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

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.

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.

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

A multi-scale model of edge coding based on normalized Gaussian derivative filters successfully predicts perceived scale (blur) for a wide variety of edge profiles [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]. Our model spatially differentiates the luminance profile, half-wave rectifies the 1st derivative, and then differentiates twice more, to give the 3rd derivative of all regions with a positive gradient. This process is implemented by a set of Gaussian derivative filters with a range of scales. Peaks in the inverted normalized 3rd derivative across space and scale indicate the positions and scales of the edges. The edge contrast can be estimated from the height of the peak. The model provides a veridical estimate of the scale and contrast of edges that have a Gaussian integral profile. Therefore, since scale and contrast are independent stimulus parameters, the model predicts that the perceived value of either of these parameters should be unaffected by changes in the other. This prediction was found to be incorrect: reducing the contrast of an edge made it look sharper, and increasing its scale led to a decrease in the perceived contrast. Our model can account for these effects when the simple half-wave rectifier after the 1st derivative is replaced by a smoothed threshold function described by two parameters. For each subject, one pair of parameters provided a satisfactory fit to the data from all the experiments presented here and in the accompanying paper [May, K. A. & Georgeson, M. A. (2007). Added luminance ramp alters perceived edge blur and contrast: A critical test for derivative-based models of edge coding. Vision Research, 47, 1721-1731]. Thus, when we allow for the visual system's insensitivity to very shallow luminance gradients, our multi-scale model can be extended to edge coding over a wide range of contrasts and blurs.