The mixel is a heterogeneous pixel that contains multiple constituents within a single pixel, and the statistical properties of a population of mixels can be characterized by the mixel distribution. Practically this model has a drawback that it cannot be represented in closed form, and prohibitive numerical computation is required for mixture density estimation problem. Our discovery however shows that the ``moments'' of the mixel distribution can be derived in closed form, and this solution brings about significant reduction of computation cost for mixture density estimation after slightly modifying a typical algorithm. We then show the experimental result on satellite imagery, and find out that the modified algorithm runs more than 20 times faster than our previous method, but suffers little deterioration in classification performance.

      @InProceedings{ k:spr00,
      author = {Asanobu KITAMOTO},
      title = {The Moments of the Mixel Distribution and Its Application to Statistical Image Classification},
      booktitle = {Advances in Pattern Recognition (SPR'00), Lecture Notes in Computer Science (LNCS) 1876},
      pages = {521-531},
      publisher = {Springer},
      editor = {Amin, A. and Ferri, F.J. and Inesta, J.M., and Pudil, P.},
      year = 2000,
      month = 8,
      doi = {10.1007/3-540-44522-6_54},
      note = {},
      }