whole_GregoryRobynLee-Ann1996_thesis.pdf (16.76 MB)
Construction, viewing and perception of anamorphograms
thesisposted on 2023-05-27, 00:46 authored by Gregory, RL-A
In this thesis we mathematically describe various means of constructing pictures which are camouflaged, and which can only be recognized when viewed in an uncon-ventional, but prescribed manner. Such hidden, or distorted, pictures are referred to as anamorphoses or anamorphograms. We begin by considering some physiology of the eye and examine some psycho-physical research in Vision and Perception, particularly related to stereo psis. Some confusion in this area is identified and discussed. The reader is guided through simple, but increasingly complex, experiments. These facilitate the viewing of, and the understanding of how we 'see' three-dimensional images in, Single-Image Stereograms (commercially referred to as 'Magic Eye' pictures). Construction of examples of these is one of our main foci. Various viewing techniques are described, and we identify some parallels between the psycho-physical analysis of stereopsis, and the likely results obtained by the reader in viewing the simple dot stereograms presented in our experiments. We construct anamorphograms by applying a perspective drawing rule and some basic results of Optics. To be recognizable, our initial examples must be viewed monocularly from a prescribed viewpoint; or as a reflection in a given mirror; or wrapped around a given curved surface. Some of these examples are duplicated for binocular viewing in the form of anaglyphs, which allow the viewer to perceive a three-dimensional image. Further anamorphograms, for binocular viewing, in the form of Single-Image Stereograms, are constructed. Some related geometry results are presented, culmi-nating in the non-conventional representation of Single-Image Stereograms in terms of some results of Projective Geometry. We introduce the notion of a geometrical stereoscope which leads to the definition of a special central collineation and a con-sideration of a theorem related to fixed conics. Application of this result leads to the construction of a new Single-Image Stereogram of a sphere. This stereogram has special properties. We note the implications of the results of our introductory experimental section, for its viewing. Finally, we present anamorphograms which are compositions of the preceding cases and we include transcripts, together with explanations, of the computer pro-grams for creating all of our anamorphograms. These are written in Mathematica.
Rights statementCopyright 1996 the author - The University is continuing to endeavour to trace the copyright owner(s) and in the meantime this item has been reproduced here in good faith. We would be pleased to hear from the copyright owner(s). Describes mathematically various means of constructing anamorphoses (or anamorphograms). The physiology of the eye is considered, and stereopsis in particular, and anamorphograms constructed. Cylindrical mirror and anaglyph spectacles in pocket at back of vol. Thesis (M.Sc.)--University of Tasmania, 1996. Includes bibliographical references. Describes mathematically various means of constructing anamorphoses (or anamorphograms). The physiology of the eye is considered, and stereopsis in particular, and anamorphograms constructed