For progressive transmission, the limited data streams with high encoding efficiency seem to impose a limit on the sustainable number of significant coefficients to which we can allocate bits with efficiency. But sustained improvement in transmission technology over time can offset the effects of wasting and nonreplenishable data and provide high encoding efficiency for progressive transmission. Here we show necessary and sufficient conditions for steady growth in encoding efficiency.
Under oscillatory behavior of the net profit of transmission over time, heavy losses may be incurred in the form of foregone opportunities in the future if the transmission system prefers to transmit low-cost bit resources at this time over conserving for the future. This oscillatory behavior over time necessitates devising a stabilizing scheme for its optimal use in the transmission. Here we examine an optimal bit-saving path over time. During an initial period, the transmission system prioritizes exhaustible bit reserves of low transmission cost at the maximum available capacity and allocates gross transmission income partly to transmission and the rest is saved and invested to increase the degree of knowledge; and in the second period, once these low-cost bit reserves are exhausted, it is necessary to switch to a source of transmission solely from returns on current degree of knowledge, which initially includes highly insignificant bit streams. For knowledge-poor transmission systems the optimal bit-saving path differs sharply from that for region-based approaches with higher share of knowledge in the transmission's initial wealth. Also, the bit-saving path is highly dependent on the low-cost bitstreams life. We give a comparison in performance of the state of the art codec in progressive transmission against an algorithm which implements the saving path. It appears that the bit saving may be used with acceptable image fidelity.
Current video encoding methods base their decisions (which sequence of bits must be sent at each instant t) on a single knowledge base throughout all transmission times (in most cases, the knowledge is based on energy values, so coefficients with higher energy are prioritized over to those with lower energy). This way, there are no mechanisms working simultaneously with, or in parallel with, the transmission process and imposing the need to modify the knowledge base in accordance with the requirements of the transmission process (sending the information that will produce the best possible quality per bit transmitted). Since the knowledge base is conceived statically (it does not change over time), there will come a time when all information to be transmitted is of equal relevance, even though there may still be differences in that information. Based on this reasoning, we propose a video compression method with automatic internal mechanisms that make it possible to specify a knowledge base (containing the optimal sequences to be sent for each quantizer) at each instant of the transmission process. The methodology is based on a hierarchical quantizer decomposition. In the first level we have quantizers with an high linear velocity, and in the second level, quantizers with high energy. We automatically select the best decomposition by minimizing the cost of coding the information. Comparisons with the state of the art in video coding show the advantages of the approach.
The study of the dynamics of an exploratory effort to build knowledge for progressive transmission shows that if initial knowledge about information of interest is large, most exploration to increase the knowledge base can be postponed to higher bit rates, with independence of transmission costs. On the contrary, if proved knowledge is initially small, high exploratory effort must occur at extremely low bit rates so as to increase the inventory of proved knowledge about relevant visual information. From the dynamics of exploratory effort, it follows a hierarchical quantizer partition tree at a near optimal level of exploratory effort until near the end of the progressive transmission without the necessity for any additional exploratory effort. We show an example of the application of this hierarchical quantizer partition tree for progressive transmission of video sequences, where interquantizer prioritization follows a novel hierarchical bit allocation algorithm.
The transmission system must simultaneously determine transmission rates that balance total profit from bit allocation with transmission costs. The objective is to maximize the present value of the satisfaction derived from progressive transmission over the future, subject to constraints imposed by the initial conditions and the prioritization and transmission technologies. The analytical results demonstrate an oscillatory behavior over time of the rent component of profit depending on the incremental cost of cumulative transmission and not the current marginal transmission cost. This oscillatory behavior of rent over time necessitates devising a stabilizing scheme for its optimal use in the transmission.
Bit allocation analysis is concerned with the study of efficient combinations of quantizer-based allocations and bit consumption by a model capable of numerical application. The modus operandi of bit-allocation analysis is the use of set theory and the fundamental theorems of mathematical optimization. The most important concept in this analysis is the efficient allocation process, which represents a combination of quantizer-based allocations and bit consumption such that no bit allocation of a quantizer can be increased without decreasing another quantizer's allocation or increasing consumption. The main result of this paper allows one to characterize the concept of efficient allocation process by profit maximization with respect to any allocation-consumption combination among competing quantizers. In bit allocation analysis, the system makes a choice from the set of efficient allocations at any given time by using the appropriate strategy for computing the profit vector. It may allow attending to different parameters of interest at different bit rates within the same spatial locations. It is a typical linear programming problem, for which computational methods are well known and widely used in practice. The comparative performance of the 3-D set partitioning in hierarchical trees with motion-compensated temporal filtering and the proposed coder (without motion filtering) using bit allocation analysis is here evaluated on a set of sequences of moving targets.
