Image analysis by counting on a grid

In recent object/scene recognition research images or large image regions are often represented as disorganized ”bags” of image features. This representation allows direct application of models of word counts in text. However, the image feature counts are likely to be constrained in different ways than word counts in text. As a camera pans upwards from a building entrance over its first few floors and then above the penthouse to the backdrop formed by the mountains, and then further up into the sky, some feature counts in the image drop while others rise–only to drop again giving way to features found more often at higher elevations (Fig. 1). The space of all possible feature count combinations is constrained by the properties of the larger scene as well as the size and the location of the window into it. Accordingly, our model is based on a grid of feature counts, considerably larger than any of the modeled images, and considerably smaller than the real estate needed to tile the images next to each other tightly. Each modeled image is assumed to have a representative window in the grid in which the sum of feature counts mimics the distribution in the image. We provide learning procedures that jointly map all images in the training set to the counting grid and estimate the appropriate local counts in it. Experimentally, we demonstrate that the resulting representation captures the space of feature count combinations more accurately than the traditional models, such as latent Dirichlet allocation, even when modeling images of different scenes from the same category.