Rate distortion in image coding from embedded optimization constraints in vector quantization

Statistical as well as adaptive clustering approaches are being currently used for both segmentation and vector quantization of medical images. However, a comparative evaluation of both approaches has rarely been done to identify the efficacy of such approaches to specific applications, for example, image segmentation and vector quantization. The rate distortion functions of three clustering algorithms, namely, the statistical based deterministic annealing, the adaptive fuzzy leader clustering algorithm, and LBG, have been computed for vector quantization using multi-scale vectors in the wavelet domain. Such comparative evaluation serves as a guide for proper selection of clustering algorithms for global codebook generation in vector quantization and for image segmentation.

Vector quantization (VQ) has been extensively used in image coding systems. However, when the communications system involves a noise channel, it is well known that VQ is highly sensitive to channel errors. As a consequence, a considerable degradation may be introduced in the reconstructed images. In the present paper, simulated annealing (SA) is applied to robust VQ, that is, it is used for assigning binary indexes to the VQ code vectors, as an attempt to circumvent the effect of channel errors. Simulations involving image transmission through a Rayleigh fading channel clearly indicate the suitability of SA. The authors also show that an additional improvement can be obtained by using an alternative initialization of the SA algorithm.

Image compression is a basic need for the progressive transmission or storage of image data via any media. For the effective processing of image data the coding standards were developed. The most commonly used standard in current scenario is the JPEG and JPEG-2000 coding. These standards have become the industry standards and are progressively been in use for almost all image processing applications. In the process of image coding various sub-processing operations occur which process the image blocks by transformation, quantization and encoding before transmitting or storing. In the process, quantization is observed to be a time consuming and is needed to be processed in high precision so as to achieve less processing error and also in reasonable time. The process of quantization has shown greater efficiency in vector quantization than earlier methods. Vector quantization is observed to be an efficient block based lossy compression technique. Due to simpler coding process and high compression ratio VQ are widely used. Predictive vector Quantization (PVQ) is commonly used memory based vector Quantization method. The main drawback with PVQ is the high computational complexity which limits PVQ to use in real time applications. Shorter coding time can be archived by reducing the number of code words or instructions, but the reconstructed image quality will degraded in the case of fewer code words. Hence, it is necessary to propose fast coding algorithms for PVQ. In this paper a modified version of the PVQ approach has been suggested in order to process faster, which ensue to be a compatible mechanism for real time image coding in JPEG based coding system. Keywords: Compression, quantization, PVQ encoder, mean-square-error, Discrete Cosine Transform.

Multistage vector quantization (MSVQ) can achieve very low encoding and storage complexity in comparison to unstructured vector quantization. However, the conventional stage-by-stage design of the codebooks in MSVQ is suboptimal with respect to the overall performance measure. The generation of codebooks from a set of training vectors using simulated annealing (SA) can converge to the globally optimal codebook in finite time. In this paper, SA is combined with MSVQ for optimizing the overall performance. The algorithm of multistage vector quantization based on simulated annealing (MSVQ-SA) for image coding is presented. Experimental results show that MSVQ-SA technique results in significantly better quantizer performance than that obtained with SA and MSVQ.

Efficient greyscale image compression technique based on vector quantization

The fidelity of the reconstructed image in an image coding/decoding scheme and the lowest transmission bit rate from rate-distortion theory can be predicted provided the image statistics are known. Currently popular subband image coding assumes Gaussian source with memory for optimal performance. However, most images do not follow the ideal distribution. The advantage of subband coding lies in the fact that the wavelet coefficients in decomposed subimages have probability distribution functions (pdf's) that can be modeled as a generalized Gaussian when proper parameters are chosen experimentally. However, the filter length chosen for digital implementation of a specific wavelet is crucial in shaping the pdf characteristics and hence in the ability to predict the achievable bit rate at minimum distortion in a quantization scheme. We have analyzed the pdf's of a number of wavelets and chosen filter lengths providing the best fit to a generalized Gaussian distribution for encoding an image by vector quantization of multiresolution wavelet subimages using an adaptive clustering. Our results demonstrate that the performance of the adaptive vector quantizer improves significantly when wavelet filter lengths are chosen to fit the generalized Gaussian distribution.

