Realistic modeling of reverberant sound in 3D virtual worlds provides users with important cues for localizing sound sources and understanding spatial properties of the environment. Unfortunately, current geometric acoustic modeling systems do not accurately simulate reverberant sound. Instead, they model only direct transmission and specular reflection, while diffraction is either ignored or modeled through statistical approximation. However, diffraction is important for correct interpretation of acoustic environments, especially when the direct path between sound source and receiver is occluded.The Uniform Theory of Diffraction (UTD) extends geometrical acoustics with diffraction phenomena: illuminated edges become secondary sources of diffracted rays that in turn may propagate through the environment. In this paper, we propose an efficient way for computing the acoustical effect of diffraction paths using the UTD for deriving secondary diffracted rays and associated diffraction coefficients. Our main contributions are: 1) a beam tracing method for enumerating sequences of diffracting edges efficiently and without aliasing in densely occluded polyhedral environments; 2) a practical approximation to the simulated sound field in which diffraction is considered only in shadow regions; and 3) a real-time auralization system demonstrating that diffraction dramatically improves the quality of spatialized sound in virtual environments.

Virtual environment research has focused on interactive image generation and has largely ignored acoustic modeling for spatialization of sound. Yet, realistic auditory cues can complement and enhance visual cues to aid navigation, comprehension, and sense of presence in virtual environments. A primary challenge in acoustic modeling is computation of reverberation paths from sound sources fast enough for real-time auralization. We have developed a system that uses precomputed spatial subdivision and "beam tree" data structures to enable real-time acoustic modeling and auralization in interactive virtual environments. The spatial subdivision is a partition of 3D space into convex polyhedral regions (cells) represented as a cell adjacency graph. A beam tracing algorithm recursively traces pyramidal beams through the spatial subdivision to construct a beam tree data structure representing the regions of space reachable by each potential sequence of transmission and specular reflection events at cell boundaries. From these precomputed data structures, we can generate high-order specular reflection and transmission paths at interactive rates to spatialize fixed sound sources in real-time as the user moves through a virtual environment. Unlike previous acoustic modeling work, our beam tracing method: 1) supports evaluation of reverberation paths at interactive rates, 2) scales to compute highorder reflections and large environments, and 3) extends naturally to compute paths of diffraction and diffuse reflection efficiently. We are using this system to develop interactive applications in which a user experiences a virtual environment immersively via simultaneous auralization and visualization.

A difficult challenge in geometrical acoustic modeling is computing propagation paths from sound sources to receivers fast enough for interactive applications. This paper describes a beam tracing method that enables interactive updates of propagation paths from a stationary source to a moving receiver in large building interiors. During a precomputation phase, convex polyhedral beams traced from the location of each sound source are stored in a "beam tree" representing the regions of space reachable by potential sequences of transmissions, diffractions, and specular reflections at surfaces of a 3D polygonal model. Then, during an interactive phase, the precomputed beam tree(s) are used to generate propagation paths from the source(s) to any receiver location at interactive rates. The key features of this beam tracing method are (1) it scales to support large building environments, (2) it models propagation due to edge diffraction, (3) it finds all propagation paths up to a given termination criterion without exhaustive search or risk of under-sampling, and (4) it updates propagation paths at interactive rates. The method has been demonstrated to work effectively in interactive acoustic design and virtual walkthrough applications.

Realistic acoustic modeling is essential for spatializing sound in distributed virtual environments where multiple networked users move around and interact visually and aurally in a shared virtual world. Unfortunately, current methods for computing accurate acoustical models are not fast enough for real-time auralization of sounds for simultaneously moving sources and receivers. In this paper, we present three new beam tracing algorithms that greatly accelerate computation of reverberation paths in a distributed virtual environment by taking advantage of the fact that sounds can only be generated or heard at the positions of "avatars" representing the users. The priority-driven beam tracing algorithm performs a bestfirst search of a cell adjacency graph, and thus enables new termination criteria with which all early reflection paths can be found very efficiently. The bidirectional beam tracing algorithm combines sets of beams traced from pairs of avatar locations to find reverberation paths between them while requiring significantly less computation than previous unidirectional algorithms. The amortized beam tracing algorithm computes beams emanating from box-shaped regions of space containing predicted avatar locations and re-uses those beams multiple times to compute reflections paths as each avatar moves inside the box. Cumulatively, these algorithms enable speedups of approximately two orders of magnitude over previous methods. They are incorporated into a time-critical multiprocessing system that allocates its computational resources dynamically in order to compute the highest priority reverberation paths between moving avatar locations in real-time with graceful degradation and adaptive refinement.

Cancer diagnosis is based on visual examination under a microscope of tissue sections from biopsies. But whereas pathologists rely on tissue stains to identify morphological features, automated tissue recognition using color is fraught with problems that stem from image intensity variations due to variations in tissue preparation, variations in spectral signatures of the stained tissue, spectral overlap and spatial aliasing in acquisition, and noise at image acquisition. We present a blind method for color decomposition of histological images. The method decouples intensity from color information and bases the decomposition only on the tissue absorption characteristics of each stain. By modeling the charge-coupled device sensor noise, we improve the method accuracy. We extend current linear decomposition methods to include stained tissues where one spectral signature cannot be separated from all combinations of the other tissues' spectral signatures. We demonstrate both qualitatively and quantitatively that our method results in more accurate decompositions than methods based on non-negative matrix factorization and independent component analysis. The result is one density map for each stained tissue type that classifies portions of pixels into the correct stained tissue allowing accurate identification of morphological features that may be linked to cancer.