisy or lacking in large 
objects, such regions are very small. As a matter of fact, when these 
methods are used, initial values of high quality are usually 
required. Consequently, there is a definite need for automatic 
procedures generating initial values for matching problems. 
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