Harmonic Analysis Inspired Data Fusion for Applications in Remote Sensing

This thesis will address the fusion of multiple data sources arising in remote sensing, such as hyperspectral and LIDAR. Fusing of multiple data sources provides better data representation and classification results than any of the independent data sources would alone. We begin our investigation with the well-studied Laplacian Eigenmap (LE) algorithm. This algorithm offers a rich template to which fusion concepts can be added. For each phase of the LE algorithm (graph, operator, and feature space) we develop and test different data fusion techniques. We also investigate how partially labeled data and approximate LE preimages can used to achieve data fusion. Lastly, we study several numerical acceleration techniques that can be used to augment the developed algorithms, namely the Nystrom extension, Random Projections, and Approximate Neighborhood constructions. The Nystrom extension is studied in detail and the application of Frame Theory and Sigma-Delta Quantization is proposed to enrich the Nystrom extension

Rotationally Invariant Image Representation for Viewing Direction Classification in Cryo-EM

We introduce a new rotationally invariant viewing angle classification method for identifying, among a large number of Cryo-EM projection images, similar views without prior knowledge of the molecule. Our rotationally invariant features are based on the bispectrum. Each image is denoised and compressed using steerable principal component analysis (PCA) such that rotating an image is equivalent to phase shifting the expansion coefficients. Thus we are able to extend the theory of bispectrum of 1D periodic signals to 2D images. The randomized PCA algorithm is then used to efficiently reduce the dimensionality of the bispectrum coefficients, enabling fast computation of the similarity between any pair of images. The nearest neighbors provide an initial classification of similar viewing angles. In this way, rotational alignment is only performed for images with their nearest neighbors. The initial nearest neighbor classification and alignment are further improved by a new classification method called vector diffusion maps. Our pipeline for viewing angle classification and alignment is experimentally shown to be faster and more accurate than reference-free alignment with rotationally invariant K-means clustering, MSA/MRA 2D classification, and their modern approximations

Multi-atlas segmentation using clustering, local non-linear manifold embeddings and target-specific templates

Multi-atlas segmentation (MAS) has become an established technique for the automated delineation of anatomical structures. The often manually annotated labels from each of multiple pre-segmented images (atlases) are typically transferred to a target through the spatial mapping of corresponding structures of interest. The mapping can be estimated by pairwise registration between each atlas and the target or by creating an intermediate population template for spatial normalisation of atlases and targets. The former is done at runtime which is computationally expensive but provides high accuracy. In the latter approach the template can be constructed from the atlases offline requiring only one registration to the target at runtime. Although this is computationally more efficient, the composition of deformation fields can lead to decreased accuracy. Our goal was to develop a MAS method which was both efficient and accurate. In our approach we create a target-specific template (TST) which has a high similarity to the target and serves as intermediate step to increase registration accuracy. The TST is constructed from the atlas images that are most similar to the target. These images are determined in low-dimensional manifold spaces on the basis of deformation fields in local regions of interest. We also introduce a clustering approach to divide atlas labels into meaningful sub-regions of interest and increase local specificity for TST construction and label fusion. Our approach was tested on a variety of MR brain datasets and applied to an in-house dataset. We achieve state-of-the-art accuracy while being computationally much more efficient than competing methods. This efficiency opens the door to the use of larger sets of atlases which could lead to further improvement in segmentation accuracy