This paper describes a study on texture segmentation based on a two-dimensional linear prediction method. The principle that the division of an image which gives the minimum of the total sum of final prediction errors over the whole image corresponds to the true segmentation is shown if each texture region consisting the image can be assumed to be a homogeneous gaussian random field. An edge detection method which is based on the principle is also given. Although this method needs a great amount of computation, a practical procedure of computation using Dynamic Programming is developed. The effectiveness of this edge detection method is demonstrated experimentally.