Object recognition in primates is mediated by the ventral visual pathway and is classically described as a feedforward hierarchy of increasingly sophisticated representations. Neurons in macaque monkey area V4, an intermediate stage along the ventral pathway, have been shown to exhibit selectivity to complex boundary conformation and invariance to spatial translation. How could such a representation be derived from the signals in lower visual areas such as V1? We show that a quantitative model of hierarchical processing, which is part of a larger model of object recognition in the ventral pathway, provides a plausible mechanism for the translation-invariant shape representation observed in area V4. Simulated model neurons successfully reproduce V4 selectivity and invariance through a nonlinear, translation-invariant combination of locally selective subunits, suggesting that a similar transformation may occur or culminate in area V4. Specifically, this mechanism models the selectivity of individual V4 neurons to boundary conformation stimuli, exhibits the same degree of translation invariance observed in V4, and produces observed V4 population responses to bars and non-Cartesian gratings. This work provides a quantitative model of the widely described shape selectivity and invariance properties of area V4 and points toward a possible canonical mechanism operating throughout the ventral pathway.

Human and non-human primates excel at visual recognition tasks. The primate visual system exhibits a strong degree of selectivity while at the same time being robust to changes in the input image. We have developed a quantitative theory to account for the computations performed by the feedforward path in the ventral stream of the primate visual cortex. Here we review recent predictions by a model instantiating the theory about physiological observations in higher visual areas. We also show that the model can perform recognition tasks on datasets of complex natural images at a level comparable to psychophysical measurements on human observers during rapid categorization tasks. In sum, the evidence suggests that the theory may provide a framework to explain the first 100-150 ms of visual object recognition. The model also constitutes a vivid example of how computational models can interact with experimental observations in order to advance our understanding of a complex phenomenon. We conclude by suggesting a number of open questions, predictions, and specific experiments for visual physiology and psychophysics.

Object recognition requires both selectivity among different objects and tolerance to vastly different retinal images of the same object, resulting from natural variation in (e.g.) position, size, illumination, and clutter. Thus, discovering neuronal responses that have object selectivity and tolerance to identity-preserving transformations is fundamental to understanding object recognition. Although selectivity and tolerance are found at the highest level of the primate ventral visual stream [the inferotemporal cortex (IT)], both properties are highly varied and poorly understood. If an IT neuron has very sharp selectivity for a unique combination of object features ("diagnostic features"), this might automatically endow it with high tolerance. However, this relationship cannot be taken as given; although some IT neurons are highly object selective and some are highly tolerant, the empirical connection of these key properties is unknown. In this study, we systematically measured both object selectivity and tolerance to different identity-preserving image transformations in the spiking responses of a population of monkey IT neurons. We found that IT neurons with high object selectivity typically have low tolerance (and vice versa), regardless of how object selectivity was quantified and the type of tolerance examined. The discovery of this trade-off illuminates object selectivity and tolerance in IT and unifies a range of previous, seemingly disparate results. This finding also argues against the idea that diagnostic conjunctions of features guarantee tolerance. Instead, it is naturally explained by object recognition models in which object selectivity is built through AND-like tuning mechanisms.

A few distinct cortical operations have been postulated over the past few years, suggested by experimental data on nonlinear neural response across different areas in the cortex. Among these, the energy model proposes the summation of quadrature pairs following a squaring nonlinearity in order to explain phase invariance of complex V1 cells. The divisive normalization model assumes a gain-controlling, divisive inhibition to explain sigmoid-like response profiles within a pool of neurons. A gaussian-like operation hypothesizes a bell-shaped response tuned to a specific, optimal pattern of activation of the presynaptic inputs. A max-like operation assumes the selection and transmission of the most active response among a set of neural inputs. We propose that these distinct neural operations can be computed by the same canonical circuitry, involving divisive normalization and polynomial nonlinearities, for different parameter values within the circuit. Hence, this canonical circuit may provide a unifying framework for several circuit models, such as the divisive normalization and the energy models. As a case in point, we consider a feedforward hierarchical model of the ventral pathway of the primate visual cortex, which is built on a combination of the gaussian-like and max-like operations. We show that when the two operations are approximated by the circuit proposed here, the model is capable of generating selective and invariant neural responses and performing object recognition, in good agreement with neurophysiological data.

