Neural Expectation Maximization

Many real world tasks such as reasoning and physical interaction require identification and manipulation of conceptual entities. A first step towards solving these tasks is the automated discovery of distributed symbol-like representations. In this paper, we explicitly formalize this problem as inference in a spatial mixture model where each component is parametrized by a neural network. Based on the Expectation Maximization framework we then derive a differentiable clustering method that simultaneously learns how to group and represent individual entities. We evaluate our method on the (sequential) perceptual grouping task and find that it is able to accurately recover the constituent objects. We demonstrate that the learned representations are useful for next-step prediction.Comment: Accepted to NIPS 201

Local and global gestalt laws: A neurally based spectral approach

A mathematical model of figure-ground articulation is presented, taking into account both local and global gestalt laws. The model is compatible with the functional architecture of the primary visual cortex (V1). Particularly the local gestalt law of good continuity is described by means of suitable connectivity kernels, that are derived from Lie group theory and are neurally implemented in long range connectivity in V1. Different kernels are compatible with the geometric structure of cortical connectivity and they are derived as the fundamental solutions of the Fokker Planck, the Sub-Riemannian Laplacian and the isotropic Laplacian equations. The kernels are used to construct matrices of connectivity among the features present in a visual stimulus. Global gestalt constraints are then introduced in terms of spectral analysis of the connectivity matrix, showing that this processing can be cortically implemented in V1 by mean field neural equations. This analysis performs grouping of local features and individuates perceptual units with the highest saliency. Numerical simulations are performed and results are obtained applying the technique to a number of stimuli.Comment: submitted to Neural Computatio

Unsupervised colour image segmentation by low-level perceptual grouping

This paper proposes a new unsupervised approach for colour image segmentation. A hierarchy of image partitions is created on the basis of a function that merges spatially connected regions according to primary perceptual criteria. Likewise, a global function that measures the goodness of each defined partition is used to choose the best low-level perceptual grouping in the hierarchy. Contributions also include a comparative study with five unsupervised colour image segmentation techniques. These techniques have been frequently used as a reference in other comparisons. The results obtained by each method have been systematically evaluated using four well-known unsupervised measures for judging the segmentation quality. Our methodology has globally shown the best performance, obtaining better results in three out of four of these segmentation quality measures. Experiments will also show that our proposal finds low-level perceptual solutions that are highly correlated with the ones provided by human