The concept of group and the theory of perception.

Prompted by the title of Ernst Cassirer's 1944 essay, the origin of the idea of a Group theoretical approach, in the mathematical sense, in vision science is here explored, as well as the several ways in which its implementation had been attempted. That object recognition might proceed by a more generative approach rather than by separate individual cataloging had already been argued by Kant, and Cassirer examined how mathematical group theory might be called on for this purpose, in view of the success of its use in geometry and in the physical sciences. However, such a promise appears unlikely in view of the categorical differences between analysis of mental phenomena and of the physical world.

Retinal image quality for multifocal lenses with on- and off-axis annular zones.

Multi-focal intra-ocular or contact lenses, intended to increase depth of focus, conventionally have annular zones of additional refractive power, generating wavefront rings of coaxial spherical surfaces. It is, however, possible to influence depth of focus by changing not only the curvature of the wavefront, refractive power, in the annulus, but also the tilt, circularly symmetrical linear radial deviation imposed on the spherical wavefront. Employing the example of a single annulus bifocal, retinal image light distributions in the two regimes are calculated, using standard diffraction theory.

Gestalt theory in 20th-century history.

During the century from the 1890 publication of Ehrenfels's proposition on Gestaltqualitäten to the 1989 dissolution of the European states governed by Marxist orthodoxy, Gestalt theory was drawn into the political fray in several ways. It was grotesquely misappropriated during the Nazi regime in support of race, territorial expansion, and war aims. On the other side, because it was seen as having a subjectivist taint, the Gestalt approach was anathema where dialectical materialist dogma reigned.

Topical Review: Pilocarpine-induced Miosis as Help for Early Presbyopes?

The clinical utility of ophthalmic pilocarpine-induced pupil constriction to help overcome image blur of close-up targets in patients with failing accommodation is examined.Pilocarpine in low-concentration ophthalmic solution eye drops constricts the pupil to approximately 2 mm and thus reduces defocus blur. To gain regulatory approval of this drug for the treatment of presbyopia, clinical trials were conducted with 1.

Multifocal contact lens myopia control: central and peripheral retinal image quality.

Clinical Relevance: That myopic defocus, even if restricted to the peripheral retina, inhibits eye growth in young monkey eyes has motivated the therapy of myopia control through multifocal contact lens wear in children.

Background: To understand how eye-length regulating mechanisms are triggered by light requires knowledge of retinal light spread. That is largely lacking for the multifocal contact lenses used in the therapy because empirical methods identifying just the defocus in dioptres are inadequate.

Objective Measures of Retinal Image Degradation Due to Refractive Corrections.

Significance: There is a need for a measure, as simple and yet as informative as possible, to describe objectively the retinal image quality when a patient views targets at various distances through spectacle, contact, or intraocular corrections with optics more elaborate than single vision.

Purpose: The purposes of this study are to examine the current status of quantitative descriptions of retinal image blur and find optimal characterization of image degradation.

Methods: A variety of indexes of image degradation are computed for a typical eye and polychromatic light, in and out of focus, and as exemplars of sophisticated wave shaping, when the pupil transmission has been modified to a truncated Bessel amplitude function and to a "fractal" phase function.

Focused and defocused retinal images with Bessel and axicon pupil functions.

Retinal image light distributions in a standard optical model of a diffraction-limited eye with round pupils are presented for several patterns of amplitude and phase modulation of the light admitted into the eye. Of special interest are circularly symmetrical configurations of truncated Bessel amplitude transmission functions, and of light subjected to axicon deviation. It is shown by several examples that this kind of beam shaping allows generation of retinal imagery, which can be more robust to defocus while maintaining minimal image degradation, and it points to situations of two separate zones simultaneously in sharp focus, several diopters apart.

Hering Hermeneutics: Supplement to (1899) by Strasburger et al.

Strasburger et al.'s welcome translation of Hering's seminal paper, and reminder of what Hering actually said about eye movements and spatial averaging in vernier acuity, is supplemented by references to further trends on how the subject has evolved to the present state of knowledge.

Preferential processing of cardinal over oblique orientations in human vision.

The oblique effect-poorer performance when contours are in oblique meridians-is here extended from the discrimination of line-orientation to the tilt illusion and to the detection and contextual induction of curvature. The distinction is made between a contour's susceptibility to contextual perturbation and its capacity to induce such perturbation, for which the oblique effect is only about one half. That the cardinal/oblique superiority is retained for the orientation of illusory borders and for the implicit orientation of shapes lacking explicit rectilinear delineation has implications for its neural substrate.

The Road to Certainty and Back.

The author relates his intellectual journey from eye-testing clinician to experimental vision scientist. Starting with the quest for underpinning in physics and physiology of vague clinical propositions and of psychology's acceptance of thresholds as "fuzzy-edged," and a long career pursuing a reductionist agenda in empirical vision science, his journey led to the realization that the full understanding of human vision cannot proceed without factoring in an observer's awareness, with its attendant uncertainty and open-endedness. He finds support in the loss of completeness, finality, and certainty revealed in fundamental twentieth-century formulations of mathematics and physics.

Optotype recognition under degradation: comparison of size, contrast, blur, noise and contour-perturbation effects.

Background: Visual acuity is measured by diminishing letter size till recognition threshold is reached, letters varying in legibility. In this experiment, size reduction was compared with other means of handicapping letter legibility.

