This paper presents robust methods for determining the order of a sequence of stripes captured in an uncoded structured light scanning system, i.e. where all the stripes are projected with uniform colour, width and spacing. A single bitmap image shows a pattern of vertical stripes from a projected source, which are deformed by the surface of the target object. If a correspondence can be determi...

This paper concerns the memoryless quasi-Newton method, that is precisely the quasi-Newton method for which the approximation to the inverse of Hessian, at each step, is updated from the identity matrix. Hence its search direction can be computed without the storage of matrices. In this paper, a scaled memoryless symmetric rank one (SR1) method for solving large-scale unconstrained optimization...

We propose a randomized second-order method for optimization known as the Newton Sketch: it is based on performing an approximate Newton step using a randomly projected or sub-sampled Hessian. For self-concordant functions, we prove that the algorithm has super-linear convergence with exponentially high probability, with convergence and complexity guarantees that are independent of condition nu...

In recent years, structured online discriminative learning methods using second order statistics have been shown to outperform conventional generative and discriminative models in the grapheme-to-phoneme (g2p) conversion task. However, these methods update the parameters by sequentially using N -best hypotheses predicted with the current parameters. Thus, the parameters appearing in early hypot...

The k-Hessian is the k-trace, or the kth elementary symmetric polynomial of eigenvalues of the Hessian matrix. When k ≥ 2, the k-Hessian equation is a fully nonlinear partial differential equations. It is elliptic when restricted to k-admissible functions. In this paper we establish the existence and regularity of k-admissible solutions to the Dirichlet problem of the k-Hessian equation. By a g...

We present a new Hessian estimator based on the simultaneous perturbation procedure, that requires three system simulations regardless of the parameter dimension. We then present two Newton-based simulation optimization algorithms that incorporate this Hessian estimator. The two algorithms differ primarily in the manner in which the Hessian estimate is used. Both our algorithms do not compute t...

In this paper, we study the constrained shrinking dimer dynamics (CSDD) which leads to numerical procedures for locating saddle points (transition states) associated with an energy functional defined on a constrained manifold. We focus on the most generic case corresponding to a constrained stationary point where the projected Hessian of the energy onto the tangent hyperplane of the constrained...

This paper proposes a novel curvilinear structure detector, called Optimally Oriented Flux (OOF). OOF finds an optimal axis on which image gradients are projected in order to compute the image gradient flux. The computation of OOF is localized at the boundaries of local spherical regions. It avoids considering closely located adjacent structures. The main advantage of OOF is its robustness agai...

We develop the first results on the local sensitivity analysis for the solution of a broad class of equality-constrained convex network optimization problems when perturbations are made on the constraints. In the context of the minimum-cost network flow problem — a paradigm in the theory of optimization — these results suggest a notion of decay of correlation for constrained optimization proced...

In this paper, we propose a new trust-region algorithm for solving a constrained optimization problem with equality and inequality constraints. In this algorithm, an active-set technique is used to convert the constrained optimization problem with equality and inequality constraints to equality constrained optimization problem. A projected Hessian technique is used together with a conjugate gra...