Achieving Real-Time Mode Estimation through Offline Compilation

As exploration of our solar system and outerspace move into the future, spacecraft are being developed to venture on increasingly challenging missions with bold objectives. The spacecraft tasked with completing these missions are becoming progressively more complex. This increases the potential for mission failure due to hardware malfunctions and unexpected spacecraft behavior. A solution to this problem lies in the development of an advanced fault management system. Fault management enables spacecraft to respond to failures and take repair actions so that it may continue its mission. The two main approaches developed for spacecraft fault management have been rule-based and model-based systems. Rules map sensor information to system behaviors, thus achieving fast response times, and making the actions of the fault management system explicit. These rules are developed by having a human reason through the interactions between spacecraft components. This process is limited by the number of interactions a human can reason about correctly. In the model-based approach, the human provides component models, and the fault management system reasons automatically about system wide interactions and complex fault combinations. This approach improves correctness, and makes explicit the underlying system models, whereas these are implicit in the rule-based approach. We propose a fault detection engine, Compiled Mode Estimation (CME) that unifies the strengths of the rule-based and model-based approaches. CME uses a compiled model to determine spacecraft behavior more accurately. Reasoning related to fault detection is compiled in an off-line process into a set of concurrent, localized diagnostic rules. These are then combined on-line along with sensor information to reconstruct the diagnosis of the system. These rules enable a human to inspect the diagnostic consequences of CME. Additionally, CME is capable of reasoning through component interactions automatically and still provide fast and correct responses. The implementation of this engine has been tested against the NEAR spacecraft advanced rule-based system, resulting in detection of failures beyond that of the rules. This evolution in fault detection will enable future missions to explore the furthest reaches of the solar system without the burden of human intervention to repair failed components.

Optical Flow From 1D Correlation: Application to a Simple Time-To-Crash Detector

In the first part of this paper we show that a new technique exploiting 1D correlation of 2D or even 1D patches between successive frames may be sufficient to compute a satisfactory estimation of the optical flow field. The algorithm is well-suited to VLSI implementations. The sparse measurements provided by the technique can be used to compute qualitative properties of the flow for a number of different visual tsks. In particular, the second part of the paper shows how to combine our 1D correlation technique with a scheme for detecting expansion or rotation ([5]) in a simple algorithm which also suggests interesting biological implications. The algorithm provides a rough estimate of time-to-crash. It was tested on real image sequences. We show its performance and compare the results to previous approaches.

Fast Pose Estimation with Parameter Sensitive Hashing

Example-based methods are effective for parameter estimation problems when the underlying system is simple or the dimensionality of the input is low. For complex and high-dimensional problems such as pose estimation, the number of required examples and the computational complexity rapidly becme prohibitively high. We introduce a new algorithm that learns a set of hashing functions that efficiently index examples relevant to a particular estimation task. Our algorithm extends a recently developed method for locality-sensitive hashing, which finds approximate neighbors in time sublinear in the number of examples. This method depends critically on the choice of hash functions; we show how to find the set of hash functions that are optimally relevant to a particular estimation problem. Experiments demonstrate that the resulting algorithm, which we call Parameter-Sensitive Hashing, can rapidly and accurately estimate the articulated pose of human figures from a large database of example images.

Virtual Visual Hulls: Example-Based 3D Shape Estimation from a Single Silhouette

Recovering a volumetric model of a person, car, or other object of interest from a single snapshot would be useful for many computer graphics applications. 3D model estimation in general is hard, and currently requires active sensors, multiple views, or integration over time. For a known object class, however, 3D shape can be successfully inferred from a single snapshot. We present a method for generating a ``virtual visual hull''-- an estimate of the 3D shape of an object from a known class, given a single silhouette observed from an unknown viewpoint. For a given class, a large database of multi-view silhouette examples from calibrated, though possibly varied, camera rigs are collected. To infer a novel single view input silhouette's virtual visual hull, we search for 3D shapes in the database which are most consistent with the observed contour. The input is matched to component single views of the multi-view training examples. A set of viewpoint-aligned virtual views are generated from the visual hulls corresponding to these examples. The 3D shape estimate for the input is then found by interpolating between the contours of these aligned views. When the underlying shape is ambiguous given a single view silhouette, we produce multiple visual hull hypotheses; if a sequence of input images is available, a dynamic programming approach is applied to find the maximum likelihood path through the feasible hypotheses over time. We show results of our algorithm on real and synthetic images of people.

