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Delboeuf illusion
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The Delboeuf illusion is an optical illusion of relative size perception. In the best-known version of the illusion, two circles of identical size have been placed near to each other and one is surrounded by an annulus; the surrounded circle then appears larger than the non-surrounded circle if the annulus is close, while appearing smaller than the non-surrounded circle if the annulus is distant. A 2005 study suggests it is caused by the same visual processes that cause the Ebbinghaus illusion.

Eponym
It was named for the Belgian philosopher, mathematician, experimental psychologist, hypnotist and psychophysicist Joseph Remi Leopold Delboeuf (1831–1896), who created it in 1865.

Factors
According to Joan s. Girgus, and Stanley Coren, the Delfbouf illusion uses both assimilation and contrast as elements in it visual distortion. Assimilation, is the predominate factor in the circle with the smaller outer ring (the example on the right in the image above). Girgus, and Coren mentioned that this inner circle “tends to be overestimated” when compared to a regular circle without the additional concentric circle. As the two circles are so close, they are perceived as a pair and the inner circle is overestimated.

The circle on the right however, will often appear smaller when compared to a simple circle of the same size. This is attributed to the contrast effect. As the larger circumferencing circle dwarfs the smaller central circle and causes it to be perceived as smaller when compared to a lone circle.

The combined effects however are susceptible to being diminished when held under scrutiny for a long period of time.

Studies regarding variations of the Delboeuf illusion found that when the outer circle is incomplete, the perceived size of the inner circle is not as heavy influenced by the illusion. When an additional circle was added surrounding the original two, the effect of the illusion was augmented.

Dieting
In 2012, Koert Van Ittersum and Brian Wansink published a study that hinted to the Delboeuf illusion as a factor in increased food servings. The study tested three different bowl diameters and measured how individuals served themselves differently depending on the bowl's diameter. The results showed that consumers poured 9.9% more soup in larger bowls, and 8.2% less in smaller bowls, as compared to the control bowls. It was mentioned that this reaction could be driven by the Delboeuf illusion.

This illusion in connection to food however appears to be nuanced. A study conducted by Ganel Tzvi and N Zitron-Emnual in 2018 highlighted how effects of the Delboeuf illusion when related to food items are less potent when the participants are experiencing mild hunger. The studies conductors referenced this finding as potential grounds for mitigating the use of the Delbeuf illusion as a dieting aid.

Role in Animal Cognition
The Delboeuf illusion (often in connection with the Ebbinghaus illusion) has been used with great frequency in testing animal perception. The ability to discern size is relevant for many aspects of survival. The perception of the Delboulf illusion seems to differ greatly depending on the species.

Primates
In 2014, Audrey E. Parrish and Michael J. Beran found that Chimpanzees would regularly select food platters that contained more food. Further testing showed that when chimpanzees were offered food on small and large plates, as they often picked the food on the smaller plate, even when the amounts were the same. This was discussed as a sign of the chimpanzee’s susceptibility to the Delboeuf illusion.

A later study showed that capuchin and rhesus monkeys however were unaffected by the illusion when asked to discriminate between the two circles. In contrast, when the illusion was presented to the monkey’s as part of an absolute classification task (deciding if the circles were "big" or "small"), The effects of the illusion were apparent in their actions to some degree.

An attempt to run tests of portion discrimination in connection to the delboulf illusion on ring-tailed lemurs was unsuccessful because the lemurs did not seem to use the increased food portions as a factor in meal selection, unless one option was nearly 40% larger.

Dogs
Maria Elena Miletto Petrazzini, Angelo Bisazza & Christian Agrillo, replicated the study conducted by Audrey E. Parrish and Michael J. Beran in 2014, but used dogs as the participants instead of chimpanzees. In this study, conducted in 2016, the dogs were allowed to select whichever appeared larger as presented on larger and smaller plates. The response however was reversed from what humans usually exhibit. Dogs elected the meal presented on the larger plate most often as the larger meal. The authors went on to discuss how this may hint towards the dogs reactions to the Delboeuf illusion as a matter of Assimilated learning.

Fish
Fish have been repeatedly studied as well to understand if they perceive the Delboeuf illusion. Fish trained to select larger center circles for reward, responded to the illusion differently depending on the species of fish. A 2008 study of damselfish seemed to show that damselfish responded to variations of the Dolboeuf  illusion in a similar ways to humans and Dolphins, while guppies responded in reverse, selecting the circles with the larger annulus. Bamboo sharks did not generally make selections significantly higher than chance during the testing, and only showed preference to larger diagrams in general.

Reptiles
Bearded dragons and Red-footed tortoise were both studied to understand if these species can perceive the Delboulf illusion. Bearded dragons showed action that seemed to suggest that they perceive the illusion in a similar way that humans do. The tortoises however, showed no preference to larger portions (a similar problem found in the study of ring-tailed lemurs) and were thus not testable by the method that had been outlined by the test designers.