Subitizing with Variational Autoencoders

Numerosity, the number of objects in a set, is a basic property of a given visual scene. Many animals develop the perceptual ability to subitize: the near-instantaneous identification of the numerosity in small sets of visual items. In computer vision, it has been shown that numerosity emerges as a statistical property in neural networks during unsupervised learning from simple synthetic images. In this work, we focus on more complex natural images using unsupervised hierarchical neural networks. Specifically, we show that variational autoencoders are able to spontaneously perform subitizing after training without supervision on a large amount images from the Salient Object Subitizing dataset. While our method is unable to outperform supervised convolutional networks for subitizing, we observe that the networks learn to encode numerosity as basic visual property. Moreover, we find that the learned representations are likely invariant to object area; an observation in alignment with studies on biological neural networks in cognitive neuroscience

The Challenge of Modeling the Acquisition of Mathematical Concepts

As a full-blown research topic, numerical cognition is investigated by a variety of disciplines including cognitive science, developmental and educational psychology, linguistics, anthropology and, more recently, biology and neuroscience. However, despite the great progress achieved by such a broad and diversified scientific inquiry, we are still lacking a comprehensive theory that could explain how numerical concepts are learned by the human brain. In this perspective, I argue that computer simulation should have a primary role in filling this gap because it allows identifying the finer-grained computational mechanisms underlying complex behavior and cognition. Modeling efforts will be most effective if carried out at cross-disciplinary intersections, as attested by the recent success in simulating human cognition using techniques developed in the fields of artificial intelligence and machine learning. In this respect, deep learning models have provided valuable insights into our most basic quantification abilities, showing how numerosity perception could emerge in multi-layered neural networks that learn the statistical structure of their visual environment. Nevertheless, this modeling approach has not yet scaled to more sophisticated cognitive skills that are foundational to higher-level mathematical thinking, such as those involving the use of symbolic numbers and arithmetic principles. I will discuss promising directions to push deep learning into this uncharted territory. If successful, such endeavor would allow simulating the acquisition of numerical concepts in its full complexity, guiding empirical investigation on the richest soil and possibly offering far-reaching implications for educational practice

Nonparametric Bayesian methods in robotic vision

In this dissertation non-parametric Bayesian methods are used in the application of robotic vision. Robots make use of depth sensors that represent their environment using point clouds. Non-parametric Bayesian methods can (1) determine how good an object is recognized, and (2) determine how many objects a particular scene contains. When there is a model available for the object to be recognized and the nature of perceptual error is known, a Bayesian method will act optimally.In this dissertation Bayesian models are developed to represent geometric objects such as lines and line segments (consisting out of points). The infinite line model and the infinite line segment model use a non-parametric Bayesian model, to be precise, a Dirichlet process, to represent the number of objects. The line or the line segment is represented by a probability distribution. The lines can be represented by conjugate distributions and then Gibbs sampling can be used. The line segments are not represented by conjugate distributions and therefore a split-merge sampler is used.A split-merge sampler fits line segments by assigning points to a hypothetical line segment. Then it proposes splits of a single line segment or merges of two line segments. A new sampler, the triadic split-merge sampler, introduces steps that involve three line segments. In this dissertation, the new sampler is compared to a conventional split-merge sampler. The triadic sampler can be applied to other problems as well, i.e., not only problems in robotic perception.The models for objects can also be learned. In the dissertation this is done for more complex objects, such as cubes, built up out of hundreds of points. An auto-encoder then learns to generate a representative object given the data. The auto-encoder uses a newly defined reconstruction distance, called the partitioning earth mover’s distance. The object that is learned by the auto-encoder is used in a triadic sampler to (1) identify the point cloud objects and to (2) establish multiple occurrences of those objects in the point cloud.Algorithms and the Foundations of Software technolog