The convergence of emerging challenges in biological research and developments in imaging and computing technologies suggests that image analysis will play an important role in providing a better understanding of biological phenomenon. The ability of imaging to localize molecular information is a key capability in the post-genomic era and will be critical in discovering the roles of genes and the relationships that connect them. The scale of the data in these emerging challenges is daunting; high throughput microscopy can generate hundreds of gigabytes to terabytes of high-resolution imagery even for studies limited in scope to a single gene or interaction. In addition to the scale of the data, the analysis of microscopic image content presents significant problems for the state-of-the-art in image analysis.

This dissertation addresses two significant problems in the analysis of large histological images: reconstruction and tissue segmentation. The proposed methods form a framework that is intended to provide researchers with tools to explore and quantitatively analyze large image datasets.

The works on reconstruction address several problems in the reconstruction of tissue from sequences of serial sections using image registration. A scalable algorithm for nonrigid registration is presented that features a novel method for the matching small nondescript anatomical features using geometric reasoning. Methods for the nonrigid registration of images with different stains are presented for two application scenarios. Correlation sharpness is proposed as a new measure for image similarity, and is used to map tumor suppressor gene expression to structure in mouse mammary tissues. An extended process of geometric reasoning based on the matching of cliques of anatomical features is presented and demonstrated for the nonrigid registration of immunohistochemical stain to hemotoxylin and eosin stain for human cancer images. Finally, a method for the incorporation of structural constraints into the reconstruction process is proposed and demonstrated on the reconstruction of ducts in mammary tissues.

The work on tissue segmentation focuses on the use of statistical geometrical methods to describe the spatial distributions of biologically meaningful elements such as nuclei in tissue. The two point correlation function is demonstrated to be an effective feature for the segmentation of tissues, and is shown to possess a peculiar low-dimensional distribution in feature space that permits unsupervised segmentation by robust methods. The relationship between two-point functions for proximal image regions is derived and used to accelerate computation, resulting in a 7-68x improvement over a naive FFT-based implementation.

In addition to the methods proposed for reconstruction and segmentation, a significant portion of this dissertation is devoted to applying high performance computing to enable the analysis of large datasets. In particular, multi-node parallelization as well as multi-core and general purpose computing on graphics processing are used to form a heterogeneous multiprocessor platform that is used to demonstrate the segmentation and reconstruction methods on images up to 62K × 23K in size.