Color image processing by using binary quaternion-moment-preserving thresholding technique

This paper presents a new moment-preserving thresholding technique, called the binary quaternion-moment-preserving (BQMP) thresholding, for color image data. Based on representing color data by the quaternions, the statistical parameters of color data can be expressed through the definition of quaternion moments. Analytical formulas of the BQMP thresholding can thus be determined by using the algebra of the quaternions. The computation time for the BQMP thresholding is of order of the data size. By using the BQMP thresholding, quaternion-moment-based operators are designed for the application of color image processing, such as color image compression, multiclass clustering of color data, and subpixel color edge detection. The experimental results show that the proposed operator for color image compression can have output picture quality acceptable to human eyes. In addition, the proposed edge operator can detect the color edge at the subpixel level. Therefore, the proposed BQMP thresholding can be used as a tool for color image processing.

[1]  Ja-Chen Lin,et al.  Feature-Preserving Clustering of 2-D Data for Two-Class Problems Using Analytical Formulas: An Automatic and Fast Approach , 1994, IEEE Trans. Pattern Anal. Mach. Intell..

[2]  Ja-Chen Lin,et al.  Color image sharpening by moment-preserving technique , 1995, Signal Process..

[3]  E.E. Pissaloux,et al.  Image Processing , 1994, Proceedings. Second Euromicro Workshop on Parallel and Distributed Processing.

[4]  Keith Phillips,et al.  Applications of Vector Fields to Image Processing , 1983, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[5]  Anil K. Jain.  Fundamentals of Digital Image Processing , 2018, Control of Color Imaging Systems.

[6]  Glenn Healey,et al.  Segmenting images using normalized color , 1992, IEEE Trans. Syst. Man Cybern..

[7]  Paul M. Weichsel,et al.  A first course in abstract algebra , 1966 .

[8]  H. V. Trees.  Detection, Estimation, And Modulation Theory , 2001 .

[9]  A. Gualtierotti.  H. L. Van Trees, Detection, Estimation, and Modulation Theory, , 1976 .

[10]  Hisashi Kobayashi,et al.  Modeling and analysis , 1978 .

[11]  David C. Coll,et al.  Single Bit-Map Block Truncation Coding of Color Images , 1992, IEEE J. Sel. Areas Commun..

[12]  Wen-Hsiang Tsai,et al.  Moment-preserving thresolding: A new approach , 1985, Comput. Vis. Graph. Image Process..

[13]  E. Parzen.  1. Random Variables and Stochastic Processes , 1999 .

[14]  Paul S. Heckbert.  Color image quantization for frame buffer display , 1982, SIGGRAPH.

[15]  Ling-Hwei Chen,et al.  Moment-preserving curve detection , 1988, IEEE Trans. Syst. Man Cybern..

[16]  Wen-Hsiang Tsai,et al.  Moment-preserving thresholding: a new approach , 1995 .

[17]  Athanasios Papoulis,et al.  Probability, Random Variables and Stochastic Processes , 1965 .

[18]  John B. Fraleigh.  A first course in abstract algebra , 1967 .

[19]  Chrysostomos L. Nikias,et al.  Parameter estimation of exponentially damped sinusoids using higher order statistics , 1990, IEEE Trans. Acoust. Speech Signal Process..

[20]  J. Wolfowitz,et al.  An Introduction to the Theory of Statistics , 1951, Nature.

[21]  Soo-Chang Pei,et al.  A fast two-class classifier for 2D data using complex-moment-preserving principle , 1996, Pattern Recognit..

[22]  Owen Robert Mitchell,et al.  Edge Location to Subpixel Values in Digital Imagery , 1984, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[23]  W. M. Carey,et al.  Digital spectral analysis: with applications , 1986 .

[24]  P.K Sahoo,et al.  A survey of thresholding techniques , 1988, Comput. Vis. Graph. Image Process..

[25]  Bruno O. Shubert,et al.  Random variables and stochastic processes , 1979 .

[26]  Averill M. Law,et al.  Simulation Modeling and Analysis , 1982 .

[27]  Wen-Hsiang Tsai,et al.  Moment-preserving corner detection , 1990, Pattern Recognit..

[28]  Hsien-Che Lee,et al.  Detecting boundaries in a vector field , 1991, IEEE Trans. Signal Process..