Most prevalent statistical models of natural images characterize only the univariate distributions of divisively normalized bandpass responses or wavelet-like decompositions of them. However, the higher-order dependencies between spatially neighboring responses are not yet well understood. Towards filling this gap, we propose a new closed-form spatial-oriented correlation model that captures statistical regularities between perceptually decomposed natural image luminance samples. We validate the new correlation model on a variety of natural images. Experimental results demonstrate the robustness of the new correlation model across image content. A software release that implements the new closed-form spatial-oriented correlation model is available at http://live.ece.utexas.edu/research/3dnss/bicorr_release.zip.

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.

We perform bivariate statistical analysis and modeling of the joint distributions of spatially adjacent sub-band responses for both luminance/chrominance and range data in natural scenes. In particular, we introduce a multivariate generalized Gaussian distribution and an exponentiated sine function to model the underlying statistics and correlations. The experimental results show that the bivariate statistics relating spatially adjacent pixels in both 2D color images and range maps are well described by the proposed models. We validate the robustness of the proposed bivariate models using a multi-variate statistical hypothesis test, and further demonstrate their effectiveness with application to a prototype depth estimation algorithm.

We develop a no-reference binocular image quality assessment model that operates on static stereoscopic images. The model deploys 2D and 3D features extracted from stereopairs to assess the perceptual quality they present when viewed stereoscopically. Both symmetric- and asymmetric-distorted stereopairs are handled by accounting for binocular rivalry using a classic linear rivalry model. The NSS features are used to train a support vector machine model to predict the quality of a tested stereopair. The model is tested on the LIVE 3D Image Quality Database, which includes both symmetric- and asymmetric-distorted stereoscopic 3D images. The experimental results show that our proposed model significantly outperforms the conventional 2D full-reference QA algorithms applied to stereopairs, as well as the 3D full-reference IQA algorithms on asymmetrically distorted stereopairs.

Natural scene statistics have played an increasingly important role in both our understanding of the function and evolution of the human vision system, and in the development of modern image processing applications. Because range (egocentric distance) is arguably the most important thing a visual system must compute (from an evolutionary perspective), the joint statistics between image information (color and luminance) and range information are of particular interest. It seems obvious that where there is a depth discontinuity, there must be a higher probability of a brightness or color discontinuity too. This is true, but the more interesting case is in the other direction--because image information is much more easily computed than range information, the key conditional probabilities are those of finding a range discontinuity given an image discontinuity. Here, the intuition is much weaker; the plethora of shadows and textures in the natural environment imply that many image discontinuities must exist without corresponding changes in range. In this paper, we extend previous work in two ways--we use as our starting point a very high quality data set of coregistered color and range values collected specifically for this purpose, and we evaluate the statistics of perceptually relevant chromatic information in addition to luminance, range, and binocular disparity information. The most fundamental finding is that the probabilities of finding range changes do in fact depend in a useful and systematic way on color and luminance changes; larger range changes are associated with larger image changes. Second, we are able to parametrically model the prior marginal and conditional distributions of luminance, color, range, and (computed) binocular disparity. Finally, we provide a proof of principle that this information is useful by showing that our distribution models improve the performance of a Bayesian stereo algorithm on an independent set of input images. To summarize, we show that there is useful information about range in very low-level luminance and color information. To a system sensitive to this statistical information, it amounts to an additional (and only recently appreciated) depth cue, and one that is trivial to compute from the image data. We are confident that this information is robust, in that we go to great effort and expense to collect very high quality raw data. Finally, we demonstrate the practical utility of these findings by using them to improve the performance of a Bayesian stereo algorithm.

We develop an algorithm that predicts the best presentation of a stereo 3D image in the sense of viewers' preference. The algorithm operates in three steps. First, the 3D image is classified as either a “foreground dominant” or “background dominant” image. Next, for “foreground dominant” images, a model of the stereoacuity function is used to optimize the perceptual 3D resolution; for “background dominant” images, the nearest surface is placed in the 3D plane of the display screen. A human study was conducted to assess the algorithm and showed that the proposed model produced 3D images which had the best 3D quality scores among several candidate algorithms.

Color and depth play important roles in natural scenes and in vision, and their perception is related. Extensive work has been conducted on studying the luminance statistics of natural scenes; however, there is very little work done on analyzing the statistics between luminance and range in natural scenes, not to mention color and range. In this paper, we present the LIVE Color+3D Database, which contains 12 sets of color images with corresponding ground truth range maps in a high-definition resolution of 1280×720. We examined the statistical distribution of range gradients conditioned on the Gabor responses of the color images, as well as the variations of statistical measures of range gradients with changes in the Gabor responses. The analysis results show that the distributions of range gradients conditioned on the Gabor responses have very similar exponential shapes for both luminance and chrominance channels. Moreover, we also found that the depth difference between neighboring pixels increases as the corresponding magnitudes of the Gabor responses rise.