We propose a video coding scheme to improve moving-target detection at very low bit rate, based on two key features: energy-based quantizer formation, and optimized interquantizer and intraquantizer prioritization. Rational Embedded Wavelet Video Coding (REVIC) is a fully implemented software video codec of low complexity and without motion compensated filtering to provide additional simplicity, adaptivity, and error resilience. It is shown to be quite effective in video coding of moving targets (e.g., military vehicles) at very low bit rates, while retaining the attributes of complete embeddedness for progressive transmission and scalability by fidelity and resolution. The proposed coding technique improves the explanatory power of decoded sequences (to achieve maximum target detection versus bit-rate performance) for a video compression system. The explanatory power of compressed sequences is important in surveillance applications, where trained video analysts may utilize decoded sequences to support decision processes in strategic, operational, and tactical tasks.
We offer a method for the a priori evaluation of the division of power among the various wavelet coefficients when they are used to reconstruct the original scene through a prioritization protocol. The method is based on applying a technique of the mathematical theory of games to social power. The analysis is fairly general and not specific to wavelet transform configurations. It is equally applicable to linearly spaced subband decompositions, and to other more general subband decompositions, such as wavelet packets and Laplacian pyramids. Here we show a prioritization protocol based on the utility-per-coding-bit optimization that is consistent with the power distribution imposed by the set partitioning sorting algorithm on the set of wavelet coefficients.
In the absence of a priori knowledge about regions of interest, does dysfunctional behavior in the subband pyramid lead to the emergence of a region-based approach to image transmission as complexity grows? A model of image transmission that links simplification of information and time to produce a transmission plan to the bit-rate cost of the transmission, and where the decoded output is affected negatively by those factors that reduce the quality of the transmission plan and delay its preparation, answers the question in two steps. First, we characterize the variables (degrees of simplification and subordination) through which we expect to control, at any truncation time, the optimum transmission system. We observe that transform-domain coefficients exhibit self-seeking behavior if errors that result from the transmission plan increase as the distance of the coefficient from the top of the hierarchy grows. Then we use the degree of detail that arrives at the central control in any system of progressive transmission to derive conditions under which the likelihood of emergence of a region-based approach to progressive transmission grows with the increase of complexity of the picture. We find that the presence of self-seeking coefficients leads to a higher likelihood of emergence of a region-based approach as complexity rises. On a data set composed of 100 standard gray-scale test images, 26% of the test images exhibit self-seeking behavior, from very low bit rates, using the state of the art codec based on set partitioning in hierarchical trees.
In rational progressive transmission, the spatial orientation trees define the relationship on the pyramid that results from the wavelet transformation. Each tree is associated with one subregion of the original image. The trees may by grouped together into a reduced number of quantizers that convey structural information about the picture to the transmission system. We propose a quantizer formation that will give neither tree a cause for "reasonable regret" in rational progressive transmission. In this sense, we call it a "just" quantizer formation. We introduce the basic concept of "reasonable regret" for justice and give conditions for a just quantizer formation. We show that the definition of a priori importance of a spatial orientation tree is pivotal in the development of a theory for just quantizer formation. The estimation of the a priori importance of a tree must be solved using a large number of insignificant wavelet coefficients—as measured by their magnitudes—that are still effective via coalitions for the reconstruction of the tree. This problem falls into the realm of cooperative game theory with one exogenously given communication graph that results from the wavelet transformation. We provide a cooperative game in this particular communication situation, named after the "SOT-Restricted Game" that naturally induces a game-theoretic solution to the estimation problem: the "zerotree" solution of an SOT-restricted game. Experimental results illustrate the comparative performance of the rational progressive transmission with a just quantizer formation against the state of the art in progressive transmission.
The authors present a sound, practical approach to information prioritization in progressive image transmission. The method, suitable for a variety of imaging applications from consumer products to the defense, publishing, science, and law enforcement industries, first states some general principles that the solution must obey and then derives the solution that satisfies exactly those principles. The text is intended for graduate students as well as engineers and research scientists in the field of image coding.
KEYWORDS: Visualization, Image filtering, Visual process modeling, Sensors, Target detection, Image processing, Digital imaging, Distortion, Image sensors, Signal to noise ratio
This book, originally published February 8th, 2001, has been republished as an eBook October 21st, 2022.
The more a target stands out from its background, the easier it is to detect and the quicker it will be found. This book looks at two situations for predicting visual target distinctness by means of a computer vision model.
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