Invariant Relationship

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In So Kweon - One of the best experts on this subject based on the ideXlab platform.

  • 3 d object recognition using a new Invariant Relationship by single view
    Pattern Recognition, 2000
    Co-Authors: Kyoung Sig Roh, In So Kweon
    Abstract:

    Abstract We propose a new method for recognizing three-dimensional objects using a three-dimensional Invariant Relationship and geometric hashing by single-view. We develop a special structure consisting of four co-planar points and any two non-planar points with respect to the plane. We derive an Invariant Relationship for the structure, which is represented by a plane equation. For the recognition of three-dimensional objects using the geometric hashing, a set of points on the plane, thereby satisfying the Invariant Relationship, are mapped into a set of points intersecting the plane and the unit sphere. Since the structure is much more general than the previous structures proposed by Rothwell et al. (Oxford University TR-OUEL 1927/92, 1992) and Zhu et al. (Proceedings of the 12th International Conference on Robotics and Automation, Nagoya, Japan, 1995, pp. 1726–1731), it gives enough many voting to generate hypotheses. We also show that from the proposed Invariant Relationship, an Invariant for the structure by two-view and an Invariant for a structure proposed by Zhu et al. (Proceedings of the 12th International Conference on Robotics and Automation, Nagoya, Japan, 1995, pp. 1726–1731) can also be derived. Experiments using three-dimensional polyhedral objects are carried out to demonstrate the feasibility of our method for three-dimensional objects.

  • 3 d object recognition using projective Invariant Relationship by single view
    International Conference on Robotics and Automation, 1998
    Co-Authors: Kyoung Sig Roh, Bume Jae You, In So Kweon
    Abstract:

    We propose a new method for recognizing three-dimensional objects using a three-dimensional Invariant Relationship for a special structure and geometric hashing by single-view. We use a special structure consisting of four co-planar points and any two non-coplanar points with respect to the plane. We derive an Invariant Relationship for the structure, which is represented by a plane equation. For recognition of 3-D objects using geometric hashing, a set of points on the plane is mapped into a set of points intersecting the plane and the unit sphere, thereby satisfying the Invariant Relationship. Experiments using 3-D polyhedral objects are carried out to demonstrate the feasibility of our method for 3-D object recognition.

Kyoung Sig Roh - One of the best experts on this subject based on the ideXlab platform.

  • 3 d object recognition using a new Invariant Relationship by single view
    Pattern Recognition, 2000
    Co-Authors: Kyoung Sig Roh, In So Kweon
    Abstract:

    Abstract We propose a new method for recognizing three-dimensional objects using a three-dimensional Invariant Relationship and geometric hashing by single-view. We develop a special structure consisting of four co-planar points and any two non-planar points with respect to the plane. We derive an Invariant Relationship for the structure, which is represented by a plane equation. For the recognition of three-dimensional objects using the geometric hashing, a set of points on the plane, thereby satisfying the Invariant Relationship, are mapped into a set of points intersecting the plane and the unit sphere. Since the structure is much more general than the previous structures proposed by Rothwell et al. (Oxford University TR-OUEL 1927/92, 1992) and Zhu et al. (Proceedings of the 12th International Conference on Robotics and Automation, Nagoya, Japan, 1995, pp. 1726–1731), it gives enough many voting to generate hypotheses. We also show that from the proposed Invariant Relationship, an Invariant for the structure by two-view and an Invariant for a structure proposed by Zhu et al. (Proceedings of the 12th International Conference on Robotics and Automation, Nagoya, Japan, 1995, pp. 1726–1731) can also be derived. Experiments using three-dimensional polyhedral objects are carried out to demonstrate the feasibility of our method for three-dimensional objects.

  • 3 d object recognition using projective Invariant Relationship by single view
    International Conference on Robotics and Automation, 1998
    Co-Authors: Kyoung Sig Roh, Bume Jae You, In So Kweon
    Abstract:

    We propose a new method for recognizing three-dimensional objects using a three-dimensional Invariant Relationship for a special structure and geometric hashing by single-view. We use a special structure consisting of four co-planar points and any two non-coplanar points with respect to the plane. We derive an Invariant Relationship for the structure, which is represented by a plane equation. For recognition of 3-D objects using geometric hashing, a set of points on the plane is mapped into a set of points intersecting the plane and the unit sphere, thereby satisfying the Invariant Relationship. Experiments using 3-D polyhedral objects are carried out to demonstrate the feasibility of our method for 3-D object recognition.

