Mathematical Handbook for Scientists and Engineers

Although the study of visual perception has made more progress in the past 40 years than any other area of cognitive science, there remain major disagreements as to how closely vision is tied to cognition. This target article sets out some of the arguments for both sides (arguments from computer vision, neuroscience, psychophysics, perceptual learning, and other areas of vision science) and defends the position that an important part of visual perception, corresponding to what some people have called early vision, is prohibited from accessing relevant expectations, knowledge, and utilities in determining the function it computes - in other words, it is cognitively im- penetrable. That part of vision is complex and involves top-down interactions that are internal to the early vision system. Its function is to provide a structured representation of the 3-D surfaces of objects sufficient to serve as an index into memory, with somewhat differ- ent outputs being made available to other systems such as those dealing with motor control. The paper also addresses certain concep- tual and methodological issues raised by this claim, such as whether signal detection theory and event-related potentials can be used to assess cognitive penetration of vision. A distinction is made among several stages in visual processing, including, in addition to the inflexible early-vision stage, a pre-per- ceptual attention-allocation stage and a post-perceptual evaluation, selection, and inference stage, which accesses long-term memory. These two stages provide the primary ways in which cognition can affect the outcome of visual perception. The paper discusses argu- ments from computer vision and psychology showing that vision is "intelligent" and involves elements of "problem solving." The cases of apparently intelligent interpretation sometimes cited in support of this claim do not show cognitive penetration; rather, they show that certain natural constraints on interpretation, concerned primarily with optical and geometrical properties of the world, have been com- piled into the visual system. The paper also examines a number of examples where instructions and "hints" are alleged to affect what is seen. In each case it is concluded that the evidence is more readily assimilated to the view that when cognitive effects are found, they have a locus outside early vision, in such processes as the allocation of focal attention and the identification of the stimulus.

/pdf/is-vision-continuous-with-cognition-the-case-for-cognitive-t2qx5udnjk.pdf

Is vision continuous with cognition? The case for cognitive impenetrability of visual perception

https://www.cs.princeton.edu/courses/archive/spr08/cos598B/Readings/AhissarHochstein_TCS2004.pdf

The Reverse Hierarchy Theory of Visual Perceptual Learning

Crowding—An essential bottleneck for object recognition: A mini-review

A letter in the peripheral visual field is much harder to identify in the presence of nearby letters. This is “crowding.” Both crowding and ordinary masking are special cases of “masking,” which, in general, refers to any effect of a “mask” pattern on the discriminability of a signal. Here we characterize crowding, and propose a diagnostic test to distinguish it from ordinary masking. In ordinary masking, the signal disappears. In crowding, it remains visible, but is ambiguous, jumbled with its neighbors. Masks are usually effective only if they overlap the signal, but the crowding effect extends over a large region. The width of that region is proportional to signal eccentricity from the fovea and independent of signal size, mask size, mask contrast, signal and mask font, and number of masks. At 4 deg eccentricity, the threshold contrast for identification of a 0.32 deg signal letter is elevated (up to six-fold) by mask letters anywhere in a 2.3 deg region, 7 times wider than the signal. In ordinary masking, threshold contrast rises as a power function of mask contrast, with a shallow log-log slope of 0.5 to 1, whereas, in crowding, threshold is a sigmoidal function of mask contrast, with a steep log-log slope of 2 at close spacing. Most remarkably, although the threshold elevation decreases exponentially with spacing, the threshold and saturation contrasts of crowding are independent of spacing. Finally, ordinary masking is similar for detection and identification, but crowding occurs only for identification, not detection. More precisely, crowding occurs only in tasks that cannot be done based on a single detection by coarsely coded feature detectors. These results (and observers’ introspections) suggest that ordinary masking blocks feature detection, so the signal disappears, while crowding (like “illusory conjunction”) is excessive feature integration — detected features are integrated over an inappropriately large area because there are no smaller integration fields — so the integrated signal is ambiguous, jumbled with the mask. In illusory conjunction, observers see an object that is not there made up of features that are. A survey of the illusory conjunction literature finds that most of the illusory conjunction results are consistent with the spatial crowding described here, which depends on spatial proximity, independent of time pressure. The rest seem to arise through a distinct phenomenon that one might call “temporal crowding,” which depends on time pressure (“overloading attention”), independent of spatial proximity.

