Blurred edges look faint, and faint edges look sharp: The effect of a gradient threshold in a multi-scale edge coding model

The dichoptic contrast ordering test: A method for measuring the depth of binocular imbalance

In binocular vision, the relative strength of the input from the two eyes can have significant functional impact. These inputs are typically balanced; however, in some conditions (e.g., amblyopia), one eye will dominate over the other. To quantify imbalances in binocular vision, we have developed the Dichoptic Contrast Ordering Test (DiCOT). Implemented on a tablet device, the program uses rankings of perceived contrast (of dichoptically presented stimuli) to find a scaling factor that balances the two eyes. We measured how physical interventions (applied to one eye) affect the DiCOT measurements, including neutral density (ND) filters, Bangerter filters, and optical blur introduced by a +3-diopter (D) lens. The DiCOT results were compared to those from the Dichoptic Letter Test (DLT). Both the DiCOT and the DLT showed excellent test-retest reliability; however, the magnitude of the imbalances introduced by the interventions was greater in the DLT. To find consistency between the methods, rescaling the DiCOT results from individual conditions gave good results. However, the adjustments required for the +3-D lens condition were quite different from those for the ND and Bangerter filters. Our results indicate that the DiCOT and DLT measures partially separate aspects of binocular imbalance. This supports the simultaneous use of both measures in future studies.

Covariance properties under natural image transformations for the generalised Gaussian derivative model for visual receptive fields

The property of covariance, also referred to as equivariance, means that an image operator is well-behaved under image transformations, in the sense that the result of applying the image operator to a transformed input image gives essentially a similar result as applying the same image transformation to the output of applying the image operator to the original image. This paper presents a theory of geometric covariance properties in vision, developed for a generalised Gaussian derivative model of receptive fields in the primary visual cortex and the lateral geniculate nucleus, which, in turn, enable geometric invariance properties at higher levels in the visual hierarchy. It is shown how the studied generalised Gaussian derivative model for visual receptive fields obeys true covariance properties under spatial scaling transformations, spatial affine transformations, Galilean transformations and temporal scaling transformations. These covariance properties imply that a vision system, based on image and video measurements in terms of the receptive fields according to the generalised Gaussian derivative model, can, to first order of approximation, handle the image and video deformations between multiple views of objects delimited by smooth surfaces, as well as between multiple views of spatio-temporal events, under varying relative motions between the objects and events in the world and the observer. We conclude by describing implications of the presented theory for biological vision, regarding connections between the variabilities of the shapes of biological visual receptive fields and the variabilities of spatial and spatio-temporal image structures under natural image transformations. Specifically, we formulate experimentally testable biological hypotheses as well as needs for measuring population statistics of receptive field characteristics, originating from predictions from the presented theory, concerning the extent to which the shapes of the biological receptive fields in the primary visual cortex span the variabilities of spatial and spatio-temporal image structures induced by natural image transformations, based on geometric covariance properties.

Normative theory of visual receptive fields

This article gives an overview of a normative theory of visual receptive fields. We describe how idealized functional models of early spatial, spatio-chromatic and spatio-temporal receptive fields can be derived in a principled way, based on a set of axioms that reflect structural properties of the environment in combination with assumptions about the internal structure of a vision system to guarantee consistent handling of image representations over multiple spatial and temporal scales. Interestingly, this theory leads to predictions about visual receptive field shapes with qualitatively very good similarities to biological receptive fields measured in the retina, the LGN and the primary visual cortex (V1) of mammals.

Human vision model in relation to characteristics of shapes for the Mach band effect

For human vision to recognize the contours of objects means that, as the contrast variation at the object's edges increases, so will the Mach band effect of human vision. This paper more deeply investigates the relationship between changes in the contours of an object and the Mach band effect of human vision. Based on lateral inhibition and the Mach band effect, we studied subjects' eyes as they watched images of different shapes under a fixed brightness at 34  cd/m2, with changes of contrast and spatial frequency. Three types of display were used: a television, a computer monitor, and a projector. For each display used, we conducted a separate experiment for each shape. Although the maximum values for the contrast sensitivity function curves of the displays were different, their variations were minimal. As the spatial frequency changed, the diminishing effect of the different lines also was minimal. However, as the shapes at the contour intersections were modified by the Mach band effect, a greater degree of variation occurred. In addition, as the spatial frequency at a contour intersection increased, the Mach band effect became lower, along with changes in the corresponding contrast sensitivity function curve. Our experimental results on the characteristics of human vision have led to what we believe is a new vision model based on tests with different shapes. This new model may be used for future development and implementation of an artificial vision system.

Edges, curvature, and primal sketches

Marr described two versions of the primal sketch: the basic image-processing level in human vision. In line with his broader view of how one should construct explanatory theories in vision, he provided some details of the computational theory for this stage, the algorithms used, and how they might be implemented in neural systems. In this paper I consider how Marr ideas have continued over the past 30 years. In this regard, I pay particular attention to three stages: locating edges; describing edge curvature; linking local edge segments into elongated contours.

Electronic magnification and perceived contrast of video

Electronic magnification of an image results in a decrease in its perceived contrast. The decrease in perceived contrast could be due to a perceived blur or to limited sampling of the range of contrasts in the original image. We measured the effect on perceived contrast of magnification in two contexts: either a small video was enlarged to fill a larger area, or a portion of a larger video was enlarged to fill the same area as the original. Subjects attenuated the source video contrast to match the perceived contrast of the magnified videos, with the effect increasing with magnification and decreasing with viewing distance. These effects are consistent with expectations based on both the contrast statistics of natural images and the contrast sensitivity of the human visual system. We demonstrate that local regions within videos usually have lower physical contrast than the whole, and that this difference accounts for a minor part of the perceived differences. Instead, visibility of 'missing content' (blur) in a video is misinterpreted as a decrease in contrast. We detail how the effects of magnification on perceived contrast can be measured while avoiding confounding factors.

