Greg Welch

Bio: Greg Welch is an academic researcher from University of Central Florida. The author has contributed to research in topics: Augmented reality & Kalman filter. The author has an hindex of 32, co-authored 123 publications receiving 9686 citations. Previous affiliations of Greg Welch include University of North Carolina at Chapel Hill.

An Introduction to the Kalman Filter

Abstract: In 1960, R.E. Kalman published his famous paper describing a recursive solution to the discrete-data linear filtering problem. Since that time, due in large part to advances in digital computing, the Kalman filter has been the subject of extensive research and application, particularly in the area of autonomous or assisted navigation. The Kalman filter is a set of mathematical equations that provides an efficient computational (recursive) means to estimate the state of a process, in a way that minimizes the mean of the squared error. The filter is very powerful in several aspects: it supports estimations of past, present, and even future states, and it can do so even when the precise nature of the modeled system is unknown. The purpose of this paper is to provide a practical introduction to the discrete Kalman filter. This introduction includes a description and some discussion of the basic discrete Kalman filter, a derivation, description and some discussion of the extended Kalman filter, and a relatively simple (tangible) example with real numbers & results.

An Introduction to the Kalman Filter

Abstract: In 1960, R.E. Kalman published his famous paper describing a recursive solution to the discrete-data linear filtering problem. Since that time, due in large part to advances in digital computing, the Kalman filter has been the subject of extensive research and application, particularly in the area of autonomous or assisted navigation. The Kalman filter is a set of mathematical equations that provides an efficient computational (recursive) means to estimate the state of a process, in a way that minimizes the mean of the squared error. The filter is very powerful in several aspects: it supports estimations of past, present, and even future states, and it can do so even when the precise nature of the modeled system is unknown. The purpose of this paper is to provide a practical introduction to the discrete Kalman filter. This introduction includes a description and some discussion of the basic discrete Kalman filter, a derivation, description and some discussion of the extended Kalman filter, and a relatively simple (tangible) example with real numbers & results.

The office of the future: a unified approach to image-based modeling and spatially immersive displays

Abstract: We introduce ideas, proposed technologies, and initial results for an office of the future that is based on a unified application of computer vision and computer graphics in a system that combines and builds upon the notions of the CAVE™, tiled display systems, and image-based modeling . The basic idea is to use real-time computer vision techniques to dynamically extract per-pixel depth and reflectance information for the visible surfaces in the office including walls, furniture, objects, and people, and then to either project images on the surfaces, render images of the surfaces , or interpret changes in the surfaces. In the first case, one could designate every-day (potentially irregular) real surfaces in the office to be used as spatially immersive display surfaces, and then project high-resolution graphics and text onto those surfaces. In the second case, one could transmit the dynamic image-based models over a network for display at a remote site. Finally, one could interpret dynamic changes in the surfaces for the purposes of tracking, interaction, or augmented reality applications. To accomplish the simultaneous capture and display we envision an office of the future where the ceiling lights are replaced by computer controlled cameras and “smart” projectors that are used to capture dynamic image-based models with imperceptible structured light techniques, and to display high-resolution images on designated display surfaces. By doing both simultaneously on the designated display surfaces, one can dynamically adjust or autocalibrate for geometric, intensity, and resolution variations resulting from irregular or changing display surfaces, or overlapped projector images. Our current approach to dynamic image-based modeling is to use an optimized structured light scheme that can capture per-pixel depth and reflectance at interactive rates. Our system implementation is not yet imperceptible, but we can demonstrate the approach in the laboratory. Our approach to rendering on the designated (potentially irregular) display surfaces is to employ a two-pass projective texture scheme to generate images that when projected onto the surfaces appear correct to a moving headtracked observer. We present here an initial implementation of the overall vision, in an office-like setting, and preliminary demonstrations of our dynamic modeling and display techniques.

Shader Lamps: Animating Real Objects with Image-Based Illumination

Abstract: We describe a new paradigm for three-dimensional computer graphics, using projectors to graphically animate physical objects in the real world. The idea is to replace a physical object— with its inherent color, texture, and material properties—with a neutral object and projected imagery, reproducing the original (or alternative) appearance directly on the object. Because the approach is to effectively "lift" the visual properties of the object into the projector, we call the projectors shader lamps. We address the central issue of complete and continuous illumination of non-trivial physical objects using multiple projectors and present a set of new techniques that makes the process of illumination practical. We demonstrate the viability of these techniques through a variety of table-top applications, and describe preliminary results to reproduce life-sized virtual spaces.

