Drexel University

We present a 3D matching framework based on a many-to-many matching algorithm that works with skeletal representations of 3D volumetric objects. We demonstrate the performance of this approach on a large database of 3D objects containing more than 1000 exemplars. The method is especially suited to matching objects with distinct part structure and is invariant to part articulation. Skeletal matching has an intuitive quality that helps in defining the search and visualizing the results. In particular, the matching algorithm produces a direct correspondence between two skeletons and their parts, which can be used for registration and juxtaposition. 1

Algorithms for multi-modal human movement and behaviour monitoring

This thesis describes investigations into improvements in the field of automated people tracking using multi-modal infrared (IR) and visible image information. The research question posed is; “To what extent can infrared image information be used to improve visible light based human tracking systems?” Automated passive tracking of human subjects is an active research area which has been approached in many ways. Typical approaches include the segmentation of the foreground, the location of humans, model initialisation and subject tracking. Sensor reliability evaluation and fusion methods are also key research areas in multi-modal systems. Shifting illumination and shadows can cause issues with visible images when attempting to extract foreground regions. Images from thermal IR cameras, which use long-wavelength infrared (LWIR) sensors, demonstrate high invariance to illumination. It is shown that thermal IR images often provide superior foreground masks using pixel level statistical extraction techniques in many scenarios. Experiments are performed to determine if cues are present at the data level that may indicate the quality of the sensor as an input. Modality specific measures are proposed as possible indicators of sensor quality (determined by foreground extraction capability). A sensor and application specific method for scene evaluation is proposed, whereby sensor quality is measured at the pixel level. A neuro-fuzzy inference system is trained using the scene quality measures to assess a series of scenes and make a modality decision

Sublinear algorithms for Earth Mover's Distance

Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2009.Includes bibliographical references (p. 14-15).We study the problem of estimating the Earth Mover's Distance (EMD) between probability distributions when given access only to samples. We give closeness testers and additive-error estimators over domains in [0, [delta]]d, with sample complexities independent of domain size - permitting the testability even of continuous distributions over infinite domains. Instead, our algorithms depend on other parameters, such as the diameter of the domain space, which may be significantly smaller. We also prove lower bounds showing our testers to be optimal in their dependence on these parameters. Additionally, we consider whether natural classes of distributions exist for which there are algorithms with better dependence on the dimension, and show that for highly clusterable data, this is indeed the case. Lastly, we consider a variant of the EMD, defined over tree metrics instead of the usual L₁ metric, and give optimal algorithms.by Khanh Do Ba.S.M

Summary of Work for Joint Research Interchanges with DARWIN Integrated Product Team 1998

The intent of Stanford University's SciVis group is to develop technologies that enabled comparative analysis and visualization techniques for simulated and experimental flow fields. These techniques would then be made available under the Joint Research Interchange for potential injection into the DARWIN Workspace Environment (DWE). In the past, we have focused on techniques that exploited feature based comparisons such as shock and vortex extractions. Our current research effort focuses on finding a quantitative comparison of general vector fields based on topological features. Since the method relies on topological information, grid matching and vector alignment is not needed in the comparison. This is often a problem with many data comparison techniques. In addition, since only topology based information is stored and compared for each field, there is a significant compression of information that enables large databases to be quickly searched. This report will briefly (1) describe current technologies in the area of comparison techniques, (2) will describe the theory of our new method and finally (3) summarize a few of the results

Summary of Work for Joint Research Interchanges with DARWIN Integrated Product Team

The intent of Stanford University's SciVis group is to develop technologies that enabled comparative analysis and visualization techniques for simulated and experimental flow fields. These techniques would then be made available un- der the Joint Research Interchange for potential injection into the DARWIN Workspace Environment (DWE). In the past, we have focused on techniques that exploited feature based comparisons such as shock and vortex extractions. Our current research effort focuses on finding a quantitative comparison of general vector fields based on topological features. Since the method relies on topological information, grid matching an@ vector alignment is not needed in the comparison. This is often a problem with many data comparison techniques. In addition, since only topology based information is stored and compared for each field, there is a significant compression of information that enables large databases to be quickly searched. This report will briefly (1) describe current technologies in the area of comparison techniques, (2) will describe the theory of our new method and finally (3) summarize a few of the results