Humans can rapidly recognize a multitude of objects despite differences in their appearance. The neural mechanisms that endow high-level sensory neurons with both selectivity to complex stimulus features and "tolerance" or invariance to identity-preserving transformations, such as spatial translation, remain poorly understood. Previous studies have demonstrated that both tolerance and selectivity to conjunctions of features are increased at successive stages of the ventral visual stream that mediates visual recognition. Within a given area, such as visual area V4 or the inferotemporal cortex, tolerance has been found to be inversely related to the sparseness of neural responses, which in turn was positively correlated with conjunction selectivity. However, the direct relationship between tolerance and conjunction selectivity has been difficult to establish, with different studies reporting either an inverse or no significant relationship. To resolve this, we measured V4 responses to natural scenes, and using recently developed statistical techniques, we estimated both the relevant stimulus features and the range of translation invariance for each neuron. Focusing the analysis on tuning to curvature, a tractable example of conjunction selectivity, we found that neurons that were tuned to more curved contours had smaller ranges of position invariance and produced sparser responses to natural stimuli. These trade-offs provide empirical support for recent theories of how the visual system estimates 3D shapes from shading and texture flows, as well as the tiling hypothesis of the visual space for different curvature values.A lthough object recognition feels effortless, it is in fact a challenging computational problem (1). There are two important properties that any system that mediates robust object recognition must have. The first property is known as "invariance": the ability of the system to respond similarly to different views of the same object. The second property is known as "selectivity." Selectivity requires that systems' components, such as neurons within the ventral visual stream, produce different responses to potentially quite similar objects (such as different faces) even when presented from similar viewpoints. It is straightforward to make detectors that are invariant but not selective or selective but not invariant. The difficulty lies in how to make detectors that are both selective and invariant.To address this problem, both computer object recognition algorithms (2) and neural systems use a series of hierarchical stimulus representations, increasing both in complexity and the range of invariance (1, 3). For example, in each successive area of visual processing, neurons become selective for increasingly complex stimulus features (4-9) and grow more tolerant to identity-preserving transformations, such as image translation, scaling, and, to some degree, rotation and the presence of "clutter" from other objects in the scene (3,(10)(11)(12). This has led to the idea that high-level sensory neurons are...

This paper compares a family of methods for characterizing neural feature selectivity using natural stimuli in the framework of the linear-nonlinear model. In this model, the spike probability depends in a nonlinear way on a small number of stimulus dimensions. The relevant stimulus dimensions can be found by optimizing a Rényi divergence that quantifies a change in the stimulus distribution associated with the arrival of single spikes. Generally, good reconstructions can be obtained based on optimization of Rényi divergence of any order, even in the limit of small numbers of spikes. However, the smallest error is obtained when the Rényi divergence of order 1 is optimized. This type of optimization is equivalent to information maximization, and is shown to saturate the Cramér-Rao bound describing the smallest error allowed for any unbiased method. We also discuss conditions under which information maximization provides a convenient way to perform maximum likelihood estimation of linear-nonlinear models from neural data.

Our visual system is capable of recognizing complex objects even when their appearances change drastically under various viewing conditions. Especially in the higher cortical areas, the sensory neurons reflect such functional capacity in their selectivity for complex visual features and invariance to certain object transformations, such as image translation. Due to the strong nonlinearities necessary to achieve both the selectivity and invariance, characterizing and predicting the response patterns of these neurons represents a formidable computational challenge. A related problem is that such neurons are poorly driven by randomized inputs, such as white noise, and respond strongly only to stimuli with complex high-order correlations, such as natural stimuli. Here we describe a novel two-step optimization technique that can characterize both the shape selectivity and the range and coarseness of position invariance from neural responses to natural stimuli. One step in the optimization involves finding the template as the maximally informative dimension given the estimated spatial location where the response could have been triggered within each image. The estimates of the locations that triggered the response are subsequently updated in the next step. Under the assumption of a monotonic relationship between the firing rate and stimulus projections on the template at a given position, the most likely location is the one that has the largest projection on the estimate of the template. The algorithm shows quick convergence during optimization, and the estimation results are reliable even in the regime of small signal-to-noise ratios. When we apply the algorithm to responses of complex cells in the primary visual cortex (V1) to natural movies, we find that responses of the majority of cells were significantly better described by translation invariant models based on one template compared with position-specific models with several relevant features.

In an introductory physics course where students first learn about vectors, they oftentimes struggle with the concept of vector addition and decomposition. For example, the classic physics problem involving a mass on an inclined plane requires the decomposition of the force of gravity into two directions that are parallel and perpendicular to the ramp. It takes time and effort for the students to become proficient with such a vector decomposition process. Here, we present simple lab experiments to help students learn and practice the vector concepts, by working with a familiar low-cost accelerometer, the Wii Remote (“Wiimote”).