We studied the empirical distributions of luminance, range and disparity wavelet coefficients using a coregistered database of luminance and range images. The marginal distributions of range and disparity are observed to have high peaks and heavy tails, similar to the well-known properties of luminance wavelet coefficients. However, we found that the kurtosis of range and disparity coefficients is significantly larger than that of luminance coefficients. We used generalized Gaussian models to fit the empirical marginal distributions. We found that the marginal distribution of luminance coefficients have a shape parameter p between 0.6 and 0.8, while range and disparity coefficients have much smaller parameters p < 0.32, corresponding to a much higher peak. We also examined the conditional distributions of luminance, range and disparity coefficients. The magnitudes of luminance and range (disparity) coefficients show a clear positive correlation, which means, at a location with larger luminance variation, there is a higher probability of a larger range (disparity) variation. We also used generalized Gaussians to model the conditional distributions of luminance and range (disparity) coefficients. The values of the two shape parameters (p,s) reflect the observed luminance-range (disparity) dependency. As an example of the usefulness of luminance statistics conditioned on range statistics, we modified a well-known Bayesian stereo ranging algorithm using our natural scene statistics models, which improved its performance.

We conducted eye tracking experiments on naturalistic stereo images presented through a haploscope, and found that fixated luminance contrast and luminance gradient were generally higher than randomly selected luminance contrast and luminance gradient, which agrees with previous literatures. However we also found that the fixated disparity contrast and disparity gradient were generally lower than randomly selected disparity contrast and disparity gradient. We discuss the implications of this remarkable result.

We present the results of a recent large-scale subjective study of video quality on a collection of videos distorted by a variety of application-relevant processes. Methods to assess the visual quality of digital videos as perceived by human observers are becoming increasingly important, due to the large number of applications that target humans as the end users of video. Owing to the many approaches to video quality assessment (VQA) that are being developed, there is a need for a diverse independent public database of distorted videos and subjective scores that is freely available. The resulting Laboratory for Image and Video Engineering (LIVE) Video Quality Database contains 150 distorted videos (obtained from ten uncompressed reference videos of natural scenes) that were created using four different commonly encountered distortion types. Each video was assessed by 38 human subjects, and the difference mean opinion scores (DMOS) were recorded. We also evaluated the performance of several state-of-the-art, publicly available full-reference VQA algorithms on the new database. A statistical evaluation of the relative performance of these algorithms is also presented. The database has a dedicated web presence that will be maintained as long as it remains relevant and the data is available online.

We present information-theoretic underpinnings of a computation theory of low-level visual fixations in natural images. In continuation of our prior work on optimal contrast-based fixations [1], we develop an optimum texture- based fixation selection algorithm based on a recent theory of non-stationarity measurement in natural images [2]. Thereafter we propose a simple coupling of the optimal texture-based and contrast-based fixation features to produce a new algorithm called CONTEXT, which exhibits robust performance for fixation selection in natural images. The performance of the fixation algorithms are evaluated for natural images by comparison to randomized fixation strategies via actual human fixations performed on the images. The fixation patterns obtained outperform randomized, GAFFE-based [3], and Itti [4] fixation strategies in terms of matching human fixation patterns. These results also demonstrate the important role that contrast and textural information play in low-level visual processes in the Human Visual System (HVS).

Exploiting the quasi-linear relationship between local phase and disparity, phase-differencing registration algorithms provide a fast, powerful means for disparity estimation. Unfortunately, these phase-differencing techniques suffer a significant impediment: phase nonlinearities. In regions of phase nonlinearity, the signals under consideration possess properties that invalidate the use of phase for disparity estimation. This paper uses the amenable properties of Gaussian white noise images to analytically quantify these properties. The improved understanding gained from this analysis enables us to better understand current methodologies for detecting regions of phase instability. Most importantly, we introduce a new, more effective means for identifying these regions based on the second derivative of phase.

The ability to automatically detect visually interesting regions in images has many practical applications, especially in the design of active machine vision and automatic visual surveillance systems. Analysis of the statistics of image features at observers' gaze can provide insights into the mechanisms of fixation selection in humans. Using a foveated analysis framework, we studied the statistics of four low-level local image features: luminance, contrast, and bandpass outputs of both luminance and contrast, and discovered that image patches around human fixations had, on average, higher values of each of these features than image patches selected at random. Contrast-bandpass showed the greatest difference between human and random fixations, followed by luminance-bandpass, RMS contrast, and luminance. Using these measurements, we present a new algorithm that selects image regions as likely candidates for fixation. These regions are shown to correlate well with fixations recorded from human observers.

If precise calibration information is unavailable, as is often the case for active binocular vision systems, the determination of epipolar lines becomes untenable. Yet, even without instantaneous knowledge of the geometry, the search for corresponding points can be restricted to areas called epipolar spaces. For each point in one image, we define the corresponding epipolar space in the other image as the union of all associated epipolar lines over all possible system geometries. Epipolar spaces eliminate the need for calibration at the cost of an increased search region. One approach to mitigate this increase is the application of a space variant sampling or foveation strategy. While the application of such strategies to stereo vision tasks is not new, only rarely has a foveation scheme been specifically tailored for a stereo vision task. In this paper we derive a foundation of theorems that provide a means for obtaining optimal sampling schemes for a given set of epipolar spaces. An optimal sampling scheme is defined as a strategy that minimizes the average area per epipolar space.

