An image pixel, generally assumed to be the smallest element of imagery, may actually be a mixture of multiple constituents. To establish a probabilistic model for such a heterogeneous pixel called a mixel, we propose a novel probabilistic model, area proportion distribution, which is the distribution of the area proportions for a population of mixels. Next we investigate the properties of this model in association with the internal structure of mixels. This model has been implicitly assumed to be the uniform distribution; however, based on the results of theoretical distributions derived from figure models and of empirical distributions derived from fractal synthetic images, we propose Beta distribution as the generalized model of the area proportion distribution. We then incorporate this model into the finite mixture density model, and apply to the classification of satellite images. Finally the performance of our proposed model is evaluated to be superior using information criterion.

      @Article{ kt:scj00,
      author = {Asanobu KITAMOTO and Mikio TAKAGI},
      title = {Area Proportion Distribution -- Relationship with the Internal Structure of Mixels and its Application to Image Classification},
      journal = {Systems and Computers in Japan},
      volume = {31},
      number = {5},
      pages = {57-76},
      publisher = {John Wiley & Sons},
      year = 2000,
      month = 5,
      doi = {10.1002/(SICI)1520-684X(200005)31:5<57::AID-SCJ6>3.0.CO;2-1},
      note = { (in English)},
      }