Methods: In five normal observers, discrimination thresholds for 13 sans-serif capital letters in a 5 × 4 format were obtained by a staircase procedure for size reduction, as well as for 20 minutes of arc (logMAR = 0.

Optometric Trajectory--Gerald Westheimer.

A narrative starting with the author's entering the Optometry program at the Sydney Technical College in 1940, taking him through his days as an optometry and science student, an optometrist in private practice, and participant in organized optometry in Sydney. It described his steps to become an optometric scientist and his service as faculty member in three optometry schools in the United States. Finally, it follows him into a long career in vision science and neurophysiology at Berkeley.

The law of equal innervation of both eyes: Thomas Reid preceded Hering by a century. An historical note.

The law of equal innervation of the two eyes, positing that conjugacy of movement of our two eyes is basic and innate, was enunciated in Hering's 1868 persuasively argued monograph. It has prevailed over Helmholtz's contrary view that conjugacy is learned. Yet 100 years earlier, Thomas Reid (1710-1796), Scottish clergyman and professor of philosophy, advanced exactly the same view as Hering, using almost identical arguments.

Retinal light distributions, the Stiles-Crawford effect and apodization.

Analysis of retinal image formation for beams of coherent and incoherent radiation emphasizes the role of the Poynting vector's inclination with respect to the retinal image plane. Coherent beams interfere and give rise to a single Poynting vector that highlights the unique direction of incidence of energy flow, whereas multiple incoherent beams, especially incoherent extended sources in the pupil, generate electro-magnetic disturbances in the image plane each characterized by Poynting vectors of their own. As a result, the Stiles-Crawford diminution of luminant efficiency adds differently depending on the coherence of the entering light.

Can perceptual learning compensate for optical image blur?

Tests of target recognition under blur mostly fail to separate factors of resolution and contrast from the influences of pure blur, i.e., shallow luminance edge gradients.

Perceptual learning of orientation judgments in oblique meridians.

Fourteen daily training sessions in orientation discrimination of foveal lines in the 45-deg meridian improved thresholds in the trained meridian by an average of 25 % in five observers. A substantial amount of training transferred to the other obliques, but none to the cardinal meridians, with a consequent reduction in the oblique effect. The data were interpreted as showing perceptual learning at two levels: performance facilitation specific to the trained orientation and improved proficiency globally.

Measuring visual form discrimination with blur thresholds.

A method is described for gauging the discriminability of spatial forms. Rather than challenging form discrimination by size reduction as is done in testing visual acuity, the maximum image degradation by blurring is determined that still allows shape recognition. The procedure has the advantage that tests are substantially independent of optical (resolution) and retinal (light-processing) stages of vision and concentrate on the perceptual demands of distinguishing form.

Clinical evaluation of stereopsis.

Principles of the design and administration of clinical stereopsis tests are outlined. Once the presence of the distinct sense of the third dimension by binocular vision alone and without help from monocular cues has been established in a patient, the examination can proceed to the measurement of stereoscopic acuity. Best results are obtained with high-contrast, sharp, well-articulated and uncrowded elements from easily-recognized target sets, displayed with no time constraints.

Spatial and spatial-frequency analysis in visual optics.

Background: In the specification of visual targets and their transmission through the eye's optics to form retinal images, the spatial distribution of energy and its Fourier transform, the spatial-frequency spectrum, are equivalent, so long as linearity constraints are obeyed. The power spectrum, in which phase has been discarded, is an insufficient descriptor; it does not enable the original object to be reconstituted.

Procedure: Not so well known, and explored here, are joint representations in the space and spatial-frequency dimensions.

Optical superresolution and visual hyperacuity.

Classically, diffraction theory sets a boundary for the resolving capacity of optical instruments. Yet some visual thresholds have values much better than the traditional resolution limit. Recent developments in superresolution, an area of optical physics and engineering with claims of transcending the stated resolution limits of optical instruments, are reviewed and their possible relevance to visual spatial processing and to the exploration of the eye's structure are assessed.

Lack of spatial remapping of the visual field surrounding a monocular scotoma.

Background:   Changes in cortical receptive fields following deafferentation raise the question of whether interruption of optic nerve fibres engenders spatial distortion in the region bordering the resulting scotoma.

Methods:   The regularity and uniformity of the spatial metric surrounding a monocular Bjerrum scotoma were studied in both the affected and unaffected eyes of a glaucoma patient, using rigorous psychometric measurements and Amsler grid observations.

Results:   No expansion of distances towards the edge of the scotoma was found; however, such a change occurs at the border of the normal blind spot, though not binocularly and not in the corresponding field of the other eye.

Depth rendition of three-dimensional displays.

The third dimension in the reproduction of real scenes in three-dimensional displays is commonly subject to scale changes. The geometry of the situation is laid out, permitting the depth rendition of displays to be characterized and subjected to empirical examination. Psychophysical experiments are presented showing, even when geometrical deformations have been factored out, specific deviations from veridicality in observers' depth reports for stereograms of simple static patterns devoid of secondary cues.

Three-dimensional displays and stereo vision.

Procedures for three-dimensional image reconstruction that are based on the optical and neural apparatus of human stereoscopic vision have to be designed to work in conjunction with it. The principal methods of implementing stereo displays are described. Properties of the human visual system are outlined as they relate to depth discrimination capabilities and achieving optimal performance in stereo tasks.