Zhanyi Hu - One of the best experts on this subject based on the ideXlab platform.

  • a robust method to recognize critical configuration for camera calibration
    Image and Vision Computing, 2006
    Co-Authors: Yihong Wu, Zhanyi Hu
    Abstract:

    When space points and camera optical center lie on a twisted cubic, no matter how many pairs there are used from the space points to their image points, camera parameters cannot be determined uniquely. This configuration is critical for camera calibration. We set up Invariant Relationship between six space points and their image points for the critical configuration. Then based on the Relationship, an algorithm to recognize the critical configuration of at least six pairs of space and image points is proposed by using a constructed criterion function, where no any explicit computation on camera projective matrix or optical center is needed. Experiments show the efficiency of the proposed method.

  • detecting critical configuration of six points
    Lecture Notes in Computer Science, 2006
    Co-Authors: Yihong Wu, Zhanyi Hu
    Abstract:

    When space points and camera optical center lie on a twisted cubic, no matter how many corresponding pairs there are from space points to their image points, camera projection matrix cannot be uniquely determined, in other words, the configuration of camera and space points in this case is critical for camera parameter estimation. In practice, it is important to detect this critical configuration before the estimated camera parameters are used. In this work, a new method is introduced to detect this critical configuration, which is based on an effective criterion function constructed from an Invariant Relationship between six space points and their corresponding image points. The advantage of this method is that no explicit computation on camera projection matrix or optical center is needed. Simulations show it is quite robust and stable against noise. Experiments on real data show the criterion function can be faithfully trusted for camera parameter estimation.

Yihong Wu - One of the best experts on this subject based on the ideXlab platform.

  • a robust method to recognize critical configuration for camera calibration
    Image and Vision Computing, 2006
    Co-Authors: Yihong Wu, Zhanyi Hu
    Abstract:

    When space points and camera optical center lie on a twisted cubic, no matter how many pairs there are used from the space points to their image points, camera parameters cannot be determined uniquely. This configuration is critical for camera calibration. We set up Invariant Relationship between six space points and their image points for the critical configuration. Then based on the Relationship, an algorithm to recognize the critical configuration of at least six pairs of space and image points is proposed by using a constructed criterion function, where no any explicit computation on camera projective matrix or optical center is needed. Experiments show the efficiency of the proposed method.

  • detecting critical configuration of six points
    Lecture Notes in Computer Science, 2006
    Co-Authors: Yihong Wu, Zhanyi Hu
    Abstract:

    When space points and camera optical center lie on a twisted cubic, no matter how many corresponding pairs there are from space points to their image points, camera projection matrix cannot be uniquely determined, in other words, the configuration of camera and space points in this case is critical for camera parameter estimation. In practice, it is important to detect this critical configuration before the estimated camera parameters are used. In this work, a new method is introduced to detect this critical configuration, which is based on an effective criterion function constructed from an Invariant Relationship between six space points and their corresponding image points. The advantage of this method is that no explicit computation on camera projection matrix or optical center is needed. Simulations show it is quite robust and stable against noise. Experiments on real data show the criterion function can be faithfully trusted for camera parameter estimation.

Bume Jae You - One of the best experts on this subject based on the ideXlab platform.

  • 3 d object recognition using projective Invariant Relationship by single view
    International Conference on Robotics and Automation, 1998
    Co-Authors: Kyoung Sig Roh, Bume Jae You, In So Kweon
    Abstract:

    We propose a new method for recognizing three-dimensional objects using a three-dimensional Invariant Relationship for a special structure and geometric hashing by single-view. We use a special structure consisting of four co-planar points and any two non-coplanar points with respect to the plane. We derive an Invariant Relationship for the structure, which is represented by a plane equation. For recognition of 3-D objects using geometric hashing, a set of points on the plane is mapped into a set of points intersecting the plane and the unit sphere, thereby satisfying the Invariant Relationship. Experiments using 3-D polyhedral objects are carried out to demonstrate the feasibility of our method for 3-D object recognition.