The perception of mirror-reflected objects

Image Forensics

From mainstream media outlets to social media and everything in between, doctored photographs are appearing with growing frequency and sophistication. The resulting lack of trust is impacting law enforcement, national security, the media, e-commerce, and more. While some types of manipulations can be detected with a careful visual examination, our visual system seems unable to reliably detect other types of manipulations. The field of image forensics has emerged to help return some trust in photography. I describe the perceptual limits of detecting manipulated images, as well as representative examples of computational techniques for authenticating images.

Mental-Rotation Effect: A Function of Elementary Stimulus Discriminability?

It is well known that when humans have to decide whether two differently oriented shapes are identical or mirror images their performance deteriorates as a function of the orientation disparity (mental-rotation effect). Here it is shown that the effect can also be obtained reliably with non-mirror-image, arbitrarily different polygons provided they are previously selected to be hard to discriminate. The slope of the decision speed versus orientation disparity functions was found to be inversely related to the discriminability of shapes under conditions of no, ie 0°, orientation disparity. Easily discriminable polygon pairs yielded essentially flat, no-effect functions. The arbitrary polygons that were more difficult to discriminate produced a rotation effect that was similar to those of mirror-image polygon pairs. Mirror images in this context may only be a special case of hard-to-discriminate stimuli. We also show that the speed of judging whether simple lines were of the same or different length was similarly subject to a rotation effect provided that the length differences were sufficiently small, ie when their baseline dicriminability was poor enough. It is suggested that the mental rotation of complex shapes (eg polygons) may build on rotation effects pertaining to the simpler elements of which they are composed. Further, some special effects associated with the rotation of such simpler components may explain certain peculiarities apparent in orientation invariance functions obtained with complex stimuli.

Differences between predictions of how a reflection behaves based on the behaviour of an object, and how an object behaves based on the behaviour of its reflection

We studied adults' understanding of the relationship between objects and their reflections. Two studies investigated whether adults performed in a similar way when asked to predict the movement of a reflection in a flat mirror based on the movement of the corresponding object or, vice versa, predict the movement of the material object based on the movement of its reflection. We used simple movements in the experiments: movements in a straight line at various angles with respect to the mirror. Despite the simplicity of the task, some of the participants made incorrect predictions in a percentage of cases ranging from 0% to 54%, depending on the angle. Asymmetries between the two directions of prediction emerged, in particular in terms of types of error. Results confirmed a cognitive difference between deriving the reflected (virtual) world from the "real" (material) world and vice versa. In particular the expectation that something will be opposite in a mirror is more salient when people imagine how a reflection will be with respect to the material world rather than when they imagine how the material world will be with respect to a reflection.

Through the looking glass: how the relationship between an object and its reflection affects the perception of distance and size

This is the first study to test the extent to which reflections help locate objects in space and perceive their size. For planar mirrors, the relative size of a target and its reflection is informative about the absolute distance of the target in units of the distance between target and mirror surface. When the target is near the mirror, target and reflection are similar in size; as the target moves away from the mirror, the difference in size increases. Observers saw a pair of objects in front of a mirror and judged relative size and distance (separately). Other visual cues to size and distance were eliminated, except lateral offset, which was tested in experiment 3. Experiment 2 controlled for the presence of directional feedback. Results showed orderly psychophysical functions for both size and distance with steeper slopes for distance judgments. In experiments 4 and 5 stereograms were used. Even when binocular information was present, the additional cue provided by reflections increased the accuracy of size and distance judgments. The same pattern of results was observed in the absence of feedback.

The Relationship Perceived between the Real Body and the Mirror Image

We analyse here people's perception of their reflections in mirrors placed in different positions. In two experiments, participants looked at their mirror image, in a third experiment they looked at another person's image. In both cases they were asked to answer a series of questions about how the virtual body appeared relative to the real body, focusing on different aspects. In experiment 1, they were asked to decide whether the reflections were identical, similar, different, or opposite in terms of the global relationship, orientation, and lateralisation (left-right arm). In experiment 2 they were instructed to make simple gestures and to evaluate if the gestures in the reflection were identical, opposite, similar, or different from theirs. Results show that ‘identity’ was preferred when the mirror was in front, and ‘opposition’ was preferred when the mirror was below. When opposition was experienced, it was attributed mainly to the exocentric frame of reference. Egocentric left – right reversal was not a common experience, although it was reported more frequently when the mirror was in front. The different roles of the exocentric and egocentric frames of reference were further tested in experiment 3, in which the condition of an observer looking at another person's reflection was studied. Contrary to the emphasis on the egocentric frame of reference in the literature on the ‘mirror question’, results presented in this paper demonstrate the importance of the exocentric frame of reference in influencing how observers react to their reflections.

