The Geometries of Visual Space


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ABSTRACT THOUGHT AND THE POSITIVISTIC DENIAL OF TIME.

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When most people think of space, they think of physical space. However, visual space concerns space as consciously experienced, and it is studied through subjective matters, such as asking people to use numbers to estimate perceived distances, areas, angles, or volumes.


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This book explores the mismatch between perception and physical reality, and describes the many factors that influence the perception of space including the meaning assigned to geometric concepts like distance, the judgment methods used to report the experience, the presence or absence of cues to depth, and the orientation of a stimulus with respect to point of view.

The main theme of the text is that no single geometry describes visual space, but that the geometric of visual space depends upon the stimulus conditions and mental shifts in the subjective meaning of size and distance. While this book is primarily intended for scholars in perception, mathematical psychology, and psychophysics, it will also be accessible to a wider audience since it is written at a readable level. It will make a good graduate-level textbook on space perception.

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    Visual Signature of High-Dimensional Geometry in Parallel Coordinates Abstract: Although we can interactively rotate a 3D projected high-dimensional geometry and observe its dynamic changes, this traditional visualization method is limited and highly sensitive to the choice of viewing direction. Parallel-coordinates plots supplement this visualization scenario by providing statistical analysis of the geometry for distinct pairs of co-dimensions.

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    Such analysis results in visual signatures that embed geometric structures such as symmetry, and thus allows us to overview the status of the missing dimensions while exploring the projected geometry. This paper presents a blue-noise sampling approach for efficient construction of continuous parallel-coordinates plots of high-dimensional geometric surfaces defined by mathematical equations. We employ the parallel-coordinates plots with the embedded visual signatures to assist the interactive exploration of high-dimensional geometries, typically for 2-manifold embedded in 4-space.

    The Geometries of Visual Space The Geometries of Visual Space
    The Geometries of Visual Space The Geometries of Visual Space
    The Geometries of Visual Space The Geometries of Visual Space
    The Geometries of Visual Space The Geometries of Visual Space
    The Geometries of Visual Space The Geometries of Visual Space
    The Geometries of Visual Space The Geometries of Visual Space
    The Geometries of Visual Space The Geometries of Visual Space
    The Geometries of Visual Space The Geometries of Visual Space
    The Geometries of Visual Space

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