Perspective Projection

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David G. Lowe - One of the best experts on this subject based on the ideXlab platform.

  • Rigidity checking of 3D point correspondences under Perspective Projection
    IEEE Transactions on Pattern Analysis and Machine Intelligence, 1996
    Co-Authors: Daniel Mcreynolds, David G. Lowe
    Abstract:

    An algorithm is described which rapidly verifies the potential rigidity of three-dimensional point correspondences from a pair of two-dimensional views under Perspective Projection. The output of the algorithm is a simple yes or no answer to the question "Could these corresponding points from two views be the Projection of a rigid configuration?" Potential applications include 3D object recognition from a single previous view and correspondence matching for stereo or motion over widely separated views. The rigidity checking problem is different from the structure-from-motion problem because it is often the case that two views cannot provide an accurate structure-from-motion estimate due to ambiguity and ill conditioning, whereas it is still possible to give an accurate yes/no answer to the rigidity question. Rigidity checking verifies point correspondences using 3D recovery equations as a matching condition. The proposed algorithm improves upon other methods that fall under this approach because it works with as few as six corresponding points under full Perspective Projection, handles correspondences from widely separated views, makes full use of the disparity of the correspondences, and is integrated with a linear algorithm for 3D recovery due to Kontsevich (1993). Results are given for experiments with synthetic and real image data. A complete implementation of this algorithm is being made publicly available.

  • rigidity checking of 3d point correspondences under Perspective Projection
    International Conference on Computer Vision, 1995
    Co-Authors: Daniel Mcreynolds, David G. Lowe
    Abstract:

    An algorithm is described which rapidly verifies the potential rigidity of three dimensional point correspondences from a pair of three dimensional views under Perspective Projection. The output of the algorithm is a simple yes or no answer to the question "Could these corresponding points from two views be the Projection of a rigid configuration?" Potential applications include 3D object recognition from a single previous view and correspondence matching for stereo or motion over widely separated views. Rigidity checking verifies point correspondences by using 3D recovery equations as a matching condition. The proposed algorithm improves upon other methods that fall under this approach because it works with as few as six corresponding points under full Perspective Projection, handles correspondences from widely separated views, makes full use of the disparity of the correspondences, and is integrated with a linear algorithm for 3D recovery due to Kontsevich (1991). Results are given for experiments with synthetic and real image data. A complete implementation of this algorithm is being made publicly available. >

Arie E Kaufman - One of the best experts on this subject based on the ideXlab platform.

  • 3d virtual colonoscopy with real time volume rendering
    Medical Imaging 2000: Physiology and Function from Multidimensional Images, 2000
    Co-Authors: Wei-jian Li, Ingmar Bitter, Kevin Kreeger, Arie E Kaufman, Zhengrong Liang, Dongqing Chen
    Abstract:

    In our previous work, we developed a virtual colonoscopy system on a high-end 16-processor SGI Challenge with an expensive hardware graphics accelerator. The goal of this work is to port the system to a low cost PC in order to increase its availability for mass screening. Recently, Mitsubishi Electric has developed a volume-rendering PC board, called VolumePro, which includes 128 MB of RAM and vg500 rendering chip. The vg500 chip, based on Cube-4 technology, can render a 256 3 volume at 30 frames per second. High image quality of volume rendering inside the colon is guaranteed by the full lighting model and 3D interpolation supported by the vg500 chip. However, the VolumePro board is lacking some features required by our interactive colon navigation. First, VolumePro currently does not support Perspective Projection which is paramount for interior colon navigation. Second, the patient colon data is usually much larger than 256 3 and cannot be rendered in real-time. In this paper, we present our solutions to these problems, including simulated Perspective Projection and axis aligned boxing techniques, and demonstrate the high performance of our virtual colonoscopy system on low cost PCs.

  • a ray slice sweep volume rendering engine
    International Conference on Computer Graphics and Interactive Techniques, 1997
    Co-Authors: Ingmar Bitter, Arie E Kaufman
    Abstract:

    Ray-slice-sweeping is a plane sweep algorithm for volume rendering, The compositing buffer sweeps through the volume and combines the accumulated image with the new slice of just-projected voxels. The image combination is guided by sight rays from the view point through every voxel of the new slice. Cube-.#L is a volume rendering architecture which employs a ray-slice-sweeping algorithm. It improves the Cube-4 architecture in three ways. First, during Perspective Projection all voxels of the dataset contribute to the rendering. Second, it computes gradients at the voxel positions which improves accuracy and allows a more compact implementation, Third, Cube-AL has less control overhead than Cube-C

Hongbin Zha - One of the best experts on this subject based on the ideXlab platform.