In this paper, we propose novel progressive scalable region of interest (ROI) image compression schemes with rate, distortion, and complexity trade-off based on vector quantization. The proposed schemes are unbalanced in the sense that the decoder has less computational requirements than the encoder. Moreover, the proposed method provides an interactive tool for fast ROI based browsing from image archives. Residual vector quantization (RVQ) equips the encoder with a multi-resolution apparatus which is useful for rate-distortion trade-of. Having all the advantages of RVQ, jointly sub-optimized RVQ provides a distortion-complexity adjustment. Since the bitstreams associated with the earlier stages of the RVQ encoder are more important for the reconstructed image quality than that of the later stages, an unequal error protection scheme, base on Reed-Solomon codes, has been considered to protect the transmitted bitstream against channel noise.

Vector quantization and fuzzy ranks for image reconstruction

An image that is mapped into a bit stream suitable for communication over or storage in a digital medium is said to have been compressed. Using tree-structured vector quantizers (TSVQs) is an approach to image compression in which clustering algorithms are combined with ideas from tree-structured classification to provide code books that can be searched quickly and simply. The overall goal is to optimize the quality of the compressed image subject to a constraint on the communication or storage capacity, i.e. on the allowed bit rate. General goals of image compression and vector quantization are summarized in this paper. There is discussion of methods for code book design, particularly the generalized Lloyd algorithm for clustering, and methods for splitting and pruning that have been extended from the design of classification trees to TSVQs. The resulting codes, called pruned TSVQs, are of variable rate, and yield lower distortion than fixed-rate, full-search vector quantizers for a given average bit rate. They have simple encoders and a natural successive approximation (progressive) property. Applications of pruned TSVQs are discussed, particularly compressing computerized tomography images. In this work, the key issue is not merely the subjective attractiveness of the compressed image but rather whether the diagnostic accuracy is adversely aflected by compression. In recent work, TSVQs have been combined with other types of image processing, including segmentation and enhancement. The relationship between vector quantizer performance and the size of the training sequence used to design the code and other asymptotic properties of the codes are discussed.

We deal with zero-delay source coding of a vector-valued Gauss-Markov source subject to a mean-squared error (MSE) fidelity criterion characterized by the operational zero-delay vector-valued Gaussian rate distortion function (RDF). We address this problem by considering the nonanticipative RDF (NRDF) which is a lower bound to the causal optimal performance theoretically attainable (OPTA) function and operational zero-delay RDF. We recall the realization that corresponds to the optimal "test-channel" of the Gaussian NRDF, when considering a vector Gauss-Markov source subject to a MSE distortion in the finite time horizon. Then, we introduce sufficient conditions to show existence of solution for this problem in the infinite time horizon. For the asymptotic regime, we use the asymptotic characterization of the Gaussian NRDF to provide a new equivalent realization scheme with feedback which is characterized by a resource allocation (reverse-waterfilling) problem across the dimension of the vector source. We leverage the new realization to derive a predictive coding scheme via lattice quantization with subtractive dither and joint memoryless entropy coding. This coding scheme offers an upper bound to the operational zero-delay vector-valued Gaussian RDF. When we use scalar quantization, then for "r" active dimensions of the vector Gauss-Markov source the gap between the obtained lower and theoretical upper bounds is less than or equal to 0.254r + 1 bits/vector. We further show that it is possible when we use vector quantization, and assume infinite dimensional Gauss-Markov sources to make the previous gap to be negligible, i.e., Gaussian NRDF approximates the operational zero-delay Gaussian RDF. We also extend our results to vector-valued Gaussian sources of any finite memory under mild conditions. Our theoretical framework is demonstrated with illustrative numerical experiments.

