This thesis proposes two constructive methods of approaching the Shannon limit very closely. Interestingly, these two methods operate in opposite regions, one has a block length of one and the other has a block length approaching infinity. The first approach is based on novel memoryless joint source-channel coding schemes. We first show some examples of sources and channels where no coding is optimal for all values of the signal-to-noise ratio (SNR). When the source bandwidth is greater than the channel bandwidth, joint coding schemes based on space-filling curves and other families of curves are proposed. For uniform sources and modulo channels, our coding scheme based on space-filling curves operates within 1.1 dB of Shannon’s rate-distortion bound. For Gaussian sources and additive white Gaussian noise (AWGN) channels, we can achieve within 0.9 dB of the rate-distortion bound. The second scheme is based on low-density parity-check (LDPC) codes. We first demonstrate that we can translate threshold values of an LDPC code between channels accurately using a simple mapping. We develop some models for density evolution

A space-filling curve is a linear traversal of a discrete finite multi-dimensional space. In order that this traversal be useful in many applications, the curve should preserve "locality". We quantify "locality" and bound the locality of multi-dimensional space-filling curves. Classic Hilbert spacefilling curves come close to achieving optimal locality. EDICS: IP 3.1 Corresponding author: Craig Gotsman Dept. of Computer Science Technion, Haifa 32000 Israel Tel: +972-4-294336 Fax: +972-4-294353 Email: gotsman@cs.technion.ac.il # A preliminary version of this work was presented at the IEEE International Conference on Pattern Recognition, Jerusalem, 1994. 1 1

We present a technique for rendering displacement mapped geometry in a raytracing renderer. Displacement mapping is an important technique for adding detail to surface geometry in rendering systems. It allows complex geometric variation to be added to simpler geometry, without the cost in geometric complexity of completely describing the nuances of the geometry at modeling time and with the advantage that the detail can be added adaptively at rendering time. The cost of displacement mapping is geometric complexity. Renderers that provide it must be able to efficiently render scenes that have effectively millions of geometric primitives. Scan-line renderers process primitives one at a time, so this complexity doesn't tax them, but traditional ray-tracing algorithms require random access to the entire scene database, so any part of the scene geometry may need to be available at any point during rendering. If the displaced geometry is fully instantiated in memory, it is straightforward to...

Image search has been actively studied in recent years. On the other hands, image browsing has received little attention. Image browsing refers to the process of presenting some forms of overview or summary of the image relationships, thus facilitating a user to navigate across the data set and find images of interests. In this paper, we present a new data structure built on the multi-linearization of image attributes for efficient organization of the data set and fast visual browsing of the images. We describe new techniques for multi-linearization based on multiple space-filling curves and hierarchical clustering techniques. In addition to providing fast navigation, our proposed data structure allows computationally efficient insertion and deletion of images from the data set. We then present a novel image navigator and browser built on dual-linearization data structure and intuitive presentation of image relevance and relationships, demonstrate the image navigation process, and repo...

A rasterization algorithm must efficiently generate pixel fragments from geometric descriptions of primitives. In order to accomplish per-pixel shading, shading parameters must also be interpolated across the primitive in a perspective-correct manner. If some of these parameters are to be interpreted in later stages of the pipeline directly or indirectly as texture coordinates, then translating spatial and parametric coherence into temporal coherence will improve texture cache performance. Finally, if framebuffer access is also organized around cached blocks, then organizing rasterization so fragments are generated in block-sequential order will maximize framebuffer cache performance. Hilbert-order rasterization accomplishes these goals, and also permits efficient incremental evaluation of edge and interpolation equations.

The performance of full-featured ray tracers has historically been limited by the hardware’s floating point computational power. However, next generation multi-threaded multi-core architectures promise to provide sufficient CPU throughput to support real time frame rates. In such systems, limited memory system performance in terms of both on-chip cache and DRAM-to-cache bandwidth is likely to bound overall system performance. This paper presents a novel ray tracing algorithm that both improves cache utilization and reduces DRAM-to-cache bandwidth usage. The key insight is to view ray traversal as a scheduling problem, which allows our algorithm to match ray traversal computations and intersection computations with available system resources. Using a detailed simulator, we show that our algorithm significantly reduces the amount of data brought into the cache in exchange for the small overhead of maintaining the ray schedule. Moreover, our algorithm creates units of work that are more amenable to parallelization than traditional Whitted-style ray tracers. Index Terms: I.3.7 [Computer Graphics]: Ray Tracing— 1

Summary. Genomes of hundreds of species have been sequenced to date, and many more are being sequenced. As more and more sequence data sets become available, and as the challenge of comparing these massive “billion basepair DNA sequences” becomes substantial, so does the need for more powerful tools supporting the exploration of these data sets. Similarity score data used to compare aligned DNA sequences is inherently one-dimensional. One-dimensional (1D) representations of these data sets do not effectively utilize screen real estate. As a result, tools using 1D representations are incapable of providing informatory overview for extremely large data sets. We present a technique to arrange 1D data in 3D space to allow us to apply state-of-the-art interactive volume visualization techniques for data exploration. We demonstrate our technique using multi-millions-basepair-long aligned DNA sequence data and compare it with traditional 1D line plots. The results show that our technique is superior in providing an overview of entire data sets. Our technique, coupled with 1D line plots, results in effective multi-resolution visualization of very large aligned sequence data sets.