Ruben Coen-Cagli

Jonathan Vacher, Claire Launay, Pascal Mamassian et al.

Segmenting visual stimuli into distinct groups of features and visual objects is central to visual function. Classical psychophysical methods have helped uncover many rules of human perceptual segmentation, and recent progress in machine learning has produced successful algorithms. Yet, the computational logic of human segmentation remains unclear, partially because we lack well-controlled paradigms to measure perceptual segmentation maps and compare models quantitatively. Here we propose a new, integrated approach: given an image, we measure multiple pixel-based same--different judgments and perform model--based reconstruction of the underlying segmentation map. The reconstruction is robust to several experimental manipulations and captures the variability of individual participants. We demonstrate the validity of the approach on human segmentation of natural images and composite textures. We show that image uncertainty affects measured human variability, and it influences how participants weigh different visual features. Because any putative segmentation algorithm can be inserted to perform the reconstruction, our paradigm affords quantitative tests of theories of perception as well as new benchmarks for segmentation algorithms.

Jonathan Vacher, Aida Davila, Adam Kohn et al.

Texture synthesis models are important tools for understanding visual processing. In particular, statistical approaches based on neurally relevant features have been instrumental in understanding aspects of visual perception and of neural coding. New deep learning-based approaches further improve the quality of synthetic textures. Yet, it is still unclear why deep texture synthesis performs so well, and applications of this new framework to probe visual perception are scarce. Here, we show that distributions of deep convolutional neural network (CNN) activations of a texture are well described by elliptical distributions and therefore, following optimal transport theory, constraining their mean and covariance is sufficient to generate new texture samples. Then, we propose the natural geodesics (ie the shortest path between two points) arising with the optimal transport metric to interpolate between arbitrary textures. Compared to other CNN-based approaches, our interpolation method appears to match more closely the geometry of texture perception, and our mathematical framework is better suited to study its statistical nature. We apply our method by measuring the perceptual scale associated to the interpolation parameter in human observers, and the neural sensitivity of different areas of visual cortex in macaque monkeys.

Sacha Sokoloski, Ruben Coen-Cagli

Parallel recordings of neural spike counts have revealed the existence of context-dependent noise correlations in neural populations. Theories of population coding have also shown that such correlations can impact the information encoded by neural populations about external stimuli. Although studies have shown that these correlations often have a low-dimensional structure, it has proven difficult to capture this structure in a model that is compatible with theories of rate coding in correlated populations. To address this difficulty we develop a novel model based on conditional finite mixtures of independent Poisson distributions. The model can be conditioned on context variables (e.g. stimuli or task variables), and the number of mixture components in the model can be cross-validated to estimate the dimensionality of the target correlations. We derive an expectation-maximization algorithm to efficiently fit the model to realistic amounts of data from large neural populations. We then demonstrate that the model successfully captures stimulus-dependent correlations in the responses of macaque V1 neurons to oriented gratings. Our model incorporates arbitrary nonlinear context-dependence, and can thus be applied to improve predictions of neural activity based on deep neural networks.

Jonathan Vacher, Claire Launay, Ruben Coen-Cagli

Probabilistic finite mixture models are widely used for unsupervised clustering. These models can often be improved by adapting them to the topology of the data. For instance, in order to classify spatially adjacent data points similarly, it is common to introduce a Laplacian constraint on the posterior probability that each data point belongs to a class. Alternatively, the mixing probabilities can be treated as free parameters, while assuming Gauss-Markov or more complex priors to regularize those mixing probabilities. However, these approaches are constrained by the shape of the prior and often lead to complicated or intractable inference. Here, we propose a new parametrization of the Dirichlet distribution to flexibly regularize the mixing probabilities of over-parametrized mixture distributions. Using the Expectation-Maximization algorithm, we show that our approach allows us to define any linear update rule for the mixing probabilities, including spatial smoothing regularization as a special case. We then show that this flexible design can be extended to share class information between multiple mixture models. We apply our algorithm to artificial and natural image segmentation tasks, and we provide quantitative and qualitative comparison of the performance of Gaussian and Student-t mixtures on the Berkeley Segmentation Dataset. We also demonstrate how to propagate class information across the layers of deep convolutional neural networks in a probabilistically optimal way, suggesting a new interpretation for feedback signals in biological visual systems. Our flexible approach can be easily generalized to adapt probabilistic mixture models to arbitrary data topologies.

Jonathan Vacher, Pascal Mamassian, Ruben Coen-Cagli

Visual segmentation is a key perceptual function that partitions visual space and allows for detection, recognition and discrimination of objects in complex environments. The processes underlying human segmentation of natural images are still poorly understood. In part, this is because we lack segmentation models consistent with experimental and theoretical knowledge in visual neuroscience. Biological sensory systems have been shown to approximate probabilistic inference to interpret their inputs. This requires a generative model that captures both the statistics of the sensory inputs and expectations about the causes of those inputs. Following this hypothesis, we propose a probabilistic generative model of visual segmentation that combines knowledge about 1) the sensitivity of neurons in the visual cortex to statistical regularities in natural images; and 2) the preference of humans to form contiguous partitions of visual space. We develop an efficient algorithm for training and inference based on expectation-maximization and validate it on synthetic data. Importantly, with the appropriate choice of the prior, we derive an intuitive closed--form update rule for assigning pixels to segments: at each iteration, the pixel assignment probabilities to segments is the sum of the evidence (i.e. local pixel statistics) and prior (i.e. the assignments of neighboring pixels) weighted by their relative uncertainty. The model performs competitively on natural images from the Berkeley Segmentation Dataset (BSD), and we illustrate how the likelihood and prior components improve segmentation relative to traditional mixture models. Furthermore, our model explains some variability across human subjects as reflecting local uncertainty about the number of segments. Our model thus provides a viable approach to probe human visual segmentation.