Software components analysis is a critical technique for software development and maintenance. Clustering techniques have been widely used in grouping related software components. However, software is complex, but clustering techniques used in software engineering typically adopt only one metric to measure the similarity of components. This paper proposes an adaptive fuzzy clustering technique based on possibilistic clustering algorithms to address the issue of single metric. The proposed technique collaboratively considers distance, density, and the trend of density change of component instances in the membership degree calculation. The post clustering separation of clustered components based on the predefined thresholds and regrouping of the separated component points result in higher cohesive clustering. The proposed algorithm has been evaluated via experiments using a network protocol RSVP-TE system. The comparison of Hierarchical, Self-organizing map (SOM), and fuzzy c-means (FCM) against adaptive fuzzy clustering proposed in this paper indicates that the adaptive fuzzy clustering group software component instances into more cohesive clusters while it is also insensitive to parameter settings.

A vector quantizer maps a <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">k</tex> -dimensional vector into one of a finite set of output vectors or "points". Although certain lattices have been shown to have desirable properties for vector quantization applications, there are as yet no algorithms available in the quantization literature for building quantizers based on these lattices. An algorithm for designing vector quantizers based on the root lattices <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">A_{n}, D_{n}</tex> , and <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">E_{n}</tex> and their duals is presented. Also, a coding scheme that has general applicability to all vector quantizers is presented. A four-dimensional uniform vector quantizer is used to encode Laplacian and gamma-distributed sources at entropy rates of one and two bits/sample and is demonstrated to achieve performance that compares favorably with the rate distortion bound and other scalar and vector quantizers. Finally, an application using uniform four- and eight-dimensional vector quantizers for encoding the discrete cosine transform coefficients of an image at <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0.5</tex> bit/pel is presented, which visibly illustrates the performance advantage of vector quantization over scalar quantization.

Rate distortion theory is one of the areas of information transmission theory with important applications in multimodal signal processing, as for example image processing, information bottleneck and steganalysis. This article present an image characterization method based on rate distortion analysis in the feature space. This space is coded using clustering as vector quantization (k-means). Since image information usually cannot be coded by single clusters, because there are image regions corresponding to groups of clusters, the rate and distortion are specifically defined. The rate distortion curve is analyzed, extracting specific features for implementing a database image classification system.

Segmentation of images into textural homogeneous regions is a fundamental problem in an image understanding system. Most region-oriented segmentation approaches suffer from the problem of different thresholds selecting for different images. In this paper an adaptive image segmentation based on vector quantization is presented. It automatically segments images without preset thresholds. The approach contains a feature extraction module and a two-layer hierarchical clustering module, a vector quantizer (VQ) implemented by a competitive learning neural network in the first layer. A near-optimal competitive learning algorithm (NOLA) is employed to train the vector quantizer. NOLA combines the advantages of both Kohonen self- organizing feature map (KSFM) and K-means clustering algorithm. After the VQ is trained, the weights of the network and the number of input vectors clustered by each neuron form a 3- D topological feature map with separable hills aggregated by similar vectors. This overcomes the inability to visualize the geometric properties of data in a high-dimensional space for most other clustering algorithms. The second clustering algorithm operates in the feature map instead of the input set itself. Since the number of units in the feature map is much less than the number of feature vectors in the feature set, it is easy to check all peaks and find the `correct' number of clusters, also a key problem in current clustering techniques. In the experiments, we compare our algorithm with K-means clustering method on a variety of images. The results show that our algorithm achieves better performance.

Conventional RF image formation relies on a fixed waveform set that is based largely on obtaining maximum resolution for a given amount of bandwidth present in a waveform. However, the correlation process for a given waveform set varies widely depending on the cross correlation properties of the waveform and the geometry of the aperture interrogating the object to be imaged. We propose a method that maximizes quality of the imagery being reconstructed based by first using an orthogonal basis to minimize the unwanted correlation response for the waveform. We then shape the frequency and temporal correlation response of the waveform for a given target using a rate distortion criteria and demonstrate the performance of the method.