Fourier analysis and gabor filtering for texture analysis and local reconstruction of general shapes

Since the pioneering work of Gibson in 1950, Shape- From-Texture has been considered by researchers as a hard problem, mainly due to restrictive assumptions which often limit its applicability. We assume a very general stochastic homogeneity and perspective camera model, for both deterministic and stochastic textures. A multi-scale distortion is efficiently estimated with a previously presented method based on Fourier analysis and Gabor filters. The novel 3D reconstruction method that we propose applies to general shapes, and includes non-developable and extensive surfaces. Our algorithm is accurate, robust and compares favorably to the present state of the art of Shape-From- Texture. Results show its application to non-invasively study shape changes with laid-on textures, while rendering and retexturing of cloth is suggested for future work. © 2009 IEEE.

Packet error rate and bit error rate non-deterministic relationship in optical network applications

The non-deterministic relationship between Bit Error Rate and Packet Error Rate is demonstrated for an optical media access layer in common use. We show that frequency components of coded, non-random data can cause this relationship. © 2005 Optical Society of America.

Monte Carlo filtering and smoothing with application to time-varying spectral estimation

We develop methods for performing filtering and smoothing in non-linear non-Gaussian dynamical models. The methods rely on a particle cloud representation of the filtering distribution which evolves through time using importance sampling and resampling ideas. In particular, novel techniques are presented for generation of random realisations from the joint smoothing distribution and for MAP estimation of the state sequence. Realisations of the smoothing distribution are generated in a forward-backward procedure, while the MAP estimation procedure can be performed in a single forward pass of the Viterbi algorithm applied to a discretised version of the state space. An application to spectral estimation for time-varying autoregressions is described.

Filtering via approximate Bayesian computation

Approximate Bayesian computation (ABC) has become a popular technique to facilitate Bayesian inference from complex models. In this article we present an ABC approximation designed to perform biased filtering for a Hidden Markov Model when the likelihood function is intractable. We use a sequential Monte Carlo (SMC) algorithm to both fit and sample from our ABC approximation of the target probability density. This approach is shown to, empirically, be more accurate w.r.t.~the original filter than competing methods. The theoretical bias of our method is investigated; it is shown that the bias goes to zero at the expense of increased computational effort. Our approach is illustrated on a constrained sequential lasso for portfolio allocation to 15 constituents of the FTSE 100 share index.