We present methods to generate rendering sequences for triangle meshes which preserve mesh locality as much as possible. This is useful for maximizing vertex reuse when rendering the mesh using a FIFO vertex buffer, such as those available in modern 3D graphics hardware. The sequences are universal in the sense that they perform well for all sizes of vertex buffers, and generalize to progressive meshes. This has been verified experimentally. 1 Universal Rendering Sequences for Transparent Vertex Caching of Progressive Meshes Abstract We present methods to generate rendering sequences for triangle meshes which preserve mesh locality as much as possible. This is useful for maximizing vertex reuse when rendering the mesh using a FIFO vertex buffer, such as those available in modern 3D graphics hardware. The sequences are universal in the sense that they perform well for all sizes of vertex buffers, and generalize to progressive meshes. This has been verified experimentally. 1. Introdu...

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

Computational mechanics, an approach to structural complexity, defines a process’s causal states and gives a procedure for finding them. We show that the causal-state representation—an E-machine—is the minimal one consistent with

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

The maintenance of large raster images under spatial operations is still a major performance bottleneck. For reasons of storage space, images in a collection, such as satellite pictures in geographic information systems, are maintained in compressed form. Instead of performing a spatially selective operation on an image by first decompressing the compressed version, we propose in this paper to perform queries directly on the compressed version of the image. We suggest a compression technique that allows for the subsequent use of a spatial index structure to guide a spatial search. In response to a window query, our algorithm delivers a compressed partial image, or the exact uncompressed requested image region. In addition to the support of spatial queries on compressed continuous tone images, the new compression algorithm is even competitive in terms of the compression ratio that it achieves, compared to other standard lossless compression techniques. Index Terms---Lossless image comp...

We present a tensor product formulation for Hilbert space-filling curves. Both recursive and iterative formulas are expressed in the paper. We view a Hilbert space-filling curve as a permutation which maps two-dimensional ¥§¦©¨�¥� ¦ data elements stored in the row major or column major order to the order of traversing a Hilbert space-filling curve. The tensor product formula of Hilbert space-filling curves uses several permutation operations: stride permutation, radix-2 Gray permutation, transposition, and anti-diagonal transposition. The iterative tensor product formula can be manipulated to obtain the inverse Hilbert permutation. Also, the formulas are directly translated into computer programs which can be used in various applications including R-tree indexing, image processing, and process llocation, etc. Key words: tensor product, block recursive algorithm, Hilbert space-filling curve, stride

We consider the problem of sequential decision making on random fields corrupted by noise. In this scenario, the decision maker observes a noisy version of the data, yet judged with respect to the clean data. In particular, we first consider the problem of sequentially scanning and filtering noisy random fields. In this case, the sequential filter is given the freedom to choose the path over which it traverses the random field (e.g., noisy image or video sequence), thus it is natural to ask what is the best achievable performance and how sensitive this performance is to the choice of the scan. We formally define the problem of scanning and filtering, derive a bound on the best achievable performance and quantify the excess loss occurring when non-optimal scanners are used, compared to optimal scanning and filtering. We then discuss the problem of sequential scanning and prediction of noisy random fields. This setting is a natural model for applications such as restoration and coding of noisy im-ages. We formally define the problem of scanning and prediction of a noisy multidimensional array and relate the optimal performance to the clean scandictability defined by Merhav and Weissman. Moreover, bounds on the excess loss due to sub-optimal scans are derived, and a universal prediction algorithm is suggested.

The plenoptic function describes the visual information available to an observer at any point in space and time. Samples of the plenoptic function (POF) are seen in video and in general visual content (images, mosaics, panoramic scenes, etc), and represent large amounts of information. In this paper we propose a stochastic model to study the compression limits of a simplified version of the plenoptic function. In the proposed framework, we isolate the two fundamental sources of information in the POF: the one representing the camera motion and the other representing the information complexity of the “reality” being acquired and transmitted. The sources of information are combined, generating a stochastic process that we study in detail. We first propose a model for ensembles of realities that do not change over time. The proposed model is simple in that it enables us to derive precise coding bounds in the information-theoretic sense that are sharp in a number of cases of practical interest. For this simple case of static realities and camera motion, our results indicate that coding practice is in accordance with optimal coding from an information-theoretic standpoint. The model is further extended to account for visual realities that change over time. We derive bounds

We consider a variation of the Wyner–Ziv problem pertaining to lossy compression of individual sequences using finite–state encoders and decoders. There are two main results in this paper. The first characterizes the relationship between the performance of the best M–state encoder–decoder pair to that of the best block code of size ℓ for every input sequence, and shows that the loss of the latter relative to the former (in terms of both rate and distortion) never exceeds the order of (log M)/ℓ, independently of the input sequence. Thus, in the limit of large M, the best rate–distortion performance of every infinite source sequence can be approached universally by a sequence of block codes (which are also implementable by finite–state machines). While this result assumes an asymptotic regime where the number of states is fixed, and only the length n of the input sequence grows without bound, we then consider the case where the number of states M = Mn is allowed to grow concurrently with n. Our second result is then about the critical growth rate of Mn such that the rate–distortion performance of Mn–state encoder–decoder pairs can still be matched by a universal code. We show that this critical growth rate is of Mn is linear in n. Index Terms: Finite–state machines, individual sequences, side information, block codes, universal coding, Wyner–Ziv problem.

Abstract—Lempel-Ziv complexity (LZ) and derived LZ algorithms have been extensively used to solve information theoretic problems such as coding and lossless data compression. In recent years, LZ has been widely used in biomedical applications to estimate the complexity of discrete-time signals. Despite its popularity as a complexity measure for biosignal analysis, the question of LZ interpretability and its relationship to other signal parameters and to other metrics has not been previously addressed. We have carried out an investigation aimed at gaining a better understanding of the LZ complexity itself, especially regarding its interpretability as a biomedical signal analysis technique. Our results indicate that LZ is particularly useful as a scalar metric to estimate the bandwidth of random processes and the harmonic variability in quasi-periodic signals. Index Terms—Complex analysis, Lempel-Ziv complexity (LZ), nonlinear analysis.