On the Normal Distribution in the Orientation Space

The properties of model distributions used in texture analysis up to now are discussed. The normal distribution in the G-space (recently investigated by T. I. Savjolova) is analysed. Its connection with the central limit theorem of probability theory is demonstrated in a mathematically simplified manner. An analytically closed approximative expression (with very high precision for halfwidths of practical interest) for the normal distribution is derived. Possible correlations between forms of texture components and mechanisms of texture development are mentioned.