We describe a technique for image encoding in which local operators of many scales but identical shape serve as the basis functions. The representation differs from established techniques in that the code elements are localized in spatial frequency as well as in space. Pixel-to-pixel correlations are first removed by subtracting a lowpass filtered copy of the image from the image itself. The result is a net data compression since the difference, or error, image has low variance and entropy, and the low-pass filtered image may represented at reduced sample density. Further data compression is achieved by quantizing the difference image. These steps are then repeated to compress the low-pass image. Iteration of the process at appropriately expanded scales generates a pyramid data structure. The encoding process is equivalent to sampling the image with Laplacian operators of many scales. Thus, the code tends to enhance salient image features. A further advantage of the present code is tha...

The history of the theory and practice of quantization dates to 1948, although similar ideas had appeared in the literature as long ago as 1898. The fundamental role of quantization in modulation and analog-to-digital conversion was first recognized during the early development of pulsecode modulation systems, especially in the 1948 paper of Oliver, Pierce, and Shannon. Also in 1948, Bennett published the first high-resolution analysis of quantization and an exact analysis of quantization noise for Gaussian processes, and Shannon published the beginnings of rate distortion theory, which would provide a theory for quantization as analog-to-digital conversion and as data compression. Beginning with these three papers of fifty years ago, we trace the history of quantization from its origins through this decade, and we survey the fundamentals of the theory and many of the popular and promising techniques for quantization.

this paper was supported by NSF grant ECS-8206321. A shorter description of this work was published in the Proceedings of SPIE, vol. 432, Applications of Digital Image Processing VI, The International Society for Optical Engineering, Bellingham, Washington. Authors' address: RCA David Sarnoff Research Center, Princeton, NJ 08540. Permission to copy without fee all or part of this material is granted provided that the copies are not made or distributed for direct commercial advantage, the ACM copyright notice and the title of the publication and its date appear, and notice is given that copying is by permission of the Association for Computing Machinery. To copy otherwise, or to republish, requires a fee and/or specific permission. 1983 ACM 0730-0301/83/1000-0217 $00.75 ACM Transactions on Graphics, Vol. 2. No. 4, October 1983, Pages 217-236. 218 . P. J. Burt and E. H. Adelson Fig. 1. A pair of images may be represented as a pair of surfaces above the (x, y) plane. The problem of image splining is to join these surfaces with a smooth seam, with as little distortion of each surface as possible. tiple telescope photographs. In each of these cases, the mosaic technique is used to construct an image with a far larger field of view or level of detail than could be obtained with a single photograph. In advertising or computer graphics, the technique can be used to create synthetic images from possibly unrelated components. A technical problem common to all applications of photomosaics is joining two images so that the edge between them is not visible. Even slight differences in image gray level across an extended boundary can make that boundary quite noticeable. Unfortunately, such gray level differences are frequently unavoidable; they may be due to such factors as differe...

LOCO-I (LOw COmplexity LOssless COmpression for Images) is the algorithm at the core of the new ISO/ITU standard for lossless and near-lossless compression of continuous-tone images, JPEG-LS. It is conceived as a "low complexity projection" of the universal context modeling paradigm, matching its modeling unit to a simple coding unit. By combining simplicity with the compression potential of context models, the algorithm "enjoys the best of both worlds." It is based on a simple fixed context model, which approaches the capability of the more complex universal techniques for capturing high-order dependencies. The model is tuned for efficient performance in conjunction with an extended family of Golomb-type codes, which are adaptively chosen, and an embedded alphabet extension for coding of low-entropy image regions. LOCO-I attains compression ratios similar or superior to those obtained with state-of-the-art schemes based on arithmetic coding. Moreover, it is within a few percentage points of the best available compression ratios, at a much lower complexity level. We discuss the principles underlying the design of LOCO-I, and its standardization into JPEG-LS.

Algorithms for approximately optimal quantization of color images are discussed. The distortion measure used is the distance in RGB space. These algorithms are used to compute the color map for low-depth frame buffers in order to allow high-quality static images to be displayed. It is demonstrated that most color images can be very well displayed using only 256 or 512 colors. Thus frame buffers of only 8 or 9 bits can display images that normally require 15 bits or more per pixel. Work reported herein was sponsored by the IBM Corporation though a general grant agreement to MIT dated July 1, 1979. ----------------------------------------------------------------- TABLE OF CONTENTS page I. Introduction ............................................. 4 II. Frame Buffers and Colormaps .............................. 6 III. 1-Dimensional Tapered Quantization .......................17 IV. 3-Dimensional Tapered Quantization .......................27 V. Conclusions and Ideas for Further Study .......

