Bruno Cernuschi-Frías

Toward a model-based Bayesian theory for estimating and recognizing parameterized 3-D objects using two or more images taken from different positions

A parametric modeling and statistical estimation approach is proposed and simulation data are shown for estimating 3-D object surfaces from images taken by calibrated cameras in two positions. The parameter estimation suggested is gradient descent, though other search strategies are also possible. Processing image data in blocks (windows) is central to the approach. After objects are modeled as patches of spheres, cylinders, planes and general quadrics-primitive objects, the estimation proceeds by searching in parameter space to simultaneously determine and use the appropriate pair of image regions, one from each image, and to use these for estimating a 3-D surface patch. The expression for the joint likelihood of the two images is derived and it is shown that the algorithm is a maximum-likelihood parameter estimator. A concept arising in the maximum likelihood estimation of 3-D surfaces is modeled and estimated. Cramer-Rao lower bounds are derived for the covariance matrices for the errors in estimating the a priori unknown object surface shape parameters. >

3-D Space Location and Orientation Parameter Estimation of Lambertian Spheres and Cylinders From a Single 2-D Image By Fitting Lines and Ellipses to Thresholded Data

An approach to object location and orientation estimation is discussed in which objects in 3-D space are approximated by chunks of spheres, cylinders, and planes. The surface-shape parameters of these chunks of primitive subobjects are estimated in real time from a single 2-D image assuming a Lambertian reflection model. This processing is realized by partitioning an image into small square windows and processing the windows in parallel. It is assumed that a small window views a portion of one of the spherical, cylindrical or planar chunks. The paper applies standard statistical estimators in new ways to the estimation of the 3-D shape parameters for spherical and cylindrical surfaces. Linear regression and scatter matrix eigenvalue analysis techniques are used here. The algorithms are computationally simple yet are robust and can handle noisy highly variable data.

A nonparametric nonstationary procedure for failure prediction

The time between failures is a very useful measurement to analyze reliability models for time-dependent systems. In many cases, the failure-generation process is assumed to be stationary, even though the process changes its statistics as time elapses. This paper presents a new estimation procedure for the probabilities of failures; it is based on estimating time-between-failures. The main characteristics of this procedure are that no probability distribution function is assumed for the failure process, and that the failure process is not assumed to be stationary. The model classifies the failures in Q different types, and estimates the probability of each type of failure s-independently from the others. This method does not use histogram techniques to estimate the probabilities of occurrence of each failure-type; rather it estimates the probabilities directly from the values of the time-instants at which the failures occur. The method assumes quasistationarity only in the interval of time between the last 2 occurrences of the same failure-type. An inherent characteristic of this method is that it assigns different sizes for the time-windows used to estimate the probabilities of each failure-type. For the failure-types with low probability, the estimator uses wide windows, while for those with high probability the estimator uses narrow windows. As an example, the model is applied to software reliability data.

Asymptotic Bayesian surface estimation using an image sequence

A new approach is introduced to estimating object surfaces in three-dimensional space from a sequence of images. A 3D surface of interest here is modeled as a function known up to the values of a few parameters. Surface estimation is then treated as the general problem of maximum-likelihood parameter estimation based on two or more functionally related data sets. In our case, these data sets constitute a sequence of images taken at different locations and orientations. Experiments are run to illustrate the various advantages of using as many images as possible in the estimation and of distributing camera positions from first to last over as large a baseline as possible. In order to extract all the usable information from the sequence of images, all the images should be available simultaneously for the parameter estimation. We introduce the use of asymptotic Bayesian approximations in order to summarize the useful information in a sequence of images, thereby drastically reducing both the storage and the amount of processing required. This leads to a sequential Bayesian estimator for the surface parameters, where the information extracted from previous images is summarized in a quadratic form. The attractiveness of our approach is that now all the usual tools of statistical signal analysis, for example, statistical decision theory for object recognition, can be brought to bear; the information extraction appears to be robust and computationally reasonable; the concepts are geometric and simple; and essentially optimal accuracy should result. Experimental results are shown for extending this approach in two ways. One is to model a highly variable surface as a collection of small patches jointly constituting a stochastic process (e.g., a Markov random field) and to reconstruct this surface using maximum a posteriori probability (MAP) estimation. The other is to cluster together those patches constituting the same primitive object through the use of MAP segmentation. This provides a simultaneous estimation and segmentation of a surface into primitive constituent surfaces.

