In this thesis, we present three novel algorithms. The first algorithm is a method of identifying numerical landmarks (a definition coined in this thesis). The second algorithm uses the projection of image regions onto x- and y- axes and the matching of the resulting 1D projections to determine an overall 2D translation for use in registration. The third algorithm aligns SEM images of successive layers of a semiconductor device by first extracting the positions of vias in the lower layer, and then searching for the best translation for subsets of vias such that they all or mostly connect to metalization in the upper layer. / To acquire high-resolution Scanning Electron Microscopy (SEM) images over wide areas, we must acquire several images ``tiling'' the surface and assemble them into a single composite image, using a process called image stitching. While for some applications, stitching is now routine, SEM mosaics of semiconductors pose several challenges: (1) by design, the image features (wire, via and dielectric) are highly repetitive, (2) the overlap between image tiles is small, (3) sample charging causes intensity variation between captures of the same region, and (4) machine instability causes non-linear deformation within tiles and between tiles. In this study, we compare the accuracy and computational cost of three well-known pixel-based techniques: Fast Fourier Transform (FFT), Sum of Squared Differences (SSD), and Normalized Cross Correlation (NCC). We compare well-known 2D algorithms, as well as novel projection-onto-1D versions. The latter reduces the computational complexity from O(n^2) to O(n), where n is the number of pixels, without loss of accuracy, and in some cases, with greater accuracy. Another approach to reducing the computational complexity of image alignment is to compare isolated landmarks, rather than pixels. In semiconductor images, there are no natural fiducials and adding them would destroy the information required to reconstruct their circuits, so we introduce a new class of landmarks which we call numerical landmarks. Related to Harris corners, the novel numerical landmarks are insensitive to brightness variations and noise. Finally, we consider the alignment problem between layers of image mosaics. Unlike in the ``horizontal'' directions, the vertical dimension is only sparsely sampled. Consequently, image features and landmarks cannot be used for alignment. Instead, we must rely on the relationship between vias (through-plane metalization) and wires (in-plane metalization), and we have developed a novel algorithm for matching vias in the lower layer with wires above, and use this to align subimages. / Thesis / Doctor of Philosophy (PhD) / Applications in materials science often require the acquisition of images of semiconductor computer chips at very high resolution. Using cameras with even tens of millions of pixels might not give us enough resolution over a wide field of view. One approach is to acquire several images of parts of the sample at high magnification and assemble them into a single composite image. This way, we can preserve the high resolution over a wide area. Algorithms developed for assembling the composite image are known as tiling or mosaicing. This whole process is known as image stitching (and includes image registration). In this thesis, we develop specialized algorithms suited for the 2D stitching of semiconductor images, including the generalization to 3D. This case is challenging because slight alignment errors may completely change the reconstructed circuit, and the images contain both repeated patterns (such as many parallel wires) and changes in brightness and distortions caused by the scanning device.