Our thesis is that high compression efficiency for text and images can be obtained by using sophisticated statistical compression techniques, and that greatly increased speed can be achieved at only a small cost in compression efficiency. Our emphasis is on elegant design and mathematical as well as empirical analysis. We analyze arithmetic coding as it is commonly implemented and show rigorously that almost no compression is lost in the implementation. We show that high-efficiency lossless compression of both text and grayscale images can be obtained by using appropriate models in conjunction with arithmetic coding. We introduce a four-component paradigm for lossless image compression and present two methods that give state of the art compression efficiency. In the text compression area, we give a small improvement on the preferred method in the literature. We show that we can often obtain significantly improved throughput at the cost of slightly reduced compression. The extra speed c...

This paper deals with the use of some morphological tools for image and video coding. Mathematical morphology can be considered as a shape-oriented approach to signal processing and some of its features make it very useful for compression. Rather than describing a coding algorithm, the purpose of this paper is to describe some morphological tools that have recently proved to be attractive for compression. Four sets of morphological transformations are presented: connected operators, the region growing version of the watershed, the geodesic skeleton and a morphological interpolation technique. Their implementation will be discussed and we will show how they can be used for image and video segmentation, for contour coding and for texture coding. I. Introduction I MAGE and video compression techniques generally rely on the results of the information theory. In this framework, compression is achieved by a decorrelation of the signal followed by quantization and entropy coding of the infor...

The performance of unsupervised learning models for natural images is evaluated quantitatively by means of information theory. We estimate the gain in statistical independence (the multi-information reduction) achieved with independent component analysis (ICA), principal component analysis (PCA), zero-phase whitening, and predictive coding. Predictive coding is translated into the transform coding framework, where it can be characterized by the constraint of a triangular filter matrix. A randomly sampled whitening basis and the Haar wavelet are included into the comparison as well. The comparison of all these methods is carried out for different patch sizes, ranging from 2x2 to 16x16 pixels. In spite of large differences in the shape of the basis functions, we find only small differences in the multi-information between all decorrelation transforms (5% or less) for all patch sizes. Among the second-order methods, PCA is optimal for small patch sizes and predictive coding performs best for large patch sizes. The extra gain achieved with ICA is always less than 2%. In conclusion, the `edge filters‘ found with ICA lead only to a surprisingly small improvement in terms of its actual objective.

While lossy image compression techniques are vital in reducing bandwidth and storage requirements, they result in distortions in compressed images. A reliable quality measure is a much needed tool for determining the type and amount of image distortion. The traditional subjective criteria, which involve human observers, are inconvenient, time-consuming, and influenced by environmental conditions. Widely used pixelwise measures such as the mean square error (MSE) cannot capture the artifacts like blurriness or blockiness, and do not correlate well with visual error perception. Attempts to improve quality measurement include incorporation of simple models of the human visual system (HVS) and multi-dimensional tool design. We review the criteria for monochrome compressed image quality from 1974 to 1999.

Abstract—Based on the observation that a Cauchy density is more accurate in estimating the distribution of the ac coefficients than the traditional Laplacian density, rate and distortion models with improved accuracy are developed. The entropy and distortion models for quantized discrete cosine transform coefficients are justified in a frame bit-allocation application for H.264. Extensive analysis with carefully selected anchor video sequences demonstrates a 0.24-dB average peak signal-to-noise ratio (PSNR) improvement over the JM 8.4 rate control algorithm, and a 0.33-dB average PSNR improvement over the TM5-based bit-allocation algorithm that has recently been proposed for H.264 by Li et al. The analysis also demonstrates 20 % and 60% reductions in PSNR variation among the encoded pictures when compared to the JM 8.4 rate control algorithm and the TM5-based bit-allocation algorithm, respectively. Index Terms—Advanced video coding, bit allocation, H.264, rate control, rate and distortion modeling. I.