IDENTIFICATION OF OBJECTS OF COMPLEX SHAPE BY USING STOCHASTIC LOCAL FRACTAL VARIABLES - CATEGORIZING DUST PARTICLES ON LSI WAFER SURFACE

When a natural object or phenomenon is modelled mathematically by usin g a fractal dimension, it is recognized that the object or phenomenon does not often have an autocorrelation. In the fractal theory, a fract al dimension is defined as a determined value (dimension) which is ind ependent of the scale of its covering. In practice, however, the dimen sion often fluctuates depending on samples used (even with the same ob ject or phenomenon) and its scale. In published works of image analyse s using fractal dimensions, it has been assumed that fractal dimension s are determined and independent of scales, ignoring the practical exp erience. To treat a natural object or phenomenon without contradiction s, this paper introduces ''stochastic local fractal variables.'' Using these new variables, mathematical models of dust on LSI wafers are co nstructed, and they are identified by using the likelihood method. Use fulness of the proposed method has successfully been confirmed with re al data.