Classification of impossible objects

Contextuality Analysis of Impossible Figures

This paper has two purposes. One is to demonstrate contextuality analysis of systems of epistemic random variables. The other is to evaluate the performance of a new, hierarchical version of the measure of (non)contextuality introduced in earlier publications. As objects of analysis we use impossible figures of the kind created by the Penroses and Escher. We make no assumptions as to how an impossible figure is perceived, taking it instead as a fixed physical object allowing one of several deterministic descriptions. Systems of epistemic random variables are obtained by probabilistically mixing these deterministic systems. This probabilistic mixture reflects our uncertainty or lack of knowledge rather than random variability in the frequentist sense.

Concept formation and categorization of complex, asymmetric, and impossible figures

Impossible figures are striking examples of inconsistencies between global and local perceptual structures, in which the overall spatial configuration of the depicted image does not yield a coherent three-dimensional object. In order to investigate whether structural "impossibility" is an important perceptual property of depicted objects, we used a category formation task in which subjects were asked to divide pictures of shapes into groups that seemed most natural to them. Category formation is usually unidimensional, such that sorting is dominated by a single perceptual property, so this task can serve as a measure of which dimensions are most salient. In Experiment 1, subjects received sets of 12 line drawings consisting of six possible and six impossible objects. Very few subjects grouped the figures by impossibility on the first try, and only half did so after multiple attempts at sorting. In Experiment 2, we investigated other global properties of figures: symmetry and complexity. Subjects readily sorted objects by complexity, but seldom by symmetry. In Experiment 3, subjects were asked to draw each of the figures before sorting them, which had only a minimal effect on categorization. Finally, in Experiment 4, subjects were explicitly instructed to divide the shapes by symmetry or impossibility. Performance on this task was perfect for symmetry, but not for impossibility. Although global properties of figures seem extremely important to our perception, the results suggest that some of these cues are not immediately obvious or salient for most observers.

Graph/Knot Theoretical Analysis and Generation for Impossible Figures

An algorithm to represent impossible multibar figures and their subclass of torus figures is proposed based on graph and knot theory. A multibar type graph, which is an abstract concept of multibar figures, is defined by the junction graph that represents the connections of the lines. It is shown that the junction graph is able to characterize multibar figures where this characterization is realized according to the type of the multibar type graph. An automatic drawing system of torus figures is also presented by analyzing junction graphs that construct the shapes of corners of torus figures. The proposed method aims a basic tool for experiments in visual psychology and possible/impossible figures generation.

Initial storage of unfamiliar objects: examining memory stores with signal detection analyses

The memory source(s) underlying performance of the object decision task were examined. Application of signal detection theory with independent indices of sensitivity and bias indicated that greater object decision sensitivity (possible vs. impossible object discrimination) is observed for primed than for unprimed objects and a greater bias to respond "possible" is observed for primed than for unprimed objects. To test whether a single memory store underlies the two effects, we assessed whether the two effects would be influenced in similar ways by a particular experimental manipulation. Sensitivity did not differ between processing of 180 degrees -rotated primed objects vs. un-rotated primed objects, but bias to respond "possible" differed between those conditions in predictable ways depending on the cerebral hemisphere of direct test presentations. Results support a conciliatory resolution to the debate concerning memory in this task and help to clarify properties of memory stores underlying the initial storage of unfamiliar objects.

Searching for impossible objects: processing form and attributes in early vision

In five experiments, we investigated the extent to which form (shape) and metric attributes (three-dimensional, 3-D, orientation), both defined by relations between line elements, are processed in early vision. Search for a target defined by an abstract property of form (i.e., impossibility) was slow and serial. In contrast, search for a 3-D orientation target was considerably easier. Subsequent experiments suggest that this difference reflects the fact that 3-D orientation is derivable from localized sets of lines, whereas impossibility is an idiosyncratic property of the complete set of relations between lines. We conclude that only "gross" aspects of form are available in early vision as the complete set of line relations is not processed preattentively. However, localized processing of line relations is sufficient to derive 3-D orientation.

The relative effectiveness of serial and parallel viewing of line drawings depicting possible and impossible objects

In a series of experiments, subjects were asked to make judgements concerning the three-dimensional constructibility of line drawings depicting possible and impossible objects. A spectrum of objects was employed in which complexity as well as, for impossible objects, the cause and saliency of the contradiction in three-dimensional structure varied widely. The line drawings were presented under varying viewing conditions and exposure times. It was found that line drawings of possible objects were more often correctly identified than those of impossible ones. Parallel (simultaneous) viewing was more efficient than serial viewing (in which a line drawing moved behind a narrow stationary aperture). The orientation of the aperture did not cause differences in the subjects' performance. Line-drawing complexity and contradiction in three-dimensional structure were not found to be significant for accurate recognition. Finally, no consistent effect of exposure duration on performance could be determined in the range 60-1000 ms.

Putting order in the impossible

The class of visual illusions called 'impossible figures' (illusory spatial interpretations of pictures) is analyzed in order to introduce an ordering into the great variety of such figures. Such an ordering facilitates reference, unifies terminology, and establishes a conceptual framework for further investigations of the subject, making easier the choice and systematic generation of various types of figures (for example, in systematic psychological experiments). First, the notion of 'impossible figure' is defined and certain other related classes of figures (so-called 'likely' and 'unlikely' figures) are distinguished. Second, the fundamental 'impossibility sources' are identified as elementary 'building blocks' of all impossible figures. Finally, two broad classes of impossible figures, multibars (or 'impossible polygons') and striped figures, are briefly described.

A test of the minimum principle requires a perceptual coding system

The minimum principle states that a perceiver will see the simplest possible interpretation of a pattern. Some theorists of human perception take this principle as a core explanatory concept. Others, especially Rock and Hochberg, hold the view that a perceptual minimum principle is untenable. Rock presents a great number of demonstrations which, in his opinion, rule out the minimum principle. Hochberg states that 'impossible' figures especially present a difficulty for this principle. It is argued here that, in order to test the minimum principle, a method is needed to describe interpretations of patterns in such a way that they can be ordered according to simplicity. To achieve this, Leeuwenberg's coding system was used. The analyses reported here of the patterns which Rock produces as evidence against the principle show that, contrary to Rock's claim, the way these patterns are preferentially perceived provides strong support for the minimum principle. Next, it is demonstrated that interpreting certain patterns as 'impossible' figures is not incompatible with the principle. Finally, it is argued that a test of the minimum principle is necessarily conflated with two other hypotheses, one concerning the metric of simplicity and one concerning the task conception of the experimental subjects.

Mathematical structures of line drawings of polyhedrons-toward man-machine communication by means of line drawings

Mathematical structures of line drawings of polyhedrons are studied and practical as well as theoretical solutions are obtained for several fundamental problems aroused in scene analysis and in man-machine communication. First, a necessary and sufficient condition for a line drawing to correctly represent a polyhedron is obtained in terms of linear algebra. Next, combinatorial structures are investigated and practical solutions are obtained to such problems as how to discriminate between correct and incorrect line drawings and how to correct vertex-position errors in incorrect line drawings. Lastly, distribution of the degree of freedom of a line drawing is elucidated and a method is proposed for interactive reconstruction of a polyhedron from a line drawing. The results obtained here enable us to make manmachine communication more ``flexible'' in the sense that a machine can reconstruct three-dimensional objects from hand-drawn pictures even if the pictures are not perfect.