Image registration is an essential step in many image processing applications that need visual information from multiple images for comparison, integration or analysis. Recently researchers have introduced image processing techniques using the log-polar transform (LPT) for its rotation and scale invariant properties. However, limitations still exist when LPT is applied to image registration applications. The major thesis of this dissertation is to provide in depth analysis of LPT, its advantages, and problems. We introduce new formulations that are derived
to overcome the limitations of LPT and thus extend its horizon in practice. A novel techniques are proposed to address the limitations.
The first extension to be introduced is to extend the use of LPT to 2D object recognition application. Motivated by the observation
that LPT is sensitive to translation, which leads to high computation in the search process, we integrate the combination of feature extraction and feature point screening method to the recognition system. With the scale and rotation invariant properties of LPT and the low computation feature extraction and screening approach that further reduces the number of feature point, a 2D object recognition is presented.
The second limitations of LPT that is addressed in this dissertation is the nonuniform sampling and its effects. LPT suffers from nonuniform sampling which makes it not suitable for applications in which the registered images are altered or occluded. Inspired by this fact, we presents a new registration algorithm that addresses the problems of the conventional LPT while maintaining the robustness to scale and rotation. We introduce a novel Adaptive Polar Transform (APT) technique that evenly and effectively samples the image in the Cartesian coordinates. Combining APT with an innovative projection transform along with a matching mechanism, the proposed method yields less computational load and more accurate registration than that of the conventional LPT. Translation between the registered images is recovered with the new search scheme using Gabor feature extraction to accelerate the localization procedure. Moreover an image comparison scheme is proposed for locating the area where the image pairs differ. Experiments on real images demonstrate the effectiveness and robustness of the proposed approach for registering images that are subjected to occlusion and alteration in addition to scale, rotation and translation.
Lastly, this dissertation observes the accuracy of the LPT approach that is limited by the number of samples used in the mapping process. Since obtaining scale and rotation parameters involves 2D correlation method either in the spatial domain or in the frequency domain, the computational complexity of the matching procedure grows exponentially as the number of samples increases. Motivated by this limitation, we propose a novel pre-shifted logarithmic spiral (PSLS) approach that is robust to translation, scale, and rotation and requires lower computational cost. By pre-shifting the sampling point in the angular direction by π/nθ radian, the total number of samples in angular direction can be reduced by half. This yields great reduction in computational load in the matching process. Experimental results demonstrate the effectiveness and robustness of the proposed approach.