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.

Permutation Tests for Classification

We introduce and explore an approach to estimating statistical significance of classification accuracy, which is particularly useful in scientific applications of machine learning where high dimensionality of the data and the small number of training examples render most standard convergence bounds too loose to yield a meaningful guarantee of the generalization ability of the classifier. Instead, we estimate statistical significance of the observed classification accuracy, or the likelihood of observing such accuracy by chance due to spurious correlations of the high-dimensional data patterns with the class labels in the given training set. We adopt permutation testing, a non-parametric technique previously developed in classical statistics for hypothesis testing in the generative setting (i.e., comparing two probability distributions). We demonstrate the method on real examples from neuroimaging studies and DNA microarray analysis and suggest a theoretical analysis of the procedure that relates the asymptotic behavior of the test to the existing convergence bounds.

Causal and Teleological Reasoning in Circuit Recognition

This thesis presents a theory of human-like reasoning in the general domain of designed physical systems, and in particular, electronic circuits. One aspect of the theory, causal analysis, describes how the behavior of individual components can be combined to explain the behavior of composite systems. Another aspect of the theory, teleological analysis, describes how the notion that the system has a purpose can be used to aid this causal analysis. The theory is implemented as a computer program, which, given a circuit topology, can construct by qualitative causal analysis a mechanism graph describing the functional topology of the system. This functional topology is then parsed by a grammar for common circuit functions. Ambiguities are introduced into the analysis by the approximate qualitative nature of the analysis. For example, there are often several possible mechanisms which might describe the circuit's function. These are disambiguated by teleological analysis. The requirement that each component be assigned an appropriate purpose in the functional topology imposes a severe constraint which eliminates all the ambiguities. Since both analyses are based on heuristics, the chosen mechanism is a rationalization of how the circuit functions, and does not guarantee that the circuit actually does function. This type of coarse understanding of circuits is useful for analysis, design and troubleshooting.

Formal Multilevel Hierarchical Verification of Synchronous MOS Circuits

I have designed and implemented a system for the multilevel verification of synchronous MOS VLSI circuits. The system, called Silica Pithecus, accepts the schematic of an MOS circuit and a specification of the circuit's intended digital behavior. Silica Pithecus determines if the circuit meets its specification. If the circuit fails to meet its specification Silica Pithecus returns to the designer the reason for the failure. Unlike earlier verifiers which modelled primitives (e.g., transistors) as unidirectional digital devices, Silica Pithecus models primitives more realistically. Transistors are modelled as bidirectional devices of varying resistances, and nodes are modelled as capacitors. Silica Pithecus operates hierarchically, interactively, and incrementally. Major contributions of this research include a formal understanding of the relationship between different behavioral descriptions (e.g., signal, boolean, and arithmetic descriptions) of the same device, and a formalization of the relationship between the structure, behavior, and context of device. Given these formal structures my methods find sufficient conditions on the inputs of circuits which guarantee the correct operation of the circuit in the desired descriptive domain. These methods are algorithmic and complete. They also handle complex phenomena such as races and charge sharing. Informal notions such as races and hazards are shown to be derivable from the correctness conditions used by my methods.

Noise Reduction Using Low Weight and Constant Weight Coding Techniques

Signalling off-chip requires significant current. As a result, a chip's power-supply current changes drastically during certain output-bus transitions. These current fluctuations cause a voltage drop between the chip and circuit board due to the parasitic inductance of the power-supply package leads. Digital designers often go to great lengths to reduce this "transmitted" noise. Cray, for instance, carefully balances output signals using a technique called differential signalling to guarantee a chip has constant output current. Transmitted-noise reduction costs Cray a factor of two in output pins and wires. Coding achieves similar results at smaller costs.

Selecting Relevant Genes with a Spectral Approach

Array technologies have made it possible to record simultaneously the expression pattern of thousands of genes. A fundamental problem in the analysis of gene expression data is the identification of highly relevant genes that either discriminate between phenotypic labels or are important with respect to the cellular process studied in the experiment: for example cell cycle or heat shock in yeast experiments, chemical or genetic perturbations of mammalian cell lines, and genes involved in class discovery for human tumors. In this paper we focus on the task of unsupervised gene selection. The problem of selecting a small subset of genes is particularly challenging as the datasets involved are typically characterized by a very small sample size ?? the order of few tens of tissue samples ??d by a very large feature space as the number of genes tend to be in the high thousands. We propose a model independent approach which scores candidate gene selections using spectral properties of the candidate affinity matrix. The algorithm is very straightforward to implement yet contains a number of remarkable properties which guarantee consistent sparse selections. To illustrate the value of our approach we applied our algorithm on five different datasets. The first consists of time course data from four well studied Hematopoietic cell lines (HL-60, Jurkat, NB4, and U937). The other four datasets include three well studied treatment outcomes (large cell lymphoma, childhood medulloblastomas, breast tumors) and one unpublished dataset (lymph status). We compared our approach both with other unsupervised methods (SOM,PCA,GS) and with supervised methods (SNR,RMB,RFE). The results clearly show that our approach considerably outperforms all the other unsupervised approaches in our study, is competitive with supervised methods and in some case even outperforms supervised approaches.

An Immersed Interface Method for the Incompressible Navier-Stokes Equations in Irregular Domains

We present an immersed interface method for the incompressible Navier Stokes equations capable of handling rigid immersed boundaries. The immersed boundary is represented by a set of Lagrangian control points. In order to guarantee that the no-slip condition on the boundary is satisfied, singular forces are applied on the fluid at the immersed boundary. The forces are related to the jumps in pressure and the jumps in the derivatives of both pressure and velocity, and are interpolated using cubic splines. The strength of singular forces is determined by solving a small system of equations at each time step. The Navier-Stokes equations are discretized on a staggered Cartesian grid by a second order accurate projection method for pressure and velocity.