The Geometries of Visual Space

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The best understood instance is the relief space for pictures. In this case a simple formal framework the Euclidean plane augmented with an isotropic dimension has excellent, quantitative predicting power. Fairly simple heuristics apply in free viewing the daily environment. Perhaps surprisingly, various huge, systematic misjudgements concerning the geometrical structure of the daily environment - well handled by the heuristics - are rarely recognised and are not related in handbooks. Throughout the years I have collected a huge amount of empirical data.

I plan to present a selection, in suitably abstracted format, of a few conceptually relevant topics. Speaker: Farid Masrour.

The Geometries Of Visual Space - erfesvemiga.cf -

Abstract: The geometry of the visual field has been empirically studied for more than a century. In this talk I argue that the findings in this line of research have implications for, at least, three philosophical debates about visual experience, namely, the nature of visual experience, the unity of the visual field, and the format of its underlying representations. I end by broadly outlining a view that accommodates these findings.

Abstract: This paper presents a new puzzle about the visual appearance of space. We review experimental data -- including classic data and new data from our own vision lab -- showing that visual appearance of shape is systematically distorted in ways that increase with viewing distance. Given these distortions, a square coffee table appears wider than it is deep. As you walk around the table, its appearance changes.

And yet the table does not appear to change in shape. On the contrary, it appears perfectly rigid! But how can something appear to have the same shape when its apparent shape is changing? Having presented this puzzle, we take some preliminary steps towards solving it. Speaker: Susanna Schellenberg. Abstract: This paper develops a framework in which to discuss the variant and invariant aspects of perception. In light of this framework, I argue that perspectival properties are best understood as situation-dependent properties: external, mind-independent properties that are constituted by intrinsic properties and situational features, where situational features include the perceiver's location, lighting conditions, acoustic conditions and other mind-independent features that affect the way an object is presented.

I defend the situation-dependent properties approach against objections. Speaker: James Todd. Abstract: This talk will consider two different ways of conceptualizing the geometry of visual space. The extrinsic geometry of visual space examines the specific properties of the physical environment that remain invariant over the mapping between physical and perceived space. The intrinsic geometry of visual space, in contrast, examines the formal relations among an observer's spatial judgments, without considering any corresponding measures of the physical environment.

I will review several classic findings from the literature on this topic, which demonstrate conclusively that the extrinsic geometry of visual space for large open fields is neither projective, affine nor Euclidean, and that the intrinsic geometry of visual space does not have a homogeneous distance metric.

The reason why perceptual judgments can be systematically distorted is that they are based on available sensory information that can only uniquely specify certain aspects of environmental structure, whereas other aspects are inherently ambiguous. As a result of this ambiguity especially with respect to metric structure , the pattern of errors in observers' judgments can vary with the types of sensory information that are available e. Speaker: Mark Wagner.

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The Geometries of Visual Space

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Is there a consistent geometry of visual space? (Dr. James Todd)

New York: Oxford University Press. Ono, H. Accuracy and precision 2nd edition. These hybrid models were first suggested by Johannes von Kries and G. Zone theories derive the opponent dimensions from the trichromatic retinal responses by a step by step transformation or recoding across three or more stages or zones. In D. Today these opponent dimensions are the foundation for most modern color appearance models. In the 's by Leo Hurvich and Dorothea Jameson developed a quantitative hue cancellation method to measure the opponent functions by decomposing monochromatic hues into a mixture of two of the four unique hues.

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Their method uses the same color matching techniques developed to measure the cone fundamentals championed by Helmholz. In this procedure, either the viewers or the experimenters chose four wavelengths of light to match Hering's unique hues. A mixture of "red" and "violet" wavelengths must be used to produce a unique red. The intensity of each light was then adjusted so that equal parts of red and green matched the brightness of unique yellow, and equal parts of yellow and blue matched the brightness of unique green.

Next, a fifth wavelength was chosen as the test color. Viewers used a light mixing apparatus to blend the test light with the two unique hues that were nearest complementary colors opposite on the hue circle to the test light, until the mixture produced a pure "white" light. This was repeated for test lights at regular intervals across the spectrum. Finally, the proportions relative luminances of the two unique hues necessary to cancel a third monochromatic light at each wavelength were combined as two chromatic response functions.

As shown here, the horizontal zero line represents the balance between the two unique hues in a single opponent function. The distance of a curve above or below the line represents the relative quantity of each unique hue required to match rather than cancel the spectral hue at each wavelength i. The area where the yellow curve is above the horizontal line, with a maximum in "yellow green" wavelengths, indicates colors that appear to contain some yellow.

The area where the blue curve is below the line, with a maximum in "blue violet", indicates hues that contain some blue. The unique hues appear at any point where one opponent function is at the zero line where it cannot bias or alter the hue created by the other opponent function. The exact location of these unique hues varies across individuals. What about unique red?


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To produce unique red from monochromatic lights, a small amount of "violet" must be added to spectral "red" light, to neutralize the yellow hue. But this curve glosses over several problems. What Are the Opponent Functions? On a previous page I mentioned that a few studies have analyzed the reflectance curves of a large number of color samples from the Munsell color system.

The pattern of peaks and crossings of these basis functions is extremely efficient in the sense that every surface color can be defined by a unique location in just three dimensions. There are discrepancies in the exact shape and crossover points of the curves especially in function 1 , but these discrepancies can be attributed to four factors: 1 reflectance curves are a physical specification of the color stimulus, not a perceptual specification via the cone fundamentals; 2 reflectance curves define the color independent of any light source, whereas the human opponent functions are optimized for chromatic adaptation along the dimensions of chromatic variation in the daylight phases ; 3 the reflectance variations in the Munsell color samples are constrained to some degree by the limited number of pigments used to manufacture them; and 4 by far the largest proportion of natural surface colors are weakly chromatic and rather dark, which means the Munsell system contains a disproportionately large number of saturated and light valued colors.

This is persuasive evidence that, as we would expect, the perceptual structure of color vision is strongly tuned to the reflectance structure of natural surfaces. Transforming the trichromatic signals into the opponent functions would not be difficult for a neural network that could flexibly sum, difference and reweight the cone signals.

For example, the diagram right shows the Hurvich and Jameson opponent functions color overlaid on curves derived as simple weighted sums of the linear, population weighted cone fundamentals gray ; numbers indicate the weight and sign applied to each cone output. This demonstrates the perceptual overweighting of S cones when we contrast their large contribution to the opponent dimensions with their sparse numbers among the much more common rod, L and M photoreceptor cells.

All this implies that the wavelength locations of the unique hues are a byproduct of the opponent dimensions. It's the overall structure of the hue circle that color vision must reproduce, not the orientation of the hue circle to specific "unique hue" compass points.

There are in fact large individual differences in the identification of unique hues, which strongly suggests that the hues are not structurally basic to color vision. The S cones appear to desaturate yellow rather than shift its hue.

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