Depth recovery for active binocular vision systems is simplified if the camera geometry is known and corresponding points can be restricted to epipolar lines. Unfortunately, computation of epipolar lines requires calibration which can be complex and inaccurate. While it is possible to register images without geometric information, such unconstrained algorithms are usually time consuming and prone to error. In this paper we propose a compromise. Even without the instantaneous knowledge of the system geometry, we can restrict the region of correspondence by imposing limits on the possible range of configurations, and as a result, confine our search for matching points to epipolar spaces. For each point in one image, we define the corresponding epipolar space in the other image as the union of all associated epipolar lines over all possible system geometries. Epipolar spaces eliminate the need for calibration at the cost of an increased search region.

The ability to automatically detect visually interesting regions in images has practical applications in the design of active machine vision systems. Analysis of the statistics of image features at observers gaze can provide insights into the mechanisms of fixation selection in humans. Using a novel foveated analysis framework, in which features were analyzed at the spatial resolution at which they were perceived, we studied the statistics of four low-level local image features: luminance, contrast, center-surround outputs of luminance and contrast, and discovered that the image patches around human fixations had, on average, higher values of each of these features than the image patches selected at random. Center-surround contrast showed the greatest difference between human and random fixations, followed by contrast, center-surround luminance, and luminance. Using these measurements, we present a new algorithm that selects image regions as likely candidates for fixation. These regions are shown to correlate well with fixations recorded from observers.

Measurement of image or video quality is crucial for many image-processing algorithms, such as acquisition, compression, restoration, enhancement, and reproduction. Traditionally, image quality assessment (QA) algorithms interpret image quality as similarity with a "reference" or "perfect" image. The obvious limitation of this approach is that the reference image or video may not be available to the QA algorithm. The field of blind, or no-reference, QA, in which image quality is predicted without the reference image or video, has been largely unexplored, with algorithms focusing mostly on measuring the blocking artifacts. Emerging image and video compression technologies can avoid the dreaded blocking artifact by using various mechanisms, but they introduce other types of distortions, specifically blurring and ringing. In this paper, we propose to use natural scene statistics (NSS) to blindly measure the quality of images compressed by JPEG2000 (or any other wavelet based) image coder. We claim that natural scenes contain nonlinear dependencies that are disturbed by the compression process, and that this disturbance can be quantified and related to human perceptions of quality. We train and test our algorithm with data from human subjects, and show that reasonably comprehensive NSS models can help us in making blind, but accurate, predictions of quality. Our algorithm performs close to the limit imposed on useful prediction by the variability between human subjects.

The ability to automatically detect 'visually interesting' regions in an image has many practical applications especially in the design of active machine vision systems. This paper describes a data-driven approach that uses eye tracking in tandem with principal component analysis to extract low-level image features that attract human gaze. Data analysis on an ensemble of image patches extracted at the observer's point of gaze revealed features that resemble derivatives of the 2D Gaussian operator. Dissimilarities between human and random fixations are investigated by comparing the features extracted at the point of gaze to the general image structure obtained by random sampling in Monte-Carlo simulations. Finally, a simple application where these features are used to predict fixations is illustrated.

In this paper, we present two techniques to reveal image features that attract the eye during visual search: the discrimination image paradigm and principal component analysis. In preliminary experiments, we employed these techniques to identify image features used to identify simple targets embedded in 1/ƒ noise. Two main findings emerged. First, the loci of fixations were not random but were driven by local image features, even in very noisy displays. Second, subjects often searched for a component feature of a target rather that the target itself, even if the target was a simple geometric form. Moreover, the particular relevant component varied from individual to individual. Also, principal component analysis of the noise patches at the point of fixation reveals global image features used by the subject in the search task. In addition to providing insight into the human visual system, these techniques have relevance for machine vision as well. The efficacy of a foveated machine vision system largely depends on its ability to actively select 'visually interesting' regions in its environment. The techniques presented in this paper provide valuable low-level criteria for executing human-like scanpaths in such machine vision systems.

We apply an AM-FM surface albedo model to analyze the projection of surface patterns viewed through a binocular camera system. This is used to support the use of modulation-based stereo matching where local image phase is used to compute stereo disparities. The local image phase is an advantageous feature for image matching, since the problem of computing disparities reduces to identifying local phase shifts between the stereoscopic image data. Local phase shifts, however, are problematic at high frequencies due to phase wrapping when disparities exceed +/-pi. We meld powerful multichannel Gabor image demodulation techniques for multiscale (coarse-to-fine) computation of local image phase with a disparity channel model for depth computation. The resulting framework unifies phase-based matching approaches with AM-FM surface/image models. We demonstrate the concepts in a stereo algorithm that generates a dense, accurate disparity map without the problems associated with phase wrapping.