APPROXIMATION ALGORITHMS FOR POINT PATTERN MATCHING AND SEARCHI NG

Point pattern matching is a fundamental problem in computational geometry. For given a reference set and pattern set, the problem is to find a geometric transformation applied to the pattern set that minimizes some given distance measure with respect to the reference set. This problem has been heavily researched under various distance measures and error models. Point set similarity searching is variation of this problem in which a large database of point sets is given, and the task is to preprocess this database into a data structure so that, given a query point set, it is possible to rapidly find the nearest point set among elements of the database. Here, the term nearest is understood in above sense of pattern matching, where the elements of the database may be transformed to match the given query set. The approach presented here is to compute a low distortion embedding of the pattern matching problem into an (ideally) low dimensional metric space and then apply any standard algorithm for nearest neighbor searching over this metric space. This main focus of this dissertation is on two problems in the area of point pattern matching and searching algorithms: (i) improving the accuracy of alignment-based point pattern matching and (ii) computing low-distortion embeddings of point sets into vector spaces. For the first problem, new methods are presented for matching point sets based on alignments of small subsets of points. It is shown that these methods lead to better approximation bounds for alignment-based planar point pattern matching algorithms under the Hausdorff distance. Furthermore, it is shown that these approximation bounds are nearly the best achievable by alignment-based methods. For the second problem, results are presented for two different distance measures. First, point pattern similarity search under translation for point sets in multidimensional integer space is considered, where the distance function is the symmetric difference. A randomized embedding into real space under the L1 metric is given. The algorithm achieves an expected distortion of O(log2 n). Second, an algorithm is given for embedding Rd under the Earth Mover's Distance (EMD) into multidimensional integer space under the symmetric difference distance. This embedding achieves a distortion of O(log D), where D is the diameter of the point set. Combining this with the above result implies that point pattern similarity search with translation under the EMD can be embedded in to real space in the L1 metric with an expected distortion of O(log2 n log D)

Piecewise Affine Registration of Biological Images for Volume Reconstruction

This manuscript tackles the reconstruction of 3D volumes via mono-modal registration of series of 2D biological images (histological sections, autoradiographs, cryosections, etc.). The process of acquiring these images typically induces composite transformations that we model as a number of rigid or affine local transformations embedded in an elastic one. We propose a registration approach closely derived from this model. Given a pair of input images, we first compute a dense similarity field between them with a block matching algorithm. We use as a similarity measure an extension of the classical correlation coefficient that improves the consistency of the field. A hierarchical clustering algorithm then automatically partitions the field into a number of classes from which we extract independent pairs of sub-images. Our clustering algorithm relies on the Earth mover’s distribution metric and is additionally guided by robust least-square estimation of the transformations associated with each cluster. Finally, the pairs of sub-images are, independently, affinely registered and a hybrid affine/non-linear interpolation scheme is used to compose the output registered image. We investigate the behavior of our approach on several batches of histological data and discuss its sensitivity to parameters and noise

New procedures for visualizing data and diagnosing regression models

Thesis (Ph. D.)--Massachusetts Institute of Technology, Sloan School of Management, Operations Research Center, 2010.Cataloged from PDF version of thesis.Includes bibliographical references (p. 97-103).This thesis presents new methods for exploring data using visualization techniques. The first part of the thesis develops a procedure for visualizing the sampling variability of a plot. The motivation behind this development is that reporting a single plot of a sample of data without a description of its sampling variability can be uninformative and misleading in the same way that reporting a sample mean without a confidence interval can be. Next, the thesis develops a method for simplifying large scatter plot matrices, using similar techniques as the above procedure. The second part of the thesis introduces a new diagnostic method for regression called backward selection search. Backward selection search identifies a relevant feature set and a set of influential observations with good accuracy, given the difficulty of the problem, and additionally provides a description, in the form of a set of plots, of how the regression inferences would be affected with other model choices, which are close to optimal. This description is useful, because an observation, that one analyst identifies as an outlier, could be identified as the most important observation in the data set by another analyst. The key idea behind backward selection search has implications for methodology improvements beyond the realm of visualization. This is described following the presentation of backward selection search. Real and simulated examples, provided throughout the thesis, demonstrate that the methods developed in the first part of the thesis will improve the effectiveness and validity of data visualization, while the methods developed in the second half of the thesis will improve analysts' abilities to select robust models.by Rajiv Menjoge.Ph.D