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c ° 1999 Kluwer Academic Publishers. Manufactured in The Netherlands. Geometry of Distorted Visual Space and Cremona Transformation
, 1998
"... Abstract. An important issue concerning the design of any vision system is the choice of a proper space representation. In order to search for clues to a suitable representation, we look at the distortion of space arising from errors in motion or stereo estimates. Understanding this space distortio ..."
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or physiological study but rather a computational one. We show that the distortion transformation is a quadratic Cremona transformation, which is bijective almost everywhere except on the set of fundamental elements. We identify the fundamental elements of both the direct and the inverse transformations, and study
Distortions of Stereoscopic Visual Space and Quadratic Cremona Transformations
"... . When incorrect values for the extrinsic and intrinsic parameters of the two cameras of a stereo rig are used in the reconstruction of a threedimensional scene from image correspondences, the resulting reconstruction is distorted in a systematic way. We show here that the transformation betwee ..."
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between the true scene structure and its distorted reconstruction is a quadratic Cremona transformation  a rational transformation which is onetoone almost everywhere, but which does not in general preserve collinearity. We study the distortion of points in the fixation plane on a global
Distortion of Stereoscopic Visual Space
, 1997
"... A stereo vision system requires accurate knowledge of the internal parameters of its two cameras and of the relative orientation between them in order to faithfully reconstruct a scene from corresponding image points. When incorrect values for the parameters of the stereo system are used, the result ..."
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Cited by 1 (1 self)
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, the resulting reconstruction is distorted in a systematic way. The transformation between the true scene structure and its distorted reconstruction, which we call the shape distortion transformation, is a quadratic Cremona transformation  a rational transformation that is onetoone almost everywhere
Visual Space Distortion
 Biological Cybernetics
, 1997
"... We are surrounded by surfaces that we perceive by visual means. Understanding the basic principles behind this perceptual process is a central theme in visual psychology, psychophysics and computational vision. In many of the computational models employed in the past, it has been assumed that a metr ..."
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Cited by 13 (12 self)
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metric representation of physical space can be derived by visual means. Psychophysical experiments, as well as computational considerations, can convince us that the perception of space and shape has a much more complicated nature, and that only a distorted version of actual, physical space can
Explaining Human Visual Space Distortion
, 1996
"... We are surrounded by surfaces that we perceive by visual means. Understanding the basic principles behind this perceptual process is a central theme in visual psychology, psychophysics and computational vision. Metric descriptions of physical space encoding distances between features in the environm ..."
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Cited by 3 (1 self)
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We are surrounded by surfaces that we perceive by visual means. Understanding the basic principles behind this perceptual process is a central theme in visual psychology, psychophysics and computational vision. Metric descriptions of physical space encoding distances between features
Some properties of the Cremona group
, 2012
"... We recall some properties, unfortunately not all, of the Cremona group. We first begin by presenting a nice proof of the amalgamated product structure of the wellknown subgroup of the Cremona group made up of the polynomial automorphisms of C2. Then we deal with the classification of birational ma ..."
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We recall some properties, unfortunately not all, of the Cremona group. We first begin by presenting a nice proof of the amalgamated product structure of the wellknown subgroup of the Cremona group made up of the polynomial automorphisms of C2. Then we deal with the classification of birational
Visual SpaceTime Geometry and Statistics
"... Although the fundamental ideas underlying research efforts in the field of computer vision have not radically changed in the past two decades, there has been a transformation in the way work in this field is conducted. This is primarily due to the emergence of a number of tools, of both a practical ..."
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and a theoretical nature. One such tool, celebrated throughout the nineties, is the geometry of visual spacetime. It is known under a variety of headings, such as multiple view geometry, structure from motion, and model building. It is a mathematical theory relating multiple views (images) of a scene
Biological Cybernetics c ○ SpringerVerlag 1997 Visual space distortion
"... Abstract. We are surrounded by surfaces that we perceive by visual means. Understanding the basic principles behind this perceptual process is a central theme in visual psychology, psychophysics, and computational vision. In many of the computational models employed in the past, it has been assumed ..."
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that a metric representation of physical space can be derived by visual means. Psychophysical experiments, as well as computational considerations, can convince us that the perception of space and shape has a much more complicated nature, and that only a distorted version of actual, physical space can
EUCLIDEAN DISTANCE GEOMETRY AND APPLICATIONS
"... Abstract. Euclidean distance geometry is the study of Euclidean geometry based on the concept of distance. This is useful in several applications where the inputdataconsistsofanincompleteset of distances, and the output is a set of points in Euclidean space that realizes the given distances. We surv ..."
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Cited by 6 (1 self)
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Abstract. Euclidean distance geometry is the study of Euclidean geometry based on the concept of distance. This is useful in several applications where the inputdataconsistsofanincompleteset of distances, and the output is a set of points in Euclidean space that realizes the given distances. We
Results 1  10
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