SCAAT: incremental tracking with incomplete information

Abstract: The Kalman filter provides a powerful mathematical framework within which a minimum mean-square-error estimate of a user's position and orientation can be tracked using a sequence of single sensor observations, as opposed to groups of observations. We refer to this new approach as single-constraint-at-a-time or SCAAT tracking. The method improves accuracy by properly assimilating sequential observations, filtering sensor measurements, and by concurrently autocalibrating mechanical or electrical devices. The method facilitates user motion prediction, multisensor data fusion, and in systems where the observations are only available sequentially it provides estimates at a higher rate and with lower latency than a multiple-constraint approach. Improved accuracy is realized primarily for three reasons. First, the method avoids mathematically treating truly sequential observations as if they were simultaneous. Second, because each estimate is based on the observation of an individual device, perceived error (statistically unusual estimates) can be more directly attributed to the corresponding device. This can be used for concurrent autocalibration which can be elegantly incorporated into the existing Kalman filter. Third, the Kalman filter inherently addresses the effects of noisy device measurements. Beyond accuracy, the method nicely facilitates motion prediction because the Kalman filter already incorporates a model of the user's dynamics, and because it provides smoothed estimates of the user state, including potentially unmeasured elements. Finally, in systems where the observations are only available sequentially, the method can be used to weave together information from individual devices in a very flexible manner, producing a new estimate as soon as each individual observation becomes available, thus facilitating multisensor data fusion and improving the estimate rates and latencies. The most significant aspect of this work is the introduction and exploration of the SCAAT approach to 3D tracking for virtual environments. However I also believe that this work may prove to be of interest to the larger scientific and engineering community in addressing a more general class of tracking and estimation problems.

A survey of augmented reality

Abstract: This paper surveys the field of augmented reality AR, in which 3D virtual objects are integrated into a 3D real environment in real time. It describes the medical, manufacturing, visualization, path planning, entertainment, and military applications that have been explored. This paper describes the characteristics of augmented reality systems, including a detailed discussion of the tradeoffs between optical and video blending approaches. Registration and sensing errors are two of the biggest problems in building effective augmented reality systems, so this paper summarizes current efforts to overcome these problems. Future directions and areas requiring further research are discussed. This survey provides a starting point for anyone interested in researching or using augmented reality.

Recent advances in augmented reality

Abstract: In 1997, Azuma published a survey on augmented reality (AR). Our goal is to complement, rather than replace, the original survey by presenting representative examples of the new advances. We refer one to the original survey for descriptions of potential applications (such as medical visualization, maintenance and repair of complex equipment, annotation, and path planning); summaries of AR system characteristics (such as the advantages and disadvantages of optical and video approaches to blending virtual and real, problems in display focus and contrast, and system portability); and an introduction to the crucial problem of registration, including sources of registration error and error-reduction strategies.

The Ensemble Kalman Filter: Theoretical formulation and practical implementation

Abstract: The purpose of this paper is to provide a comprehensive presentation and interpretation of the Ensemble Kalman Filter (EnKF) and its numerical implementation. The EnKF has a large user group, and numerous publications have discussed applications and theoretical aspects of it. This paper reviews the important results from these studies and also presents new ideas and alternative interpretations which further explain the success of the EnKF. In addition to providing the theoretical framework needed for using the EnKF, there is also a focus on the algorithmic formulation and optimal numerical implementation. A program listing is given for some of the key subroutines. The paper also touches upon specific issues such as the use of nonlinear measurements, in situ profiles of temperature and salinity, and data which are available with high frequency in time. An ensemble based optimal interpolation (EnOI) scheme is presented as a cost-effective approach which may serve as an alternative to the EnKF in some applications. A fairly extensive discussion is devoted to the use of time correlated model errors and the estimation of model bias.

An Introduction to the Kalman Filter

Abstract: In 1960, R.E. Kalman published his famous paper describing a recursive solution to the discrete-data linear filtering problem. Since that time, due in large part to advances in digital computing, the Kalman filter has been the subject of extensive research and application, particularly in the area of autonomous or assisted navigation. The Kalman filter is a set of mathematical equations that provides an efficient computational (recursive) means to estimate the state of a process, in a way that minimizes the mean of the squared error. The filter is very powerful in several aspects: it supports estimations of past, present, and even future states, and it can do so even when the precise nature of the modeled system is unknown. The purpose of this paper is to provide a practical introduction to the discrete Kalman filter. This introduction includes a description and some discussion of the basic discrete Kalman filter, a derivation, description and some discussion of the extended Kalman filter, and a relatively simple (tangible) example with real numbers & results.