/pdf/crowding-is-unlike-ordinary-masking-distinguishing-feature-1hh3gxhbzf.pdf

Crowding is unlike ordinary masking: Distinguishing feature integration from detection

This essay makes three points. (1) From the failure of perceptual learning to transfer when stimulus parameters are changed, it cannot necessarily be concluded that the site of learning is distal: rather, the learning may be central and the specificity may lie in what is learnt. (2) Mere exposure to a stimulus may not be sufficient for learning: even in the absence of explicit feedback, other sources of information are often available in a perceptual learning task. (3) Procedural learning may sometimes be apparent only after a delay: this phenomenon has a long history and is known as reminiscence.

http://vision.psychol.cam.ac.uk/jdmollon/papers/Mollon_Danilova1996.pdf

Three remarks on perceptual learning

What spatial frequency do we use to detect the orientation of a Landolt C

We describe several experiments on contour interactions and crowding effects at the resolution limit of the visual system. As test stimuli we used characters that are often employed in optometric practice for testing visual acuity: Landolt C's, Snellen E's, and rectangular gratings. We tested several hypotheses that have been put forward to explain contour interaction and crowding effects. In Experiment 1 and Experiment 2, Landolt C's were the test stimuli, and bars, or Landolt C's, or gratings served as distractors. In Experiment 1, we showed that neither scale invariance nor spatial frequency selectivity is a characteristic of foveal crowding effects. These results allowed us to conclude that mechanisms other than lateral masking contribute to observers' performance in 'crowded' tasks. R. F. Hess, S. C. Dakin, and N. Kappor (2000) suggested that the spatial frequency band most appropriate for target recognition is shifted by the surrounding bars to higher spatial frequencies that cannot be resolved by observers. Our Experiment 2 rejects this hypothesis as the experimental data do not follow theoretical predictions. In Experiment 3, we employed Snellen E's, both as test stimuli and as distractors. The masking functions were similar to those measured in Experiment 1 when the test Landolt C was surrounded by Landolt C's. In Experiment 4, we extended the range of test stimuli to rectangular gratings; same-frequency or high-frequency gratings were distractors. In this case, if the distracting gratings had random orientation from trial to trial, the critical spacing was twice larger than in the first three experiments. If the orientation of the distractors was fixed during the whole experiment, the critical spacing was similar to that measured in the first three experiments. We suggest that the visual system can use different mechanisms for the discrimination of different test stimuli in the presence of particular surround. Different receptive fields with different spatial characteristics can be employed. To explain why crowding effects at the resolution limit of the visual system are not scale invariant, we suggest that a range of stimuli, slightly varying in size, may all be processed by the same neural channel--the channel with the smallest receptive fields of the visual system.

Foveal contour interactions and crowding effects at the resolution limit of the visual system.

We tested whether visual complexity can be modeled through the use of parameters relevant to known mechanisms of visual processing. In psychophysical experiments observers ranked the complexity of two groups of stimuli: 15 unfamiliar Chinese hieroglyphs and 24 outline images of well-known common objects. To predict image complexity, we considered: (i) spatial characteristics of the images, (ii) spatial-frequency characteristics, (iii) a combination of spatial and Fourier properties, and (iv) the size of the image encoded as a JPEG file. For hieroglyphs the highest correlation was obtained when complexity was calculated as the product of the squared spatial-frequency median and the image area. This measure accounts for the larger number of lines, strokes, and local periodic patterns in the hieroglyphs. For outline objects the best predictor of the experimental data was complexity estimated as the number of turns in the image, as Attneave (1957 Journal of Experimental Psychology 53 221-227) obtained for his abstract outlined images. Other predictors of complexity gave significant but lower correlations with the experimental ranking. We conclude that our modeling measures can be used to estimate the complexity of visual images but for different classes of images different measures of complexity may be required.

Complexity of Images: Experimental and Computational Estimates Compared

Are boundaries between color categories associated with enhanced discrimination? In the present experiments, chromatic thresholds were obtained for discriminations along lines orthogonal to the yellow-blue axis of color space. The targets were parafoveal and thresholds were measured with a spatial two-alternative forced choice. In interleaved experimental runs, we also obtained empirical estimates of the subjective yellow-blue line by asking observers to categorize colors as reddish or greenish. Both types of measurement were made in the presence of a steady background that was metameric to equal-energy white. In a limited region from desaturated yellow to desaturated blue, an enhanced discrimination is found near the subjective transition between reddish and greenish hues. This line of optimal discrimination is not aligned with either of the cardinal axes of color space: In a MacLeod-Boynton chromaticity diagram, it runs obliquely with negative slope.

http://vision.psychol.cam.ac.uk/jdmollon/papers/DanilovaMollon2010.pdf

M. V. Danilova

Papers

Three remarks on perceptual learning

What spatial frequency do we use to detect the orientation of a Landolt C

Foveal contour interactions and crowding effects at the resolution limit of the visual system.

Complexity of Images: Experimental and Computational Estimates Compared

Parafoveal color discrimination: a chromaticity locus of enhanced discrimination.