Perception is often viewed as a process that transforms physical variables, external to an observer, into internal psychological variables. Such a process can be modeled by a function coined *perceptual scale*. The *perceptual scale* can be deduced from psychophysical measurements that consist in comparing the relative differences between stimuli (i.e. difference scaling experiments). However, this approach is often overlooked by the modeling and experimentation communities. Here, we demonstrate the value of measuring the *perceptual scale* of classical (spatial frequency, orientation) and less classical physical variables (interpolation between textures) by embedding it in recent probabilistic modeling of perception. First, we show that the assumption that an observer has an internal representation of univariate parameters such as spatial frequency or orientation while stimuli are high-dimensional does not lead to contradictory predictions when following the theoretical framework. Second, we show that the measured *perceptual scale* corresponds to the transduction function hypothesized in this framework. In particular, we demonstrate that it is related to the Fisher information of the generative model that underlies perception and we test the predictions given by the generative model of different stimuli in a set a of difference scaling experiments. Our main conclusion is that the *perceptual scale* is mostly driven by the stimulus power spectrum. Finally, we propose that this measure of *perceptual scale* is a way to push further the notion of perceptual distances by estimating the perceptual geometry of images i.e. the path between images instead of simply the distance between those.

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.

We propose a family of probabilistic segmentation algorithms for videos that rely on a generative model capturing static and dynamic natural image statistics. Our framework adopts flexibly regularized mixture models (FlexMM) [1], an efficient method to combine mixture distributions across different data sources. FlexMMs of Student-t distributions successfully segment static natural images, through uncertainty-based information sharing between hidden layers of CNNs. We further extend this approach to videos and exploit FlexMM to propagate segment labels across space and time. We show that temporal propagation improves temporal consistency of segmentation, reproducing qualitatively a key aspect of human perceptual grouping. Besides, Student-t distributions can capture statistics of optical flows of natural movies, which represent apparent motion in the video. Integrating these motion cues in our temporal FlexMM further enhances the segmentation of each frame of natural movies. Our probabilistic dynamic segmentation algorithms thus provide a new framework to study uncertainty in human dynamic perceptual segmentation.

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.

A common practice to account for psychophysical biases in vision is to frame them as consequences of a dynamic process relying on optimal inference with respect to a generative model. The study presented here details the complete formulation of such a generative model intended to probe visual motion perception with a dynamic texture model. It is derived in a set of axiomatic steps constrained by biological plausibility. We extend previous contributions by detailing three equivalent formulations of this texture model. First, the composite dynamic textures are constructed by the random aggregation of warped patterns, which can be viewed as three-dimensional gaussian fields. Second, these textures are cast as solutions to a stochastic partial differential equation (sPDE). This essential step enables real-time, on-the-fly texture synthesis using time-discretized autoregressive processes. It also allows for the derivation of a local motion-energy model, which corresponds to the log likelihood of the probability density. The log likelihoods are essential for the construction of a Bayesian inference framework. We use the dynamic texture model to psychophysically probe speed perception in humans using zoom-like changes in the spatial frequency content of the stimulus. The human data replicate previous findings showing perceived speed to be positively biased by spatial frequency increments. A Bayesian observer who combines a gaussian likelihood centered at the true speed and a spatial frequency dependent width with a "slow-speed prior" successfully accounts for the perceptual bias. More precisely, the bias arises from a decrease in the observer's likelihood width estimated from the experiments as the spatial frequency increases. Such a trend is compatible with the trend of the dynamic texture likelihood width.

Perception is often described as a predictive process based on an optimal inference with respect to a generative model. We study here the principled construction of a generative model specifically crafted to probe motion perception. In that context, we first provide an axiomatic, biologically-driven derivation of the model. This model synthesizes random dynamic textures which are defined by stationary Gaussian distributions obtained by the random aggregation of warped patterns. Importantly, we show that this model can equivalently be described as a stochastic partial differential equation. Using this characterization of motion in images, it allows us to recast motion-energy models into a principled Bayesian inference framework. Finally, we apply these textures in order to psychophysically probe speed perception in humans. In this framework, while the likelihood is derived from the generative model, the prior is estimated from the observed results and accounts for the perceptual bias in a principled fashion.