Dependency reduction with divisive normalization: justification and effectiveness

Divisive normalization is an efficient code for multivariate Pareto-distributed environments

Divisive normalization is a canonical computation in the brain, observed across neural systems, that is often considered to be an implementation of the efficient coding principle. We provide a theoretical result that makes the conditions under which divisive normalization is an efficient code analytically precise: We show that, in a low-noise regime, encoding an n-dimensional stimulus via divisive normalization is efficient if and only if its prevalence in the environment is described by a multivariate Pareto distribution. We generalize this multivariate analog of histogram equalization to allow for arbitrary metabolic costs of the representation, and show how different assumptions on costs are associated with different shapes of the distributions that divisive normalization efficiently encodes. Our result suggests that divisive normalization may have evolved to efficiently represent stimuli with Pareto distributions. We demonstrate that this efficiently encoded distribution is consistent with stylized features of naturalistic stimulus distributions such as their characteristic conditional variance dependence, and we provide empirical evidence suggesting that it may capture the statistics of filter responses to naturalistic images. Our theoretical finding also yields empirically testable predictions across sensory domains on how the divisive normalization parameters should be tuned to features of the input distribution.

On the Sparse Structure of Natural Sounds and Natural Images: Similarities, Differences, and Implications for Neural Coding

Sparse coding models of natural images and sounds have been able to predict several response properties of neurons in the visual and auditory systems. While the success of these models suggests that the structure they capture is universal across domains to some degree, it is not yet clear which aspects of this structure are universal and which vary across sensory modalities. To address this, we fit complete and highly overcomplete sparse coding models to natural images and spectrograms of speech and report on differences in the statistics learned by these models. We find several types of sparse features in natural images, which all appear in similar, approximately Laplace distributions, whereas the many types of sparse features in speech exhibit a broad range of sparse distributions, many of which are highly asymmetric. Moreover, individual sparse coding units tend to exhibit higher lifetime sparseness for overcomplete models trained on images compared to those trained on speech. Conversely, population sparseness tends to be greater for these networks trained on speech compared with sparse coding models of natural images. To illustrate the relevance of these findings to neural coding, we studied how they impact a biologically plausible sparse coding network's representations in each sensory modality. In particular, a sparse coding network with synaptically local plasticity rules learns different sparse features from speech data than are found by more conventional sparse coding algorithms, but the learned features are qualitatively the same for these models when trained on natural images.

Blind Stereoscopic Video Quality Assessment: From Depth Perception to Overall Experience

Stereoscopic video quality assessment (SVQA) is a challenging problem. It has not been well investigated on how to measure depth perception quality independently under different distortion categories and degrees, especially exploit the depth perception to assist the overall quality assessment of 3D videos. In this paper, we propose a new depth perception quality metric (DPQM) and verify that it outperforms existing metrics on our published 3D video extension of High Efficiency Video Coding (3D-HEVC) video database. Furthermore, we validate its effectiveness by applying the crucial part of the DPQM to a novel blind stereoscopic video quality evaluator (BSVQE) for overall 3D video quality assessment. In the DPQM, we introduce the feature of auto-regressive prediction-based disparity entropy (ARDE) measurement and the feature of energy weighted video content measurement, which are inspired by the free-energy principle and the binocular vision mechanism. In the BSVQE, the binocular summation and difference operations are integrated together with the fusion natural scene statistic measurement and the ARDE measurement to reveal the key influence from texture and disparity. Experimental results on three stereoscopic video databases demonstrate that our method outperforms state-of-the-art SVQA algorithms for both symmetrically and asymmetrically distorted stereoscopic video pairs of various distortion types.

