• Journal of the Korea Society of Computer and Information
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• v.20 no.12
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• pp.9-14
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• 2015

In this paper, we present an color quantization method by complementing the disadvantage of K-means color quantization that is one of the well-known color quantization. We named the proposed method "octree-means" color quantization. K-means color quantization does not use all of the clusters because it initializes the centroid of clusters with random value. The proposed method complements this disadvantage by using the octree color quantization which is fast and uses the distribution of colors in image. We compare the proposed method to six well-known color quantization methods on ten test images to evaluate the performance. The experimental results show 68.29 percent of mean square error(MSE) and processing time increased by 14.34 percent compared with K-means color quantization. Therefore, the proposed method improved the K-means color quantization and perform an effective color quantization.

• ETRI Journal
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• v.45 no.1
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• pp.119-130
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• 2023

We propose a quantized gradient search algorithm that can achieve global optimization by monotonically reducing the quantization step with respect to time when quantization is composed of integer or fixed-point fractional values applied to an optimization algorithm. According to the white noise hypothesis states, a quantization step is sufficiently small and the quantization is well defined, the round-off error caused by quantization can be regarded as a random variable with identically independent distribution. Thus, we rewrite the searching equation based on a gradient descent as a stochastic differential equation and obtain the monotonically decreasing rate of the quantization step, enabling the global optimization by stochastic analysis for deriving an objective function. Consequently, when the search equation is quantized by a monotonically decreasing quantization step, which suitably reduces the round-off error, we can derive the searching algorithm evolving from an optimization algorithm. Numerical simulations indicate that due to the property of quantization-based global optimization, the proposed algorithm shows better optimization performance on a search space to each iteration than the conventional algorithm with a higher success rate and fewer iterations.

• Bulletin of the Korean Chemical Society
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• v.32 no.12
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• pp.4233-4238
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• 2011

Based on the exact quantization rule for the nonrelativistic Schrodinger equation, the exact quantization rule for the relativistic one-dimensional Klein-Gordon equation is suggested. Using the new quantization rule, the exact relativistic energies for exactly solvable potentials, e.g. harmonic oscillator, Morse, and Rosen-Morse II type potentials, are obtained. Consequently the new quantization rule is found to be exact for one-dimensional spinless relativistic quantum systems. Though the physical meanings of the new quantization rule have not been fully understood yet, the present formal derivation scheme may shed light on understanding relativistic quantum systems more deeply.

• Journal of the Korean Institute of Telematics and Electronics C
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• v.34C no.11
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• pp.20-28
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• 1997

In this paper, quantization and inverse quantizatio unit, a sa component of MPEG-2 moving picture compression system, ar edesigned. In the processing of quantization, this design adopted newly designed arithmetic units in which quantization matrices and scale code was expressed with SD(signed-digit) code. In the arithmetic unit of inverse quantization, quantization scale code, which has 5-bits length, is splited into two pieces; 2-bits for control code, 3-bits for quantization data, and the method to devise quantization step size is proposed. The design was coded with VHDL and synthesis results in that it consumed about 6,110 gates, and operating speed is 52MHz.

• Communications of the Korean Mathematical Society
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• v.38 no.2
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• pp.431-450
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• 2023

The basic goal of quantization for probability distribution is to reduce the number of values, which is typically uncountable, describing a probability distribution to some finite set and thus to make an approximation of a continuous probability distribution by a discrete distribution. It has broad application in signal processing and data compression. In this paper, first we define the uniform distributions on different curves such as a line segment, a circle, and the boundary of an equilateral triangle. Then, we give the exact formulas to determine the optimal sets of n-means and the nth quantization errors for different values of n with respect to the uniform distributions defined on the curves. In each case, we further calculate the quantization dimension and show that it is equal to the dimension of the object; and the quantization coefficient exists as a finite positive number. This supports the well-known result of Bucklew and Wise [2], which says that for a Borel probability measure P with non-vanishing absolutely continuous part the quantization coefficient exists as a finite positive number.