Response normalization and blur adaptation: data and multi-scale model

Adapting to blurred or sharpened images alters perceived blur of a focused image (M. A. Webster, M. A. Georgeson, & S. M. Webster, 2002). We asked whether blur adaptation results in (a) renormalization of perceived focus or (b) a repulsion aftereffect. Images were checkerboards or 2-D Gaussian noise, whose amplitude spectra had (log-log) slopes from -2 (strongly blurred) to 0 (strongly sharpened). Observers adjusted the spectral slope of a comparison image to match different test slopes after adaptation to blurred or sharpened images. Results did not show repulsion effects but were consistent with some renormalization. Test blur levels at and near a blurred or sharpened adaptation level were matched by more focused slopes (closer to 1/f) but with little or no change in appearance after adaptation to focused (1/f) images. A model of contrast adaptation and blur coding by multiple-scale spatial filters predicts these blur aftereffects and those of Webster et al. (2002). A key proposal is that observers are pre-adapted to natural spectra, and blurred or sharpened spectra induce changes in the state of adaptation. The model illustrates how norms might be encoded and recalibrated in the visual system even when they are represented only implicitly by the distribution of responses across multiple channels.

Perceived blur in naturally contoured images depends on phase

Perceived blur is an important measure of image quality and clinical visual function. The magnitude of image blur varies across space and time under natural viewing conditions owing to changes in pupil size and accommodation. Blur is frequently studied in the laboratory with a variety of digital filters, without comparing how the choice of filter affects blur perception. We examine the perception of image blur in synthetic images composed of contours whose orientation and curvature spatial properties matched those of natural images but whose blur could be directly controlled. The images were blurred by manipulating the slope of the amplitude spectrum, Gaussian low-pass filtering or filtering with a Sinc function, which, unlike slope or Gaussian filtering, introduces periodic phase reversals similar to those in optically blurred images. For slope-filtered images, blur discrimination thresholds for over-sharpened images were extremely high and perceived blur could not be matched with either Gaussian or Sinc filtered images, suggesting that directly manipulating image slope does not simulate the perception of blur. For Gaussian- and Sinc-blurred images, blur discrimination thresholds were dipper-shaped and were well-fit with a simple variance discrimination model and with a contrast detection threshold model, but the latter required different contrast sensitivity functions for different types of blur. Blur matches between Gaussian- and Sinc-blurred images were used to test several models of blur perception and were in good agreement with models based on luminance slope, but not with spatial frequency based models. Collectively, these results show that the relative phases of image components, in addition to their relative amplitudes, determines perceived blur.

Features and the 'primal sketch'

This review is concerned primarily with psychophysical and physiological evidence relevant to the question of the existence of spatial features or spatial primitives in human vision. The review will be almost exclusively confined to features defined in the luminance domain. The emphasis will be on the experimental and computational methods that have been used for revealing features, rather than on a detailed comparison between different models of feature extraction. Color and texture fall largely outside the scope of the review, though the principles may be similar. Stereo matching and motion matching are also largely excluded because they are covered in other contributions to this volume, although both have addressed the question of the spatial primitives involved in matching. Similarities between different psychophysically-based model will be emphasized rather than minor differences. All the models considered in the review are based on the extraction of directional spatial derivatives of the luminance profile, typically the first and second, but in one case the third order, and all have some form of non-linearity, be it rectification or thresholding.

Added luminance ramp alters perceived edge blur and contrast: a critical test for derivative-based models of edge coding

In many models of edge analysis in biological vision, the initial stage is a linear 2nd derivative operation. Such models predict that adding a linear luminance ramp to an edge will have no effect on the edge's appearance, since the ramp has no effect on the 2nd derivative. Our experiments did not support this prediction: adding a negative-going ramp to a positive-going edge (or vice-versa) greatly reduced the perceived blur and contrast of the edge. The effects on a fairly sharp edge were accurately predicted by a nonlinear multi-scale model of edge processing [Georgeson, M. A., May, K. A., Freeman, T. C. A., & Hesse, G. S. (in press). From filters to features: Scale-space analysis of edge and blur coding in human vision. Journal of Vision], in which a half-wave rectifier comes after the 1st derivative filter. But we also found that the ramp affected perceived blur more profoundly when the edge blur was large, and this greater effect was not predicted by the existing model. The model's fit to these data was much improved when the simple half-wave rectifier was replaced by a threshold-like transducer [May, K. A. & Georgeson, M. A. (2007). Blurred edges look faint, and faint edges look sharp: The effect of a gradient threshold in a multi-scale edge coding model. Vision Research, 47, 1705-1720.]. This modified model correctly predicted that the interaction between ramp gradient and edge scale would be much larger for blur perception than for contrast perception. In our model, the ramp narrows an internal representation of the gradient profile, leading to a reduction in perceived blur. This in turn reduces perceived contrast because estimated blur plays a role in the model's estimation of contrast. Interestingly, the model predicts that analogous effects should occur when the width of the window containing the edge is made narrower. This has already been confirmed for blur perception; here, we further support the model by showing a similar effect for contrast perception.