Full Reference Quality Assessment for Image Retargeting Based on Natural Scene Statistics Modeling and Bi-Directional Saliency Similarity

Image retargeting technology has been widely studied to adapt images for the devices with heterogeneous screen resolutions. Meanwhile effective objective retargeting quality assessment algorithms are also very important for optimizing and selecting favorable retargeting methods. Unlike previous assessment algorithms which rely on image local structure features and unidirectional prediction of information loss, we propose a bi-directional natural salient scene distortion model (BNSSD) including image natural scene statistics (NSS) measurement, salient global structure distortion measurement, and bi-directional salient information loss measurement. First, we propose a new NSS model in log-Gabor domain and verify its effectiveness in reflecting nature scene statistical distortions introduced during the retargeting process. Second, the concept of salient global structure distortion is proposed to measure the global structure uniformity in the corresponding salient regions between original and retargeted images. Finally, we propose a bidirectional salient information loss metric to measure the information loss between salient areas in original image and retargeted image. The effectiveness of the BNSSD model is verified on two widely recognized public databases, and the experimental results show that our method outperforms the state-of-the-art algorithms under different statistical assessment criteria.

A Biologically Inspired Appearance Model for Robust Visual Tracking

In this paper, we propose a biologically inspired appearance model for robust visual tracking. Motivated in part by the success of the hierarchical organization of the primary visual cortex (area V1), we establish an architecture consisting of five layers: whitening, rectification, normalization, coding, and pooling. The first three layers stem from the models developed for object recognition. In this paper, our attention focuses on the coding and pooling layers. In particular, we use a discriminative sparse coding method in the coding layer along with spatial pyramid representation in the pooling layer, which makes it easier to distinguish the target to be tracked from its background in the presence of appearance variations. An extensive experimental study shows that the proposed method has higher tracking accuracy than several state-of-the-art trackers.

Visual aftereffects and sensory nonlinearities from a single statistical framework

When adapted to a particular scenery our senses may fool us: colors are misinterpreted, certain spatial patterns seem to fade out, and static objects appear to move in reverse. A mere empirical description of the mechanisms tuned to color, texture, and motion may tell us where these visual illusions come from. However, such empirical models of gain control do not explain why these mechanisms work in this apparently dysfunctional manner. Current normative explanations of aftereffects based on scene statistics derive gain changes by (1) invoking decorrelation and linear manifold matching/equalization, or (2) using nonlinear divisive normalization obtained from parametric scene models. These principled approaches have different drawbacks: the first is not compatible with the known saturation nonlinearities in the sensors and it cannot fully accomplish information maximization due to its linear nature. In the second, gain change is almost determined a priori by the assumed parametric image model linked to divisive normalization. In this study we show that both the response changes that lead to aftereffects and the nonlinear behavior can be simultaneously derived from a single statistical framework: the Sequential Principal Curves Analysis (SPCA). As opposed to mechanistic models, SPCA is not intended to describe how physiological sensors work, but it is focused on explaining why they behave as they do. Nonparametric SPCA has two key advantages as a normative model of adaptation: (i) it is better than linear techniques as it is a flexible equalization that can be tuned for more sensible criteria other than plain decorrelation (either full information maximization or error minimization); and (ii) it makes no a priori functional assumption regarding the nonlinearity, so the saturations emerge directly from the scene data and the goal (and not from the assumed function). It turns out that the optimal responses derived from these more sensible criteria and SPCA are consistent with dysfunctional behaviors such as aftereffects.

Oriented correlation models of distorted natural images with application to natural stereopair quality evaluation

In recent years, bandpass statistical models of natural, photographic images of the world have been used with great success to solve highly diverse problems involving image representation, image repair, image quality assessment (IQA), and image compression. One missing element has been a reliable and generic model of spatial image correlation that reflects the distributions of oriented and relatively oriented spatial structures. We have developed such a model for bandpass pristine images and have generalized it here to also capture the spatial correlation structure of bandpass distorted images. The model applies well to both luminance and depth images. As a demonstration of the usefulness of the generalized model, we develop a new no-reference stereoscopic/3D IQA framework, dubbed stereoscopic/3D blind image naturalness quality index, which utilizes both univariate and generalized bivariate natural scene statistics (NSS) models. We first validate the robustness and effectiveness of these novel bivariate and correlation NSS features extracted from distorted stereopairs, then demonstrate that they are predictive of distortion severity. Our experimental results show that the resulting 3D image quality predictor based in part on the new model outperforms state-of-the-art full- and no-reference 3D IQA algorithms on both symmetrically and asymmetrically distorted stereoscopic image pairs.

