Abstract
Digital terrain data has widespread applications in areas such as the military, geographic information systems, and flight simulator video games. The combination of the abundance of terrain data with the limited rendering capabilities of computer graphics machines creates the necessity for algorithms which generate efficient representations of the data for rendering. This paper presents such an algorithm. Terrain data is represented using a binary tree, and the generalized BFOS algorithm, a well-known optimal tree-pruning method for regression and quantization trees is used to prune the tree optimally, resulting in a far more efficient representation of this data than known in the literature.

Abstract
Content based retrieval of image and video data from databases is a very challenging problem, whose interest is derived from the need of future databases to support efficient access to vast amounts of visual information. Typical queries to be performed in this context check attributes of objects present in image data, such as shape, color, relative locations, etc. Therefore, the way in which image data is represented plays a fundamental role in the efficient implementation of those queries. One possibility is to take the naive approach of storing images using standard compression techniques, storing image features (such as object shape descriptors, color histograms, etc.) as explicit side information, and whenever an image in involved in the evaluation of a query decoding it to full resolution; however, much more efficient techniques (in terms of storage and computational requirements) are possible. In this paper, we propose a new image coding technique which combines a wavelet image representation, embedded coding of the wavelet coefficients, and segmentation of semantically meaningful objects in the wavelet domain, to generate a bitstream in which each object is encoded independently of every other object in the image, and without explicitly storing shape boundary information. Furthermore, since the representation of each object is fully embedded applications may, independently for each object, specify the desired target bitrate and retrieve bits from the compressed bitstream. Preliminary results show that our new proposed method achieves PSNR numbers within 0.3dB of those achieved using the same coder without including segmentation information (which is one of the best within its class), thus showing that no severe performance loss results from enabling independent access to objects in the compressed domain.

Abstract
Since their introduction as a tool for signal representation, wavelets have become increasingly popular within the image coding community, because of the potential gains they offer for the construction of efficient image coding algorithms. Such potential gains are due to the fact that wavelets provide a good tradeoff between resolution in the space and frequency domains, a feature which results in mapping typical space-domain image phenomena (such as smooth regions and edges) into structured sets of coefficients in the wavelet domain. However, to be able to make use of any structure for improving coding performance, an algorithm requires a statistical characterization of the joint distribution of wavelet coefficients, capable of taking such structure into account. This work presents both an experimental study of the statistics of wavelet data, as well as the design of two different morphology-based coding algorithms, that make use of these statistics. A salient feature of the proposed method is that by a simple change of quantizers, the same basic algorithm yields high performance embedded or fixed rate coders. Another important feature is that the shape information of morphological sets used in this coder is encoded implicitly by the values of the wavelet coefficients, thus avoiding the use of explicit (and rate expensive) shape descriptors such as chain codes. These algorithms, while achieving nearly the same objective performance of state-of-the-art Zerotree based methods, are able to produce reconstructions of a somewhat superior perceptual quality, due to a property of joint compression and noise reduction they exhibit.

Abstract
Zerotree based algorithms represent the state of the art in wavelet based image coding. At a high level, these algorithms can be described as first sending some map of locations of zero coefficients (the set of zerotree symbols), and then sending the value of nonzero coefficients. However, the decision of what map to send is typically made using some simplifying assumption on the structure of the map, motivated by some empirically observed property of the data (e.g., that zero coefficients are likely to appear in tree structured sets): in this work, the map of locations of zero coefficients is optimally estimated as a hidden binary Markov Random Field (MRF) instead. Algorithms are presented for the estimation of the hidden field given the observed wavelet coefficients, for encoding the field, and for encoding the data given the field estimate. Simulation results show very competitive rate/distortion performance of the coding algorithm, equal or superior to any published Zerotree based image coder: this fact provides conclusive empirical evidence that the proposed model is appropriate for the data.

Abstract
We propose new coding techniques that combine a wavelet representation, embedded coding of the wavelet coefficients, and segmentation of semantically meaningful objects in the wavelet domain, to generate a bitstream in which semantically meaningful, arbitrarily shaped image objects are encoded independently of each other, and without explicitly storing shape boundary information. Since the representation of each object is fully embedded applications may, independently for each object, specify the desired target bitrate and retrieve bits from the compressed bitstream. Simulation results show that these new proposed indexing methods achieve coding performance which is perceptually identical to that achieved using state-of-the-art image/video coding techniques which do not support indexing, thus proving the feasibility of generating bitstreams that can support functionality required by emerging multimedia applications without sacrificing compression performance.

Abstract
In previous work, we introduced a new image representation for the field of wavelet coefficients (dubbed MRWD), based on morphological operators. This work extends the MRWD framework, by addressing the effective design of image coding algorithms. First, we design an encoder with the goal of being optimal in the operational rate-distortion sense. Second, based on the same (morphological) techniques, we design a successively refinable version of the single rate coder. Simulation results are reported.

Abstract
We study the problem of representing images within a multimedia Database Management System (DBMS), in order to support fast retrieval operations without compromising storage efficiency. To achieve this goal, we propose new image coding techniques which combine a wavelet representation, embedded coding of the wavelet coefficients, and segmentation of image-domain regions in the wavelet domain. A bitstream is generated in which each image region is encoded independently of other regions, without having to explicitly store information describing the regions. Simulation results show that our proposed algorithms achieve coding performance which compares favorably, both perceptually and objectively, to that achieved using state-of-the-art image/video coding techniques while additionally providing region-based support.