A Radial Basis Function Approach to Financial Time Series Analysis

Nonlinear multivariate statistical techniques on fast computers offer the potential to capture more of the dynamics of the high dimensional, noisy systems underlying financial markets than traditional models, while making fewer restrictive assumptions. This thesis presents a collection of practical techniques to address important estimation and confidence issues for Radial Basis Function networks arising from such a data driven approach, including efficient methods for parameter estimation and pruning, a pointwise prediction error estimator, and a methodology for controlling the "data mining'' problem. Novel applications in the finance area are described, including customized, adaptive option pricing and stock price prediction.

Parameter Estimation in Chaotic Systems

This report examines how to estimate the parameters of a chaotic system given noisy observations of the state behavior of the system. Investigating parameter estimation for chaotic systems is interesting because of possible applications for high-precision measurement and for use in other signal processing, communication, and control applications involving chaotic systems. In this report, we examine theoretical issues regarding parameter estimation in chaotic systems and develop an efficient algorithm to perform parameter estimation. We discover two properties that are helpful for performing parameter estimation on non-structurally stable systems. First, it turns out that most data in a time series of state observations contribute very little information about the underlying parameters of a system, while a few sections of data may be extraordinarily sensitive to parameter changes. Second, for one-parameter families of systems, we demonstrate that there is often a preferred direction in parameter space governing how easily trajectories of one system can "shadow'" trajectories of nearby systems. This asymmetry of shadowing behavior in parameter space is proved for certain families of maps of the interval. Numerical evidence indicates that similar results may be true for a wide variety of other systems. Using the two properties cited above, we devise an algorithm for performing parameter estimation. Standard parameter estimation techniques such as the extended Kalman filter perform poorly on chaotic systems because of divergence problems. The proposed algorithm achieves accuracies several orders of magnitude better than the Kalman filter and has good convergence properties for large data sets.

Learning-Based Approach to Real Time Tracking and Analysis of Faces

This paper describes a trainable system capable of tracking faces and facialsfeatures like eyes and nostrils and estimating basic mouth features such as sdegrees of openness and smile in real time. In developing this system, we have addressed the twin issues of image representation and algorithms for learning. We have used the invariance properties of image representations based on Haar wavelets to robustly capture various facial features. Similarly, unlike previous approaches this system is entirely trained using examples and does not rely on a priori (hand-crafted) models of facial features based on optical flow or facial musculature. The system works in several stages that begin with face detection, followed by localization of facial features and estimation of mouth parameters. Each of these stages is formulated as a problem in supervised learning from examples. We apply the new and robust technique of support vector machines (SVM) for classification in the stage of skin segmentation, face detection and eye detection. Estimation of mouth parameters is modeled as a regression from a sparse subset of coefficients (basis functions) of an overcomplete dictionary of Haar wavelets.

Certified Rapid Solution of Parametrized Linear Elliptic Equations: Application to Parameter Estimation

We present a technique for the rapid and reliable evaluation of linear-functional output of elliptic partial differential equations with affine parameter dependence. The essential components are (i) rapidly uniformly convergent reduced-basis approximations — Galerkin projection onto a space WN spanned by solutions of the governing partial differential equation at N (optimally) selected points in parameter space; (ii) a posteriori error estimation — relaxations of the residual equation that provide inexpensive yet sharp and rigorous bounds for the error in the outputs; and (iii) offline/online computational procedures — stratagems that exploit affine parameter dependence to de-couple the generation and projection stages of the approximation process. The operation count for the online stage — in which, given a new parameter value, we calculate the output and associated error bound — depends only on N (typically small) and the parametric complexity of the problem. The method is thus ideally suited to the many-query and real-time contexts. In this paper, based on the technique we develop a robust inverse computational method for very fast solution of inverse problems characterized by parametrized partial differential equations. The essential ideas are in three-fold: first, we apply the technique to the forward problem for the rapid certified evaluation of PDE input-output relations and associated rigorous error bounds; second, we incorporate the reduced-basis approximation and error bounds into the inverse problem formulation; and third, rather than regularize the goodness-of-fit objective, we may instead identify all (or almost all, in the probabilistic sense) system configurations consistent with the available experimental data — well-posedness is reflected in a bounded "possibility region" that furthermore shrinks as the experimental error is decreased.