Circuit motifs for contrast-adaptive differentiation in early sensory systems: the role of presynaptic inhibition and short-term plasticity

In natural signals, such as the luminance value across of a visual scene, abrupt changes in intensity value are often more relevant to an organism than intensity values at other positions and times. Thus to reduce redundancy, sensory systems are specialized to detect the times and amplitudes of informative abrupt changes in the input stream rather than coding the intensity values at all times. In theory, a system that responds transiently to fast changes is called a differentiator. In principle, several different neural circuit mechanisms exist that are capable of responding transiently to abrupt input changes. However, it is unclear which circuit would be best suited for early sensory systems, where the dynamic range of the natural input signals can be very wide. We here compare the properties of different simple neural circuit motifs for implementing signal differentiation. We found that a circuit motif based on presynaptic inhibition (PI) is unique in a sense that the vesicle resources in the presynaptic site can be stably maintained over a wide range of stimulus intensities, making PI a biophysically plausible mechanism to implement a differentiator with a very wide dynamical range. Moreover, by additionally considering short-term plasticity (STP), differentiation becomes contrast adaptive in the PI-circuit but not in other potential neural circuit motifs. Numerical simulations show that the behavior of the adaptive PI-circuit is consistent with experimental observations suggesting that adaptive presynaptic inhibition might be a good candidate neural mechanism to achieve differentiation in early sensory systems.

Segmentation decreases the magnitude of the tilt illusion

In the tilt illusion, the perceived orientation of a target grating depends strongly on the orientation of a surround. When the orientations of the center and surround gratings differ by a small angle, the center grating appears to tilt away from the surround orientation (repulsion), whereas for a large difference in angle, the center appears to tilt toward the surround orientation (attraction). In order to understand how segmentation/perceptual grouping of the center and surround affect the magnitude of the tilt illusion, we conducted three psychophysical experiments in which we measured observers' perception of center orientation as a function of center-surround relative contrast, relative disparity depth, and geometric features such as occlusion and collinearity. All of these manipulations affected the strength of perceived orientation bias in the center. Our results suggest that if stronger segmentation/perceptual grouping is induced between the center and surround, the tilt repulsion bias decreases/increases. A grouping-dependent tilt illusion plays an important role in visual search and detection by enhancing the sensitivity of our visual system to feature discrepancies, especially in relatively homogenous environments.

Temporal adaptation enhances efficient contrast gain control on natural images

Divisive normalization in primary visual cortex has been linked to adaptation to natural image statistics in accordance to Barlow's redundancy reduction hypothesis. Using recent advances in natural image modeling, we show that the previously studied static model of divisive normalization is rather inefficient in reducing local contrast correlations, but that a simple temporal contrast adaptation mechanism of the half-saturation constant can substantially increase its efficiency. Our findings reveal the experimentally observed temporal dynamics of divisive normalization to be critical for redundancy reduction.

The redundancy reduction hypothesis postulates that neural representations adapt to sensory input statistics such that their responses become as statistically independent as possible. Based on this hypothesis, many properties of early visual neurons—like orientation selectivity or divisive normalization—have been linked to natural image statistics. Divisive normalization, in particular, models a widely observed neural response property: The divisive inhibition of a single neuron by a pool of others. This mechanism has been shown to reduce the redundancy among neural responses to typical contrast dependencies in natural images. Here, we show that the standard model of divisive normalization achieves substantially less redundancy reduction than a theoretically optimal mechanism called radial factorization. On the other hand, we find that radial factorization is inconsistent with existing neurophysiological observations. As a solution we suggest a new physiologically plausible modification of the standard model which accounts for the dynamics of the visual input by adapting to local contrasts during fixations. In this way the dynamic version of the standard model achieves almost optimal redundancy reduction performance. Our results imply that the dynamics of natural viewing conditions are critical for testing the role of divisive normalization for redundancy reduction.