A Differential Geometric Description of the Relationships among Perceptions

Levin, David

doi:10.1006/jmps.1999.1240

Cited by 7 publications

(5 citation statements)

References 16 publications

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“…Also, providing a meaningful context appears to inoculate letter strings against the impacts of physical degradation (e.g., Prinzmetal, 1992), and orienting instructions that emphasize the meaningful nature of the task display can actually attenuate the potent effects of stimulus frequency (e.g., Strongman & Brown, 1966). If one assumes that meaning is functionally related to the level of familiarity one possesses with a particular class of stimuli (as in Tong & Nakayama, 1999), then there are also some provocative examples of how observers' ethnicity can influence their ability to perform visual search tasks with faces of individuals from other races (e.g., D. N. Levin, 2000;D. T. Levin, 1996; D. T. Levin & Angelone, 2001).…”

Section: Visual Search and The Effects Of Stimulus Organizationmentioning

confidence: 99%

On the costs and benefits of faces and words: Process characteristics of feature search in highly meaningful stimuli.

Wenger¹,

Townsend²

2006

Journal of Experimental Psychology: Human Perception and Perfor

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The authors present a comprehensive consideration of the process characteristics of visual search in contexts that vary in their meaningfulness. The authors frame hypotheses regarding process architecture, stopping rule, capacity, and channel independence, using analytic results and a rigorously specified dynamic system to characterize a set of alternative hypotheses that vary along all of these dimensions. Results of the tests of these hypotheses suggest that process architecture and the stopping rule do not distinguish the processing of meaningful and meaningless forms. The major distinction between configural and nonconfigural processing was with regard to processing capacity, potentially implicating channel interdependencies. All of these conclusions hold for both faces and words.

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Section: Visual Search and The Effects Of Stimulus Organizationmentioning

confidence: 99%

On the costs and benefits of faces and words: Process characteristics of feature search in highly meaningful stimuli.

Wenger¹,

Townsend²

2006

Journal of Experimental Psychology: Human Perception and Perfor

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“…Differential geometric descriptions of the perceptual space, excluding the large body of work on binocular depth perception where geometry is substantively involved (Luneburg, 1947;Smith, 1959;Indow, 1982Indow, , 1991, have recently been applied to the discrimination and comparison of stimuli in multi-dimensional setting invoking the notion of affine connection for vector comparison (Yamazaki, 1987;Levine, 2000), the emergence of perceptual oneness in segregated objects invoking the notion of intrinsic parallelism (Zhang & Wu, 1990;Zhang, 1995), the perception of complex visual stimuli through infinite-dimensional analysis (Townsend, Solomon, & Smith, 2001), and the characterization of perceptual distance in the large via local measurement of stimulus discrimination using the Finsler geometry approach (Dzhafarov & Colonius, 1999. Here, in the same spirit, the foundation of comparative judgment between a probe (comparison stimulus) and a referent (reference stimulus) is investigated, with a special interest in the issue of asymmetry in comparison.…”

Section: Discussionmentioning

confidence: 99%

Dual scaling of comparison and reference stimuli in multi-dimensional psychological space

Zhang

2004

Journal of Mathematical Psychology

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“…On the other hand, if two devices have experienced stimulus trajectories with different velocity covariance matrices (e.g., trajectories drawn from different statistical distributions), they will not agree on all statements about relative stimulus locations. For example, there will be striking disagreements if the trajectory-derived metric of one machine is flat and the trajectoryderived metric of the other one is curved 1 .…”

Section: Discussionmentioning

confidence: 99%

“…Observers will often have a definite sense about whether the relationship between A and B is the same (or is not the same) as the relationship between C and D; i.e., whether A:B = C:D or not. A series of such perceived analogies can be concatenated in order to describe relationships between two "distant" stimuli, by specifying how one stimulus can be transformed into the other 1 . Figure 2 shows an example in which an observer describes stimulus E as being related to stimuli A, B, and C by a succession of analogous stimulus transformations: "E is the stimulus that is produced by starting with stimulus A and performing three transformations perceptually equivalent to the C A → transformation, followed by two transformations perceptually equivalent to the B A → transformation".…”

Section: Introductionmentioning

confidence: 99%

Channel-independent and sensor-independent stimulus representations

Levin

2005

Journal of Applied Physics

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This paper shows how a machine, which observes stimuli through an uncharacterized, uncalibrated channel and sensor, can glean machine-independent information (i.e., channel-and sensor-independent information) about the stimuli. This is possible if the following two conditions are satisfied by the observed stimulus and by the observing device, respectively: 1) the stimulus' trajectory in the space of all possible configurations has a well-defined local velocity covariance matrix; 2) the observing device's sensor state is invertibly related to the stimulus state. The first condition guarantees that statistical properties of the stimulus time series endow the stimulus configuration space with a differential geometric structure (a metric and parallel transfer procedure), which can then be used to represent relative stimulus configurations in a coordinate-system-independent manner. This requirement is satisfied by a large variety of physical systems, and, in general, it is expected to be satisfied by stimuli with velocity distributions varying smoothly across stimulus state space. The second condition means that the machine defines a specific coordinate system on the stimulus state space, with the nature of that coordinate system depending on the machine's channels and detectors. Thus, machines with different channels and sensors "see" the same stimulus trajectory through state space, but in different machine-specific coordinate systems. It is shown that this requirement is almost certainly satisfied by any device that measures more than 2d independent properties of the stimulus, where d is the number of stimulus degrees of freedom. Taken together, the two conditions guarantee that the observing device can record the stimulus time series in its machine-specific coordinate system and then derive coordinate-system-independent (and, therefore, machine-independent) representations of relative stimulus configurations. The resulting description is an "inner" property of the stimulus time series in the sense that it does not depend on extrinsic factors like the observer's choice of a coordinate system in which the stimulus is viewed (i.e., the observer's choice of channels and sensors). In other words, the resulting description is an intrinsic property of the evolution of the "real" stimulus that is "out there" broadcasting energy to the observer. This methodology is illustrated with analytic examples and with a numerically simulated experiment. In an intelligent sensory device, this kind of representation "engine" could function as a "front end" that passes channel/sensor-independent stimulus representations to a pattern recognition module. After a pattern recognizer has been trained in one of these devices, it could be used without change in other devices having different channels and sensors.

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A Differential Geometric Description of the Relationships among Perceptions

Cited by 7 publications

References 16 publications

On the costs and benefits of faces and words: Process characteristics of feature search in highly meaningful stimuli.

On the costs and benefits of faces and words: Process characteristics of feature search in highly meaningful stimuli.

Dual scaling of comparison and reference stimuli in multi-dimensional psychological space

Channel-independent and sensor-independent stimulus representations

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