Human vision can detect spatiotemporal information conveyed by first-order modulations of luminance and by second-order, non-Fourier modulations of image contrast. Models for second-order motion have suggested two filtering stages separated by a rectifying nonlinearity. We explore here the encoding of stationary first-order and second-order gratings, and their interaction. Stimuli consisted of 2-D binary, broad-band, static, visual noise sinusoidally modulated in luminance (LM, first-order) or contrast (CM, second-order). Modulation thresholds were measured in a two-interval forced-choice staircase procedure. Sensitivity curves for LM and CM had similar shape as a function of spatial frequency, and as a function of the size of a circular Gaussian blob of modulation. Weak background gratings present in both intervals produced order-specific facilitation: LM background facilitated LM detection (the dipper function) and CM facilitated CM detection. LM did not facilitate CM, nor vice-versa, neither in-phase nor out-of-phase, and this is strong evidence that LM and CM are detected via separate mechanisms. This conclusion was further supported by an experiment on the detection of LM/CM mixtures. From a general mathematical model and a specific computer simulation we conclude that a single mechanism sensitive to both LM and CM cannot predict the pattern of results for mixtures, while a model containing separate pathways for LM and CM, followed by energy summation, does so successfully and is quantitatively consistent with the finding of order-specific facilitation.

The pattern of illumination on an undulating surface can be used to infer its 3-D form (shape-from-shading). But the recovery of shape would be invalid if the luminance changes actually arose from changes in reflectance. So how does vision distinguish variation in illumination from variation in reflectance to avoid illusory depth? When a corrugated surface is painted with an albedo texture, the variation in local mean luminance (LM) due to shading is accompanied by a similar modulation in local luminance amplitude (AM). This is not so for reflectance variation, nor for roughly textured surfaces. We used depth mapping and paired comparison methods to show that modulations of local luminance amplitude play a role in the interpretation of shape-from-shading. The shape-from-shading percept was enhanced when LM and AM co-varied (in-phase) and was disrupted when they were out of phase or (to a lesser degree) when AM was absent. The perceptual differences between cue types (in-phase vs out-of-phase) were enhanced when the two cues were present at different orientations within a single image. Our results suggest that when LM and AM co-vary (in-phase) this indicates that the source of variation is illumination (caused by undulations of the surface), rather than surface reflectance. Hence, the congruence of LM and AM is a cue that supports a shape-from-shading interpretation.

Abstract. Intrinsic images represent the underlying properties of a scene such as illumination (shading) and surface reflectance. Extracting intrinsic images is a challenging, ill-posed problem. Human performance on tasks such as shadow detection and shape-from-shading is improved by adding colour and texture to surfaces. In particular, when a surface is painted with a textured pattern, correlations between local mean luminance and local luminance amplitude promote the interpretation of luminance variations as illumination changes. Based on this finding, we propose a novel feature, local luminance amplitude, to separate illumination and reflectance, and a framework to integrate this cue with hue and texture to extract intrinsic images. The algorithm uses steerable filters to separate images into frequency and orientation components and constructs shading and reflectance images from weighted combinations of these components. Weights are determined by correlations between corresponding variations in local luminance, local amplitude, colour and texture. The intrinsic images are further refined by ensuring the consistency of local texture elements. We test this method on surfaces photographed under different lighting conditions. The effectiveness of the algorithm is demonstrated by the correlation between our intrinsic images and ground truth shading and reflectance data. Luminance amplitude was found to be a useful cue. Results are also presented for natural images.

We consider the overall shape of the second-order modulation sensitivity function (MSF). Because second-order modulations of local contrast or orientation require a carrier signal, it is necessary to evaluate modulation sensitivity against a variety of carriers before reaching a general conclusion about second-order sensitivity. Here we present second-order sensitivity functions for new carrier types (low pass (1/f) noise, and high pass noise) and demonstrate that, when first-order artefacts have been accounted for, the shape of the resulting MSFs are similar to one another and to those for white and broad band noise. They are all low pass with a likely upper frequency limit in the range 10-20 c/deg, suggesting that detection of second-order stimuli is relatively insensitive to the structure of the carrier signal. This result contrasts strongly with that found for (first-order) luminance modulations of the same noise types. Here the noise acts as mask and each noise type masks most those frequencies that are dominant in its spectrum. Thus the shape of second-order MSFs are largely independent of the spectrum of their noise carrier, but first-order CSFs depend on the spectrum of an additive noise mask. This provides further evidence for the separation of first- and second-order vision and characterises second-order vision as a low pass mechanism.

The human visual system is sensitive to both first-order variations in luminance and second-order variations in local contrast and texture. Although there is some debate about the nature of second-order vision and its relationship to first-order processing, there is now a body of results showing that they are processed separately. However, the amount, and nature, of second-order structure present in the natural environment is unclear. This is an important question because, if natural scenes contain little second-order structure in addition to first-order signals, the notion of a separate second-order system would lack ecological validity. Two models of second-order vision were applied to a number of well-calibrated natural images. Both models consisted of a first stage of oriented spatial filters followed by a rectifying nonlinearity and then a second set of filters. The models differed in terms of the connectivity between first-stage and second-stage filters. Output images taken from the models indicate that natural images do contain useful second-order structure. Specifically, the models reveal variations in texture and features defined by such variations. Areas of high contrast (but not necessarily high luminance) are also highlighted by the models. Second-order structure--as revealed by the models--did not correlate with the first-order profile of the images, suggesting that the two types of image 'content' may be statistically independent.