Feature Matching for Object Localization in the Presence of Uncertainty

We consider the problem of matching model and sensory data features in the presence of geometric uncertainty, for the purpose of object localization and identification. The problem is to construct sets of model feature and sensory data feature pairs that are geometrically consistent given that there is uncertainty in the geometry of the sensory data features. If there is no geometric uncertainty, polynomial-time algorithms are possible for feature matching, yet these approaches can fail when there is uncertainty in the geometry of data features. Existing matching and recognition techniques which account for the geometric uncertainty in features either cannot guarantee finding a correct solution, or can construct geometrically consistent sets of feature pairs yet have worst case exponential complexity in terms of the number of features. The major new contribution of this work is to demonstrate a polynomial-time algorithm for constructing sets of geometrically consistent feature pairs given uncertainty in the geometry of the data features. We show that under a certain model of geometric uncertainty the feature matching problem in the presence of uncertainty is of polynomial complexity. This has important theoretical implications by demonstrating an upper bound on the complexity of the matching problem, an by offering insight into the nature of the matching problem itself. These insights prove useful in the solution to the matching problem in higher dimensional cases as well, such as matching three-dimensional models to either two or three-dimensional sensory data. The approach is based on an analysis of the space of feasible transformation parameters. This paper outlines the mathematical basis for the method, and describes the implementation of an algorithm for the procedure. Experiments demonstrating the method are reported.

Free Indexation: Combinatorial Analysis and a Compositional Algorithm

In the principles-and-parameters model of language, the principle known as "free indexation'' plays an important part in determining the referential properties of elements such as anaphors and pronominals. This paper addresses two issues. (1) We investigate the combinatorics of free indexation. In particular, we show that free indexation must produce an exponential number of referentially distinct structures. (2) We introduce a compositional free indexation algorithm. We prove that the algorithm is "optimal.'' More precisely, by relating the compositional structure of the formulation to the combinatorial analysis, we show that the algorithm enumerates precisely all possible indexings, without duplicates.

The Effect of Indexing on the Complexity of Object Recognition

Many current recognition systems use constrained search to locate objects in cluttered environments. Previous formal analysis has shown that the expected amount of search is quadratic in the number of model and data features, if all the data is known to come from a sinlge object, but is exponential when spurious data is included. If one can group the data into subsets likely to have come from a single object, then terminating the search once a "good enough" interpretation is found reduces the expected search to cubic. Without successful grouping, terminated search is still exponential. These results apply to finding instances of a known object in the data. In this paper, we turn to the problem of selecting models from a library, and examine the combinatorics of determining that a candidate object is not present in the data. We show that the expected search is again exponential, implying that naﶥ approaches to indexing are likely to carry an expensive overhead, since an exponential amount of work is needed to week out each of the incorrect models. The analytic results are shown to be in agreement with empirical data for cluttered object recognition.

A Low Power Wide Dynamic Range Envelope Detector

We report a 75dB, 2.8mW, 100Hz-10kHz envelope detector in a 1.5mm 2.8V CMOS technology. The envelope detector performs input-dc-insensitive voltage-to-currentconverting rectification followed by novel nanopower current-mode peak detection. The use of a subthreshold wide- linear-range transconductor (WLR OTA) allows greater than 1.7Vpp input voltage swings. We show theoretically that this optimal performance is technology-independent for the given topology and may be improved only by spending more power. A novel circuit topology is used to perform 140nW peak detection with controllable attack and release time constants. The lower limits of envelope detection are determined by the more dominant of two effects: The first effect is caused by the inability of amplified high-frequency signals to exceed the deadzone created by exponential nonlinearities in the rectifier. The second effect is due to an output current caused by thermal noise rectification. We demonstrate good agreement of experimentally measured results with theory. The envelope detector is useful in low power bionic implants for the deaf, hearing aids, and speech-recognition front ends. Extension of the envelope detector to higher- frequency applications is straightforward if power consumption is inc

Multistep Methods for Integrating the Solar System

High order multistep methods, run at constant stepsize, are very effective for integrating the Newtonian solar system for extended periods of time. I have studied the stability and error growth of these methods when applied to harmonic oscillators and two-body systems like the Sun-Jupiter pair. I have also tried to design better multistep integrators than the traditional Stormer and Cowell methods, and I have found a few interesting ones.

Residual Vibration Reduction in Computer Controlled Machines

Control of machines that exhibit flexibility becomes important when designers attempt to push the state of the art with faster, lighter machines. Three steps are necessary for the control of a flexible planet. First, a good model of the plant must exist. Second, a good controller must be designed. Third, inputs to the controller must be constructed using knowledge of the system dynamic response. There is a great deal of literature pertaining to modeling and control but little dealing with the shaping of system inputs. Chapter 2 examines two input shaping techniques based on frequency domain analysis. The first involves the use of the first deriviate of a gaussian exponential as a driving function template. The second, acasual filtering, involves removal of energy from the driving functions at the resonant frequencies of the system. Chapter 3 presents a linear programming technique for generating vibration-reducing driving functions for systems. Chapter 4 extends the results of the previous chapter by developing a direct solution to the new class of driving functions. A detailed analysis of the new technique is presented from five different perspectives and several extensions are presented. Chapter 5 verifies the theories of the previous two chapters with hardware experiments. Because the new technique resembles common signal filtering, chapter 6 compares the new approach to eleven standard filters. The new technique will be shown to result in less residual vibrations, have better robustness to system parameter uncertainty, and require less computation than other currently used shaping techniques.

A Simple Model of Circuit Design

A simple analog circuit designer has been implemented as a rule based system. The system can design voltage followers. Miller integrators, and bootstrap ramp generators from functional descriptions of what these circuits do. While the designer works in a simple domain where all components are ideal, it demonstrates the abilities of skilled designers. While the domain is electronics, the design ideas are useful in many other engineering domains, such as mechanical engineering, chemical engineering, and numerical programming. Most circuit design systems are given the circuit schematic and use arithmetic constraints to select component values. This circuit designer is different because it designs the schematic. The designer uses a unidirectional CONTROL relation to find the schematic. The circuit designs are built around this relation; it restricts the search space, assigns purposes to components and finds design bugs.

Risk Aversion in Inventory Management

Traditional inventory models focus on risk-neutral decision makers, i.e., characterizing replenishment strategies that maximize expected total profit, or equivalently, minimize expected total cost over a planning horizon. In this paper, we propose a framework for incorporating risk aversion in multi-period inventory models as well as multi-period models that coordinate inventory and pricing strategies. In each case, we characterize the optimal policy for various measures of risk that have been commonly used in the finance literature. In particular, we show that the structure of the optimal policy for a decision maker with exponential utility functions is almost identical to the structure of the optimal risk-neutral inventory (and pricing) policies. Computational results demonstrate the importance of this approach not only to risk-averse decision makers, but also to risk-neutral decision makers with limited information on the demand distribution.