Simultaneous Motion Detection and Background Reconstruction with a Conditional Mixed-State Markov Random Field

In this work we present a new way of simultaneously solving the problems of motion detection and background image reconstruction. An accurate estimation of the background is only possible if we locate the moving objects. Meanwhile, a correct motion detection is achieved if we have a good available background model. The key of our joint approach is to define a single random process that can take two types of values, instead of defining two different processes, one symbolic (motion detection) and one numeric (background intensity estimation). It thus allows to exploit the (spatio-temporal) interaction between a decision (motion detection) and an estimation (intensity reconstruction) problem. Consequently, the meaning of solving both tasks jointly, is to obtain a single optimal estimate of such a process. The intrinsic interaction and simultaneity between both problems is shown to be better modeled within the so-called mixed-state statistical framework, which is extended here to account for symbolic states and conditional random fields. Experiments on real sequences and comparisons with existing motion detection methods support our proposal. Further implications for video sequence inpainting will be also discussed.

A derivation of the Gohberg-Semencul relation (signal analysis)

A simple proof of the Gohberg-Semencul decomposition of the inverse of the correlation matrix of an autoregressive (AR) process is given. The proof is based on the Cholesky decomposition and the centrosymmetric property of symmetric Toeplitz matrices. The Gohberg-Semencul relation is derived in a simple way by doubling the size, but not the order, of the AR process. >

Partial simultaneous updating in Hopfield memories

A simple generalization of the Hopfield memory is presented. The model proposed updates simultaneously groups of a fixed number of neurons that are disjoint in the sense that each neuron belongs to one and only one group. An analysis is presented of the case in which one of the groups is chosen at random with equal probability and then is updated according to a rule equivalent to the one given by J.J. Hopfield (1982). It is shown that the rule minimizes an energy function in the same way as the original Hopfield model. Sufficient conditions on the corresponding connection matrix as to ensure stability are given. >

Simultaneous Motion Detection and Background Reconstruction with a Mixed-State Conditional Markov Random Field

We consider the problem of motion detection by background subtraction. An accurate estimation of the background is only possible if we locate the moving objects; meanwhile, a correct motion detection is achieved if we have a good available background model. This work proposes a new direction in the way such problems are considered. The main idea is to formulate this class of problem as a joint decision-estimation unique step. The goal is to exploit the way two processes interact, even if they are of a dissimilar nature (symbolic-continuous), by means of a recently introduced framework called mixed-state Markov random fields. In this paper, we will describe the theory behind such a novel statistical framework, that subsequently will allows us to formulate the specific joint problem of motion detection and background reconstruction. Experiments on real sequences and comparisons with existing methods will give a significant support to our approach. Further implications for video sequence inpainting will be also discussed.

Mixed-State Markov Random Fields for Motion Texture Modeling and Segmentation

The aim of this work is to model the apparent motion in image sequences depicting natural dynamic scenes. We adopt the mixed-state Markov random fields (MRF) models recently introduced to represent so-called motion textures. The approach consists in describing the spatial distribution of some motion measurements which exhibit mixed-state nature: a discrete component related to the absence of motion and a continuous part for measurements different from zero. We propose several significative extensions to this model. We define an original motion texture segmentation method which does not assume conditional independence of the observations for each texture and normalizing factors are properly handled. Results on real examples demonstrate the accuracy and efficiency of our method.

Bayesian estimation of 3D surfaces from a sequence of images

An approach is introduced to estimating object surfaces in 3D space from a sequence of images. A 3D surface of interest is modeled as a function known up to the values of a few parameters. Surface estimation is then treated as the general problem of maximum-likelihood parameter estimation based on two or more functionally related data sets, which constitute a sequence of images taken at different locations and orientations. Experiments are run to illustrate the various advantages of using as many images as possible in the estimation and of distributing camera positions from first to last over as large a baseline as possible. The authors introduce the use of asymptotic Bayesian approximations to summarize the useful information in a sequence of images, thereby drastically reducing both storage and processing. This results in a Bayesian estimator for the surface parameters. All the usual tools of statistical signal analysis can be brought to bear, the information extraction appears to be robust and computationally reasonable, the concepts are geometric and simple, and essentially optimal accuracy should result.<<ETX>>