One-shot Learning - Theory - Object Category Model

Object Category Model

For each query image and training images, a constellation model is used for representation. To obtain this model for a given image, first a set of N interesting regions is detected in the image using the Kadir brady saliency detector. Each region selected is represented by a location in the image, and a description of its appearance, . Letting and and the analogous representations for training images, the expression for R becomes:

The likelihoods and are represented as mixtures of constellation models. A typical constellation model has P(3 ~ 7) parts, but there are N(~100) interest regions. Thus a P-dimensional vector h assigns one region of interest (out of N regions) to each model part (for P parts). Thus h denotes a hypothesis (an assignment of interest regions to model parts) for the model and a full constellation model is represented by summing over all possible hypotheses h in the hypothesis space . Finally the likelihood is written

The different 's represent different configurations of parts, whereas the different hypotheses h represent different assignations of regions to parts, given a part model . The assumption that the shape of the model (as represented by, the collection of part locations) and appearance are independent allows one to consider the likelihood expression as two separate likelihoods of appearance and shape.