Topic
Parallel projection
About: Parallel projection is a research topic. Over the lifetime, 838 publications have been published within this topic receiving 11038 citations.
Papers published on a yearly basis
1 / 2
Papers
26 Jun 2000
TL;DR: This paper provides a unifying theory for all central catadioptric systems and shows that all of them are isomorphic to projective mappings from the sphere to a plane with a projection center on the perpendicular to the plane.
Abstract: Omnidirectional vision systems can provide panoramic alertness in surveillance, improve navigational capabilities, and produce panoramic images for multimedia. Catadioptric realizations of omnidirectional vision combine reflective surfaces and lenses. A particular class of them, the central panoramic systems, preserve the uniqueness of the projection viewpoint. In fact, every central projection system including the well known perspective projection on a plane falls into this category.
In this paper, we provide a unifying theory for all central catadioptric systems. We show that all of them are isomorphic to projective mappings from the sphere to a plane with a projection center on the perpendicular to the plane. Subcases are the stereographic projection equivalent to parabolic projection and the central planar projection equivalent to every conventional camera. We define a duality among projections of points and lines as well as among different mappings.
This unification is novel and has a significant impact on the 3D interpretation of images. We present new invariances inherent in parabolic projections and a unifying calibration scheme from one view. We describe the implied advantages of catadioptric systems and explain why images arising in central catadioptric systems contain more information than images from conventional cameras. One example is that intrinsic calibration from a single view is possible for parabolic catadioptric systems given only three lines. Another example is metric rectification using only affine information about the scene.
605 citations
Patent•
26 Feb 2001TL;DR: In this paper, an apparatus and method for real-time volume processing and universal three-dimensional rendering is presented, which includes a block processor having a circular ray integration pipeline for processing voxel data and ray data.
Abstract: An apparatus and method for real-time volume processing and universal three-dimensional rendering. The apparatus includes a plurality of three-dimensional (3D) memory units (24); at least one pixel bus for providing global horizontal communication (34); a plurality of rendering pipelines; at least one geometry bus (46); and a control unit (38). The apparatus includes a block processor having a circular ray integration pipeline for processing voxel data and ray data. Rays are generally processed in image order thus permitting great flexibility (e.g., perspective projection, global illumination). The block processor includes a splatting unit and a scattering unit. A method for casting shadows and performing global illumination in relation to light sources, which includes sweeping a two dimensional array of rays through the volume, can also be implemented with the apparatus. A method for approximating a perspective projection includes using parallel projection.
336 citations
TL;DR: There is no evidence for any type of projection resulting from a trait which S is not aware that he possesses, which calls into question the existence and interpretive use of "classical" projection, the type of response referred to most frequently by the term "projection."
Abstract: Past confusion over the concept of projection, especially with regard to the related research evidence, has stemmed from the fact that numerous types of projections have been proposed which were not clearly differentiated from each other. In the present paper it is pointed out that theories of projection differ with regard to 2 major points: (a) whether the individual projects his own trait or a different (complementary) trait, and (b) whether the individual is aware or unaware of possessing the trait which results in the projection. The 4 possible combinations resulting from these theoretical differences are plotted in a 2 X 2 table, which provides a system in which the various types of projection and related research can be classified and compared. A critical review of the research on each type reveals that there is strong evidence for the projection of S's own trait or the complement of this trait if S is aware that he possesses the trait. There is no evidence for any type of projection resulting from a trait which S is not aware that he possesses. This finding calls into question the existence and interpretive use of \"classical\" (or similarity) projection, the type of response referred to most frequently by the term \"projection.\
226 citations
1 Dec 2001
TL;DR: A general model for central catadioptric image formation made up of three functions: a linear function mapping the world into an oriented projective plane, a nonlinear transformation between twooriented projective planes, and a collineation in the plane is established.
Abstract: An imaging system with a single effective viewpoint is called a central projection system. The conventional perspective camera is an example of a central projection system. Systems using mirrors to enhance the field of view while keeping a unique center of projection are also examples of central projection systems. Perspective image formation can be described by a linear model with well known properties. In general central catadioptric imaging, the mapping between points in the world and in the image is highly nonlinear. The paper establishes a general model for central catadioptric image formation made up of three functions: a linear function mapping the world into an oriented projective plane, a nonlinear transformation between two oriented projective planes, and a collineation in the plane. The model is used to study issues in the projection of lines. The equations and geometric properties of general catadioptric imaging of lines are derived. The application of the results in auto-calibration of central catadioptric systems and reconstruction are discussed. A method to calibrate the system using three line images is presented.
173 citations
TL;DR: Investigation of how patterns of optical texture provide information about the three-dimensional structure of objects in space revealed that judged depth increases linearly with simulated depth although the slope of this relation varies significantly among different types of texture patterns.
Abstract: The research described in the present article was designed to investigate how patterns of optical texture provide information about the three-dimensional structure of objects in space. Four experiments were performed in which observers were asked to judge the perceived depth of simulated ellipsoid surfaces under a variety of experimental conditions. The results revealed that judged depth increases linearly with simulated depth although the slope of this relation varies significantly among different types of texture patterns. Random variations in the sizes and shapes of individual surface elements have no detectable effect on observers' judgments. The perception of three-dimensional form is quite strong for surfaces displayed under parallel projection, but the amount of apparent depth is slightly less than for identical surfaces displayed under polar projection. Finally, the perceived depth of a surface is eliminated if the optical elements in a display are not sufficiently elongated or if they are not approximately aligned with one another. A theoretical explanation of these findings is proposed based on the neural network analysis of Grossberg and Mingolla. Language: en
162 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
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| 2024 | 1 |
| 2023 | 1 |
| 2022 | 3 |
| 2021 | 4 |
| 2020 | 13 |
| 2019 | 12 |