• Journal of the Korean Institute of Telematics and Electronics B
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• v.30B no.9
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• pp.54-63
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• 1993

Quantization error, generated by the quantization process of an image, is inherent in computer vision. Because, especially in stereo vision, the quantization error in a 2-D image results in position errors in the reconstructed 3-D scene, it is necessary to analyze it mathematically. In this paper, the analysis of the probability density function (pdf) of quantization error for a line-based stereo matching scheme is presented. We show that the theoretical pdf of quantization error in the reconstructed 3-D position information has more general form than the conventional analysis for pixel-based stereo matching schemes. Computer simulation is observed to surpport the theoretical distribution.

• ETRI Journal
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• v.23 no.1
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• pp.16-22
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• 2001

Efficient quantization methods of the line spectrum pairs (LSP) which have good performances, low complexity and memory are proposed. The adaptive quantization range method utilizing the ordering property of LSP parameters is used in a scalar quantizer and a vector-scalar hybrid quantizer. As the maximum quantization range of each LSP parameter is varied adaptively on the quantized value of the previous order's LSP parameter, efficient quantization methods can be obtained. The proposed scalar quantization algorithm needs 31 bits/frame, which is 3 bits less per frame than in the conventional scalar quantization method with interframe prediction to maintain the transparent quality of speech. The improved vector-scalar quantizer achieves an average spectral distortion of 1 dB using 26 bits/frame. The performances of proposed quantization methods are also evaluated in the transmission errors.

• Journal of the Korea Institute of Military Science and Technology
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• v.14 no.2
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• pp.281-288
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• 2011

In this paper, a variable quantization coefficient scanning for macroblock considering the histogram value of previous macroblock's quantization coefficient is proposed. In order to scan a quantization coefficient, the proposed method makes $4{\times}4$ histograms for various prediction modes($16{\times}16$, $16{\times}8$, $8{\times}16$, $8{\times}8$) by adding 1 if the value of quantization coefficient is not 0. After a final mode decision procedure, the $4{\times}4$ histogram of the final mode will be sorted. Then, quantization coefficients in corresponding macroblock of the next frame are scanned using the sorted order. The experimental results show that the proposed scheme reduces the total bits by approximately 0.01~2.25% with similar PSNR performance compared with the previous method.

• The Journal of the Acoustical Society of Korea
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• v.29 no.4
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• pp.286-293
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• 2010

There are two major conventional quantization algorithms: resolution-constrained quantization (RCQ) and entropy-constrained quantization (ECQ). Although RCQ works well for fixed transmission-rate, it produces the distortion outliers since the cell sizes are different. Compared with RCQ, ECQ has the constraints on the cell size but it produces the rate outliers. We propose the cell-size constrained vector quantization (CCVQ) that improves the generalized Lloyd algorithm (GLA). The CCVQ algorithm is able to make a soft-decision between RCQ and ECQ by using the flexible penalty measure according to the cell size. Although the proposed method increases the small amount of overall mean-distortion, it can reduce the distortion outliers.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.21 no.7
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• pp.1685-1695
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• 1996

The postprocessing of compressed images based on the projections onto convex sets and the constrained minimization imposes several constraints on the procesed data. The quantization constraint has been commonly used in various algorithms. Quantization is many-to-one mapping, by which all the dat in a quantization region are mapped to the corresponding representative level. The basic idea behind the projection onto the QCS(quantization constraint set) is to prevent the processed data from diverging from the original quantization region in order to redue the artifacts caused by filtering in postprocessing. However, there have been few efforts to analye the POQCS(projection onto the QCS). This paper analyzed mathematically the POQCS of filtered data from the viewpoint of minimizing the mean square error. Our analysis shows that a proper filtering technique followed by the POQCS can reduce the quantization distortion. In the conventional POQCS, the outside data of each quantization region are mapped into the corresponding boundary. Our analysis also shows that mappingthe outside data to the boundary of a subregion of the quantization region yields lower distortion than does the mapping to the boundary of the original region. In addition, several examples and discussions on the theory are introduced.