Time Warp Edit Distance with Stiffness Adjustment for Time Series Matching

In a way similar to the string-to-string correction problem we address time series similarity in the light of a time-series-to-time-series-correction problem for which the similarity between two time series is measured as the minimum cost sequence of "edit operations" needed to transform one time series into another. To define the "edit operations" we use the paradigm of a graphical editing process and end up with a dynamic programming algorithm that we call Time Warp Edit Distance (TWED). TWED is slightly different in form from Dynamic Time Warping, Longest Common Subsequence or Edit Distance with Real Penalty algorithms. In particular, it highlights a parameter which drives a kind of stiffness of the elastic measure along the time axis. We show that the similarity provided by TWED is a metric potentially useful in time series retrieval applications since it could benefit from the triangular inequality property to speed up the retrieval process while tuning the parameters of the elastic measure. In that context, a lower bound is derived to relate the matching of time series into down sampled representation spaces to the matching into the original space. Empiric quality of the TWED distance is evaluated on a simple classification task. Compared to Edit Distance, Dynamic Time Warping, Longest Common Subsequnce and Edit Distance with Real Penalty, TWED has proven to be quite effective on the considered experimental task

SIMIT : subjectively interesting motifs in time series

Numerical time series data are pervasive, originating from sources as diverse as wearable devices, medical equipment, to sensors in industrial plants. In many cases, time series contain interesting information in terms of subsequences that recur in approximate form, so-called motifs. Major open challenges in this area include how one can formalize the interestingness of such motifs and how the most interesting ones can be found. We introduce a novel approach that tackles these issues. We formalize the notion of such subsequence patterns in an intuitive manner and present an information-theoretic approach for quantifying their interestingness with respect to any prior expectation a user may have about the time series. The resulting interestingness measure is thus a subjective measure, enabling a user to find motifs that are truly interesting to them. Although finding the best motif appears computationally intractable, we develop relaxations and a branch-and-bound approach implemented in a constraint programming solver. As shown in experiments on synthetic data and two real-world datasets, this enables us to mine interesting patterns in small or mid-sized time series

Automatic Affine and Elastic Registration Strategies for Multi-dimensional Medical Images

Medical images have been used increasingly for diagnosis, treatment planning, monitoring disease processes, and other medical applications. A large variety of medical imaging modalities exists including CT, X-ray, MRI, Ultrasound, etc. Frequently a group of images need to be compared to one another and/or combined for research or cumulative purposes. In many medical studies, multiple images are acquired from subjects at different times or with different imaging modalities. Misalignment inevitably occurs, causing anatomical and/or functional feature shifts within the images. Computerized image registration (alignment) approaches can offer automatic and accurate image alignments without extensive user involvement and provide tools for visualizing combined images. This dissertation focuses on providing automatic image registration strategies. After a through review of existing image registration techniques, we identified two registration strategies that enhance the current field: (1) an automated rigid body and affine registration using voxel similarity measurements based on a sequential hybrid genetic algorithm, and (2) an automated deformable registration approach based upon a linear elastic finite element formulation. Both methods streamlined the registration process. They are completely automatic and require no user intervention. The proposed registration strategies were evaluated with numerous 2D and 3D MR images with a variety of tissue structures, orientations and dimensions. Multiple registration pathways were provided with guidelines for their applications. The sequential genetic algorithm mimics the pathway of an expert manually doing registration. Experiments demonstrated that the sequential genetic algorithm registration provides high alignment accuracy and is reliable for brain tissues. It avoids local minima/maxima traps of conventional optimization techniques, and does not require any preprocessing such as threshold, smoothing, segmentation, or definition of base points or edges. The elastic model was shown to be highly effective to accurately align areas of interest that are automatically extracted from the images, such as brains. Using a finite element method to get the displacement of each element node by applying a boundary mapping, this method provides an accurate image registration with excellent boundary alignment of each pair of slices and consequently align the entire volume automatically. This dissertation presented numerous volume alignments. Surface geometries were created directly from the aligned segmented images using the Multiple Material Marching Cubes algorithm. Using the proposed registration strategies, multiple subjects were aligned to a standard MRI reference, which is aligned to a segmented reference atlas. Consequently, multiple subjects are aligned to the segmented atlas and a full fMRI analysis is possible