Learning Montages of Transformed Latent Images as Representations of Objects That Change in Appearance
This paper introduces a novel probabilistic model for representing objects that change in appearance as a result of changes in pose, due to small deformations of their sub-parts and the relative spatial transformation of sub-parts of the object. We call the model a probabilistic montage. The model is based upon the idea that an image can be represented as a montage using many, small transformed and cropped patches from a collection of latent images. The approach is similar to that which might be employed by a police artist who might represent an image of a criminal suspect's face using a montage of face parts cut out of a "library" of face parts. In contrast, for our model, we learn the library of small latent images from a set of examples of objects that are changing in shape. In our approach, first the image is divided into a grid of sub-images. Each sub-image in the grid acts as window that crops a piece out of one of a collection of slightly larger images possible for that location in the image. We illustrate various probability models that can be used to encode the appropriate relationships for latent images and cropping transformations among the different patches. In this paper we present the complete algorithm for a tree-structured model. We show how the approach and model are able to find representations of the appearance of full body images of people in motion. We show how our approach can be used to learn representations of objects in an "unsupervised" manner and present results using our model for recognition and tracking purposes in a "supervised" manner.