Mark R. Luettgen

Non-line-of-sight single-scatter propagation model

A propagation model that describes the temporal characteristics of singly scattered radiation in a homogeneous scattering and absorbing medium is presented. The model generalizes previous results in the area and is used to analyze the angular spectrum of singly scattered energy as well as the impulse-response durations and path losses of short-range non-line-of-sight optical communication systems. It is shown that the angular response starts to drop off significantly at an off-axis angle equal to the receiver half-field of view. It is also shown that lower path losses correspond to longer impulse responses so that a lower available bandwidth is indicated. These results are based on numerical examples motivated by the operation of non-line-of-sight communications links in the middle-ultraviolet wave band.

Likelihood calculation for a class of multiscale stochastic models, with application to texture discrimination

A class of multiscale stochastic models based on scale-recursive dynamics on trees has previously been introduced. Theoretical and experimental results have shown that these models provide an extremely rich framework for representing both processes which are intrinsically multiscale, e.g., 1/f processes, as well as 1D Markov processes and 2D Markov random fields. Moreover, efficient optimal estimation algorithms have been developed for these models by exploiting their scale-recursive structure. The authors exploit this structure in order to develop a computationally efficient and parallelizable algorithm for likelihood calculation. They illustrate one possible application to texture discrimination and demonstrate that likelihood-based methods using the algorithm achieve performance comparable to that of Gaussian Markov random field based techniques, which in general are prohibitively complex computationally.

Multiscale smoothing error models

A class of multiscale stochastic models based on scale-recursive dynamics on trees has recently been introduced. These models are interesting because they can be used to represent a broad class of physical phenomena and because they lead to efficient algorithms for estimation and likelihood calculation. In this paper, we provide a complete statistical characterization of the error associated with smoothed estimates of the multiscale stochastic processes described by these models. In particular, we show that the smoothing error is itself a multiscale stochastic process with parameters that can be explicitly calculated. >

Multiscale approaches to moving target detection in image sequences

We discuss a novel multiscale approach to the detection of moving objects in a sequence of images. The approach is based in part on a multiframe generalization of an optical flow estimation algorithm previously developed by two of the authors. This algorithm provides an extremely efficient multiscale method for estimating optical flow in an image sequence and allows for the temporal accumulation of motion information. Moving objects in a sequence correspond to discontinuities in the true optical flow and, as a result, the residual image associated with the estimated optical flow can be used as a basis for detecting these objects. We propose an approach to detection based on morphological processing of the residual image, and illustrate its potential on real data.

An estimation theoretic perspective on image processing and the calculation of optical flow

Many problems of image processing and image sequence analysis involve both great computational complexity and the accommodation of noise and uncertainty through the indirect observation of quantities of interest. In this chapter we describe several aspects of an estimation theoretic approach to such problems. The vehicle for our development is the estimation of the apparent velocity field of a sequence of images. This apparent velocity field, known as the optical flow, appears as an important quantity in both the qualitative and quantitative analysis of image sequences. For example, knowledge of the optical flow is used in the detection of object boundaries and the segmentation of visual scenes [1, 2], the derivation of 3-D motion and structure [3, 4] and the compression of image sequences for efficient transmission [5, 6].

Likelihood calculation for a class of multiscale stochastic models

In this paper, we present an efficient likelihood calculation algorithm for a class of multiscale models. Our development exploits the scale-recursive structure of these models thereby leading to a computationally efficient and highly parallelizable algorithm. We illustrate one possible application of the algorithm to texture discrimination and show that likelihood-based methods using our algorithm perform have substantially better probability of error statistics than well-known least-squares methods, and achieve virtually the same performance as truly optimal techniques, which are prohibitively complex computationally.<<ETX>>

Modeling And Estimation Of Multiresolution Stochastic Processes And Random Fields

In this poster, we provide an overview of several components of a research effort aimed at the development of a theory of multiresolution stochastic modeling and associated techniques for optimal multiscale statistical signal and image processing. As we describe, a natural framework for developing such atheory is the study of stochastic processes indexed by nodes on lattices or trees in which different depths in the tree or lattice correspond to different spatial scales in representing a signal or image. In particular we show how the wavelet transform directly suggests such a modeling paradigm. This perspective then leads directly to the investigation of several classes of dynamic models and related notions of “multiscale stationarity” in which scale plays the role of a time-like variable. In particular we describe the elements of a dynamic system theory on trees based on a specific notion of stationarity on trees. This notion of stationarity leads directly to a class of state space models on homogeneous trees. We describe several elements of the system theory for such models and also describe the natural, extremely efficient algorithmic structures for optimal estimation that these models suggest: one class of algorithms has a multigrid relaxation structure; a second uses the scale-to-scale whitening property of wavelet transforms for our models; and a third leads to a new class of Riccati equations involving the usual predict and update steps and a new ‘(fusion” step as information is propagated from fine to coarse scales. This framework allows us to consider in a very natural way the fusion of data from sensors with differing resolutions. In particular we present results on the fusion of noisy 1st-order Gauss-Markov processes which demonstrate the richness of our class of models in approximating processes. These results also show the ease with which this framework allows us to interpolate sparse, non-uniformly sampled fine data using coarser measurements with fuller coverage. lLaboratory for Information and Decision Systems and Department of Electrical Engineering and Computer Science, Massachusetts Institute of Technology, Cambridge,MA 02139, USA. The work of these authors was also supported in part by the Air Force Office of Scientific Research under Grant AFOSR-88-0032, by the National Science Foundation under Grants 9015281-MIP and INT-9002393 and by the US Army Research Office under Contract DAAL03-86-K-0171. In addition some of this research was performed while KCC and ASW were visitors at IRISA and while ASW received support from INRIA.

Multiscale approaches to target tracking in image sequences

In this paper, we discuss a novel multiscale algorithm for the detection of moving objects in a sequence of images. We model the apparent image motion (optical flow) with a class of multiscale stochastic models and use these to develop efficient estimation algorithms to compute the optical flow estimates, and to detect the presence of small moving objects within this flow. The algorithm has five clear advantages over existing approaches. First, it produces estimates of optical flow and associated covariances at multiple resolutions using explicit, multiscale statistical models. Second, it achieves substantial computational savings compared with existing optical flow techniques due to the fact that it has per pixel computational complexity--independent of image size. Third, it can track pixel-level motion over time using simple temporal dynamic models, improving the results over static edge and target detection algorithms. Fourth, it employs the multiscale error covariance information to identify the optimal resolution for flow estimation across the field of view, thus pinpointing regions in which motion can be localized to finer resolutions than other areas. Finally, it can generate spatial measurement residuals that highlight and enhance localized areas of optical flow discontinuity due to target motion. In this paper, the multiscale optical flow algorithm is defined and illustrated using a digital, grayscale image sequence of a helicopter. The results of this research clearly show the feasibility of enhanced target detection through the coherent processing of image sequences.

Multiresolution statistical methods in image analysis

In this paper, we discuss a statistical framework for multiscale signal and image processing based on a class of multiresolution stochastic models, which can be used to represent spatial random processes at a range of scales. The model class is quite rich, and in fact includes the class of Markov random fields. In addition, the models have a scale recursive structure which naturally leads to efficient, scale recursive algorithms for smoothing and likelihood calculation. We discuss an application of the framework to the problem of computing optical flow in image sequence, and demonstrate computational savings on the order of one to two orders of magnitude over standard algorithms.