1. A picture region extraction method, which extracts a desired region from picture data containing an image to be subjected to region extraction by classifying each pixel on the picture into a plurality of classes, comprising: a first step in which the data space constituted by all the attribute values that may be taken by said each pixel on said picture is divided into subspaces with a given resolution, a collection of pixels, each of which takes an attribute value in said each subspace, the average of the attribute values of said pixels, and the number of said pixels are retained to constitute a coarse-grained space; a second step in which the number of pixels in said each subspace is divided by the total number of pixels contained in said picture to calculate the coarse-grained empirical probability distribution in the coarse-grained data space; a third step in which the class parameter, the number of said classes, and the mixture ratio of said classes, which define the attributes of said each class, are initialized; a fourth step in which a conditional probability distribution under said class being specified is calculated from the class parameter that defines the attributes of said each class, and the conditional probability distribution under said class being specified is averaged within said each subspace to calculate a coarse-grained conditional probability distribution; a fifth step in which a class membership probability, which is the probability that each pixel constituting said picture belongs to said each class, is calculated by multiplying said class mixture ratio by said coarse-grained conditional probability distribution; a sixth step in which said class parameter and said class mixture ratio are updated so as to increase an evaluation function; a seventh step in which a coarse-grained log-likelihood is calculated as said evaluation function using said coarse-grained conditional probability distribution; an eighth step in which whether said evaluation function satisfies a given termination condition or not is examined; and a ninth step in which after said evaluation function satisfies said given termination condition, said class parameter and said class mixture ratio are retained, and the region each pixel belongs to is determined based on said class membership probability to extract said desired region, said fourth, fifth, sixth, seventh and eighth steps being repeated until said evaluation function satisfies said given condition.