Mirror reversal: empirical tests of competing accounts

In a mirror, left and right are said to look reversed. Surprisingly, this very familiar phenomenon, mirror reversal, has still no agreed-upon account to date. This study compared a variety of accounts in the light of empirical data. In Experiment 1, 102 students judged whether the mirror image of a person or a character looked reversed or not in 15 settings and also judged the directional relation between its components. In Experiment 2, 52 students made the reversal judgements in 13 settings. It was found for the first time that a substantial proportion of people denied the left-right mirror reversal of a person, whereas virtually all of them did recognize that of a character. This discrepancy strongly suggested that these two kinds of mirror reversal are produced by different processes, respectively. A number of findings including this discrepancy clearly contradicted two accounts that are currently active: the one based on the priority of the up-down and front-back axes over the left-right axis, and the one based on the physical rotation of an object. All the findings were consistent with an account that considered mirror reversal a complex of three different phenomena produced by three different processes, respectively.

Relationship between frames of reference and mirror-image reversals

The mirror puzzle related to the perception of mirror images as left-right reversed can be more fully understood by considering an extended problem that includes also the perception of mirror images that are not left-right reversed. The purpose of the present study is to clarify the physical aspect of this extended problem logically and parsimoniously. Separate use of the intrinsic frame of reference that belongs to the object and one that belongs to its mirror image always leads to the perception of left-right reversal when the object has left-right asymmetry; on the other hand, the perception of left-right nonreversal is always due to the application of a common frame of reference to the object and its mirror image.

Representing orientation: A coordinate-system hypothesis and evidence from developmental deficits

This article concerns how the orientations of objects are represented in the human brain. We propose a coordinate-system hypothesis of orientation representation (COR) and show that the hypothesis provides an explicit basis for interpreting orientation errors. Next, we report results from three studies of individuals with developmental deficits in the processing of orientation information, demonstrating that the COR hypothesis can interpret the error patterns in each study. We conclude by discussing several issues concerning the interpretation of our results, the COR hypothesis, and the use of developmental deficits as a basis for inferences about normal cognition.

Naive Optics: Acting on Mirror Reflections

It is known that naive observers have striking misconceptions about mirror reflections. In 5 experiments, this article systematically extends the findings to graphic stimuli, to interactive visual tasks, and finally to tasks involving real mirrors. The results show that the perceptual knowledge of nonexpert adults is far superior to their conceptual knowledge. Whereas conceptual errors include the assumption of left-right reversals in mirror images and often blatant extensions of the boundary of mirror space, the perceptual context prevents most such errors. However, a consistent bias to misjudge objects in mirrors too far to the outside is demonstrable in all cases including tasks with real mirrors. The authors present a 2-stage hypothesis consisting of an implicit bias of judging the mirror surface to be turned toward the observer's line of sight followed by a normalization that becomes explicit.

Much ado about mirrors

Takano (1998) has suggested four different kinds of reversal to explain why mirrors reverse left and right and not up and down or back and front. In fact, mirrors perform only one kind of reversal: They simply reverse about their own planes, and reflection about one plane is equivalent to reflection about any other, plus a translocation and rotation. The reflection of an object is termed its enantiomorph. Perception of the enantiomorphic relation normally requires an act, either physical or mental, of alignment. In deciding whether two objects are enantiomorphs, there is a tendency to align them so that the reversal is about the axis of least asymmetry. But in deciding whether a single object is one of two possible enantiomorphic forms, people generally rotate it to some canonical orientation. In the case of objects with defined top-bottom, back-front, and left-right axes, the canonical orientation is determined by the top-bottom and back-front axes, leaving the left-right axis to carry the reversal. The main reason for this, I suggest, is that the top-bottom and back-front axes have functional priority, and the left-right axis cannot be defined until top-bottom and back-front are established. This means that the latter two axes have priority in establishing the canonical orientation. The left-right axis is usually, but not always, the axis of least asymmetry.

Mirror image reversal: is what we see what we present?

Many psychological explanations have been advanced to explain left-right reversal in mirror images, but Gregory and Haig have each proposed a physical explanation for the reversal: the first is based upon the physical rotation used to present the surface of the object to the mirror, and the second on the classical optics of reflection. These physical explanations are considered together with an explanation based on object symmetry. The apparent reversal of directional coordinates (eg left and right) that occurs in the mirror images of most objects is distinguished from reversals achieved by physical or mental rotation. It is also distinguished from the object-image match that can be achieved by mental or physical rotation of some symmetrical objects. It is concluded that the left-right reversal is not specifically optical, but is determined by multiple factors, including object symmetry, the conventional and gravitational positioning of top and bottom and back and front, and our greater familiarity with right-left than with top-bottom or back-front reversals.

Reflections on inversion and reversion

A paper published recently in Perception has drawn attention to a question that appears to mystify psychologists, yet yields simply to the well-known law of reflection. The question of why a mirror reverses left and right, but not up and down, is explained in this paper, in terms of physical optics. The question of how mirror-reflected objects are perceived remains, of course, a psychological one.

Mirror reversals: real and perceived

A mirror optically reverses the axis perpendicular to its surface, but apparent reversals (eg right-left) can be seen parallel to the surface. This poses a perceptual problem which Ittelson, Mowafy, and Magid resolved by concluding that an object appears to differ from its mirror image by an apparent reversal along its axis of greatest symmetry. Three papers--two included in this discussion (by Haig and by Morris), and an earlier one by Gregory--that disagree with this conclusion are examined, and arguments advanced in them are shown to be unconvincing. The question of apparent mirror reversals is then discussed in more detail.