Egyptian Ceremony in the Virtual Temple- Avatars for Virtual Heritage

With Virtual Reality, students can directly interact with distant times and places, giving them greater understanding and empathy for other cultures. Egyptian religious performance and ritual were central to the culture, and monumental temples were their dramatic performance spaces. The Earth Theater at Carnegie Museum of Natural History supports the Virtual Egyptian Temple, a three-dimensional, computer-graphic simulation of a Ptolemaic Era temple. We propose to stage an important religious event from that time, the Egyptian Oracle, virtually “in” the temple at the Earth Theater and two other large-screen theaters. An expert puppeteer will control the temple virtual High Priest and lesser constructs, a live educator, and even with the audience in the role of the Egyptian public. A live puppeteer can experiment and improvise in ways no artificial intelligence can and decades of educational research show the best way to learn about a social activity is to see it and do it

Simultaneous Estimation of Attenuation and Activity Images Using Optimization Transfer

This paper addresses the application of optimization transfer to simultaneous statistical estimation of attenuation and activity images in tomographic Image reconstruction. Although the technique we propose has wider applicability, we focus on the problem of reconstructing from data acquired via a post-injection transmission scan protocol. In this protocol, emission scan data Is supplemented with transmission scan data that is acquired after the patient has received the Injection of radio-tracer. The negative loglikelihood function for this data is a complicated function of the activity and attenuation images, leading to an objective function for the model that is difficult to minimize for the purpose of estimation. Previous work on this problem showed that when either the attenuation or activity image was held fixed, a paraboloidal surrogate could be found for the negative loglikelihood as a function of the remaining variables. This led to an algorithm In which the model's objective function is alternately minimized as a function of the attenuation and activity, using the optimization transfer technique. In the work we present here, however, we develop bivariate surrogates for the loglikelihood, i.e., functions that serve as surrogates with respect to both the attenuation and activity variables. Hence, simultaneous minimization in all variables can be carried out, potentially leading to convergence in fewer surrogate minimizations.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/85885/1/Fessler169.pd

An Expanded Theoretical Treatment of Iteration-Dependent Majorize-Minimize Algorithms

The majorize-minimize (MM) optimization technique has received considerable attention in signal and image processing applications, as well as in statistics literature. At each iteration of an MM algorithm, one constructs a tangent majorant function that majorizes the given cost function and is equal to it at the current iterate. The next iterate is obtained by minimizing this tangent majorant function, resulting in a sequence of iterates that reduces the cost function monotonically. A well-known special case of MM methods are expectation-maximization algorithms. In this paper, we expand on previous analyses of MM, due to Fessler and Hero, that allowed the tangent majorants to be constructed in iteration-dependent ways. Also, this paper overcomes an error in one of those earlier analyses. There are three main aspects in which our analysis builds upon previous work. First, our treatment relaxes many assumptions related to the structure of the cost function, feasible set, and tangent majorants. For example, the cost function can be nonconvex and the feasible set for the problem can be any convex set. Second, we propose convergence conditions, based on upper curvature bounds, that can be easier to verify than more standard continuity conditions. Furthermore, these conditions allow for considerable design freedom in the iteration-dependent behavior of the algorithm. Finally, we give an original characterization of the local region of convergence of MM algorithms based on connected (e.g., convex) tangent majorants. For such algorithms, cost function minimizers will locally attract the iterates over larger neighborhoods than typically is guaranteed with other methods. This expanded treatment widens the scope of the MM algorithm designs that can be considered for signal and image processing applications, allows us to verify the convergent behavior of previously published algorithms, and gives a fuller understanding overall of how these algorithms behave.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/85958/1/Fessler34.pd

Joint Estimation of Image and Deformation Parameters in Tomographic Image Reconstruction

We consider an emission tomography reconstruction problem in which projection measurements from several successive time frames are available. Two strategies for doing motion-corrected image reconstruction are compared. In the first strategy, separate images are reconstructed from the measurements at each time frame. They are then consolidated by post-registration and averaging procedures. In the second strategy, parameters to describe the effects of motion are added to the statistical model of the projections. Joint maximum likelihood estimation of image and motion parameters is then carried out.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/85809/1/Fessler184.pd

Fast interpolation operations in non-rigid image registration

Much literature on image registration1–3 has worked with purely geometric image deformation models. For such models, interpolation/resampling operations are often the computationally intensive steps when iteratively minimizing the deformation cost function. This article discusses some techniques for efficiently implementing and accelerating these operations. To simplify presentation, we discuss our ideas in the context of 2D imaging. However, the concepts readily generalize to 3D. Our central technique is a table-lookup scheme that makes somewhat liberal use of RAM, but should not strain the resources of modern processors if certain design parameters are appropriately selected. The technique works by preinterpolating and tabulating the grid values of the reference image onto a finer grid along one of the axes of the image. The lookup table can be rapidly constructed using FFTs. Our results show that this technique reduces iterative computation by an order of magnitude. When a minimization algorithm employing coordinate block alternation is used, one can obtain still faster computation by storing certain intermediate quantities as state variables. We refer to this technique as state variable hold-over. When combined with table-lookup, state variable hold-over reduces CPU time by about a factor two, as compared to table-lookup alone.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/85925/1/Fessler207.pd

Joint Estimation of Respiratory Motion and Activity in 4D PET Using CT Side Information

In previous work, we proposed a Poisson statistical model for gated PET data in which the distribution was parametrized in terms of both image intensity and motion parameters. The motion parameters related the activity image in each gate to that of a base image in some fixed gate. By doing maximum loglikelihood (ML) estimation of all parameters simultaneously, one obtains an estimate of the base gate image that exploits the full set of measured sinogram data. Previously, this joint ML approach was compared, in a highly simplified single-slice setting, to more conventional methods. Performance was measured in terms of the recovery of tracer uptake in a synthetic lung nodule. This paper reports the extension to 3D with much more realistic simulated motion. Furthermore, in addition to pure ML estimation, we consider the use of side information from a breath-hold CT scan to facilitate regularization, while preserving hot lesions of the kind seen in FDG oncology studies.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/85812/1/Fessler219.pd