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For nine popular geometrical visual-illusion figures, a mathematical analysis is provided along with a characterization of the figures' psychological effectiveness. Supported by graphical illustrations, for the L and the T, it is shown how mathematical singularities of these figures can be isolated, and the illusions annihilated. For the Poggendorff, the Hering, and the Zöllner figures, building on observations from Kennedy and Portal (1990), sighting the figures from specific vantage points at a shallow angle is proposed as a means to overcome these illusions. For the T, the Oppel–Kundt, the Müller–Lyer, and the Ebbinghaus figures, a new experiment demonstrated that observers were able to find a slant of the stimuli at which the illusory impressions vanished. Task demands on part of the beholders comprise discrimination and identification. The observed independence of response bias and sensitivity in psychometric functions can possibly be explained by the intrusion of identifying responses into discrimination tasks. [ABSTRACT FROM AUTHOR]

Geometrical visual illusions have long been used as tools in neuroscience. Most commonly, researchers have taken illusions as a given and attempted to explain phenomenal impressions in terms of known neural mechanisms. In a psychophysical approach to this topic, it is customary to modify stimuli until conditions for which illusions are enhanced, attenuated, or annihilated have been found. Additionally, the focus is not exclusively on response bias but equally on sensitivity, because observers may fall prey to an illusion but at the same time be able to discriminate between stimuli perfectly. For the T-figure, the length of the undivided line is usually overestimated relative to the length of the divided line, and evidence has accrued that suggests that the illusion may be due to the processing of the figure as a coherent unit (a "T-schema"). Dissecting the T or tilting its lines influenced the amount of illusion, suggesting that interactions between orientation-sensitive and end-inhibited neurons are at work. Examples of cognate research with the Ponzo, Ebbinghaus, and Müller-Lyer illusions are also discussed. [ABSTRACT FROM AUTHOR]

For nine popular geometrical visual-illusion figures, a mathematical analysis is provided along with a characterization of the figures’ psychological effectiveness. Supported by graphical illustrations, for the L and the T, it is shown how mathematical singularities of these figures can be isolated, and the illusions annihilated. For the Poggendorff, the Hering, and the Zöllner figures, building on observations from Kennedy and Portal (1990), sighting the figures from specific vantage points at a shallow angle is proposed as a means to overcome these illusions. For the T, the Oppel–Kundt, the Müller–Lyer, and the Ebbinghaus figures, a new experiment demonstrated that observers were able to find a slant of the stimuli at which the illusory impressions vanished. Task demands on part of the beholders comprise discrimination and identification. The observed independence of response bias and sensitivity in psychometric functions can possibly be explained by the intrusion of identifying responses into discrimination tasks.

Geometrical visual illusions have long been used as tools in neuroscience. Most commonly, researchers have taken illusions as a given and attempted to explain phenomenal impressions in terms of known neural mechanisms. In a psychophysical approach to this topic, it is customary to modify stimuli until conditions for which illusions are enhanced, attenuated, or annihilated have been found. Additionally, the focus is not exclusively on response bias but equally on sensitivity, because observers may fall prey to an illusion but at the same time be able to discriminate between stimuli perfectly. For the T-figure, the length of the undivided line is usually overestimated relative to the length of the divided line, and evidence has accrued that suggests that the illusion may be due to the processing of the figure as a coherent unit (a “T-schema”). Dissecting the T or tilting its lines influenced the amount of illusion, suggesting that interactions between orientation-sensitive and end-inhibited neurons are at work. Examples of cognate research with the Ponzo, Ebbinghaus, and Müller-Lyer illusions are also discussed.