Fast method of geometric picture transformation using logarithmic number systems and its applications for computer graphics

Tomio Kurokawa; Takanari Mizukoshi

doi:10.1117/12.24162

1 September 1990 Fast method of geometric picture transformation using logarithmic number systems and its applications for computer graphics

Tomio Kurokawa, Takanari Mizukoshi

Author Affiliations +

Proceedings Volume 1360, Visual Communications and Image Processing '90: Fifth in a Series; (1990) https://doi.org/10.1117/12.24162
Event: Visual Communications and Image Processing '90, 1990, Lausanne, Switzerland

Abstract

Logarithmic arithmetic (LA) is a very fast computational method for real numbers. And its computation precision is much better than a floating point arithmetic of equivalent word length and range. This paper shows a method of fixed point number computations by LA—just to do numeric conversion before and after LA computations. It is used to handle discrete coordinate addresses and pixel intensity data of digital images. The geometrical transformation is a typical application of the method. Linear (affine) and non-linear transformations with three interpolations of "nearest neighbor,” ”bi-linear” and "cubic convolution” in LA are demonstrated. It is the processing of coordinate addresses and pixel intensities of fixed point numbers. Experiments by 16-bit personal computer program showed that quality and speed are surprisingly high. The latter is comparable to that by using the floating point hardware chip. Some other examples of the applications are shown—curve drawing, three dimensional computer graphics and fractal image generation—all excellent.

Citation Download Citation

Tomio Kurokawa and Takanari Mizukoshi "Fast method of geometric picture transformation using logarithmic number systems and its applications for computer graphics", Proc. SPIE 1360, Visual Communications and Image Processing '90: Fifth in a Series, (1 September 1990); https://doi.org/10.1117/12.24162

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