  Topic models (e.g., pLSA, LDA, sLDA) have been widely used for segmenting
imagery. However, these models are confined to crisp segmentation, forcing a
visual word (i.e., an image patch) to belong to one and only one topic. Yet,
there are many images in which some regions cannot be assigned a crisp
categorical label (e.g., transition regions between a foggy sky and the ground
or between sand and water at a beach). In these cases, a visual word is best
represented with partial memberships across multiple topics. To address this,
we present a partial membership latent Dirichlet allocation (PM-LDA) model and
an associated parameter estimation algorithm. This model can be useful for
imagery where a visual word may be a mixture of multiple topics. Experimental
results on visual and sonar imagery show that PM-LDA can produce both crisp and
soft semantic image segmentations; a capability previous topic modeling methods
do not have.