  • fisheye lenses calibration using straight line spherical Perspective Projection constraint
    Asian Conference on Computer Vision, 2006
    Co-Authors: Xianghua Ying, Hongbin Zha
    Abstract:

    Fisheye lenses are often used to enlarge the field of view (FOV) of a conventional camera. But the images taken with fisheye lenses have severe distortions. This paper proposes a novel calibration method for fisheye lenses using images of space lines in a single fisheye image. Since some fisheye cameras’ FOV are around 180 degrees, the spherical Perspective Projection model is employed. It is well known that under spherical Perspective Projection, straight lines in space have to be projected into great circles in the spherical Perspective image. That is called straight-line spherical Perspective Projection constraint (SLSPPC). In this paper, we use SLSPPC to determine the mapping between a fisheye image and its corresponding spherical Perspective image. Once the mapping is obtained, the fisheye lenses is calibrated. The parameters to be calibrated include principal point, aspect ratio, skew factor, and distortion parameters. Experimental results for synthetic data and real images are presented to demonstrate the performances of our calibration algorithm.

  • fisheye lenses calibration using straight line spherical Perspective Projection constraint
    Lecture Notes in Computer Science, 2006
    Co-Authors: Xianghua Ying, Hongbin Zha
    Abstract:

    Fisheye lenses are often used to enlarge the field of view (FOV) of a conventional camera. But the images taken with fisheye lenses have severe distortions. This paper proposes a novel calibration method for fisheye lenses using images of space lines in a single fisheye image. Since some fish-eye cameras' FOV are around 180 degrees, the spherical Perspective Projection model is employed. It is well known that under spherical Perspective Projection, straight lines in space have to be projected into great circles in the spherical Perspective image. That is called straight-line spherical Perspective Projection constraint (SLSPPC). In this paper, we use SLSPPC to determine the mapping between a fisheye image and its correspending spherical Perspective image. Once the mapping is obtained, the fisheye lenses is calibrated. The parameters to be calibrated include principal point, aspect ratio, skew factor, and distortion parameters. Experimental results for synthetic data and real images are presented to demonstrate the performances of our calibration algorithm.

Thomas S Huang - One of the best experts on this subject based on the ideXlab platform.

  • recover human pose from monocular image under weak Perspective Projection
    International Conference on Computer Vision, 2005
    Co-Authors: Minglei Tong, Yuncai Liu, Thomas S Huang
    Abstract:

    In this paper we construct a novel human body model using convolution surface with articulated kinematic skeleton. The human body's pose and shape in a monocular image can be estimated from convolution curve through nonlinear optimization. The contribution of the paper is in three folds: Firstly, human model based convolution surface with articulated skeletons is presented and its shape is deformable when changing polynomial parameters and radius parameters. Secondly, we give convolution surface and curve correspondence theorem under weak Perspective Projection, which provide a bridge between the 3D pose and 2D contour. Thirdly, we model the human body's silhouette with convolution curve in order to estimate joint's parameters from monocular images. Evalution of the method is performed on a sequence of video frames about a walking man.

  • Optimum Fiducials Under Weak Perspective Projection
    International Journal of Computer Vision, 1999
    Co-Authors: Alfred M. Bruckstein, Thomas S Huang, Robert J. Holt, Arun N. Netravali
    Abstract:

    We investigate how a given fixed number of points should be located in space so that the pose of a camera viewing them from unknown locations can be estimated with the greatest accuracy. We show that optimum solutions are obtained when the points form concentric complete regular polyhedra. For the case of optimal configurations we provide a worst-case error analysis and use it to analyze the effects of weak Perspective approximation to true Perspective viewing. Comprehensive computer simulations validate the theoretical results.

Ingmar Bitter - One of the best experts on this subject based on the ideXlab platform.

  • 3d virtual colonoscopy with real time volume rendering
    Medical Imaging 2000: Physiology and Function from Multidimensional Images, 2000
    Co-Authors: Wei-jian Li, Ingmar Bitter, Kevin Kreeger, Arie E Kaufman, Zhengrong Liang, Dongqing Chen
    Abstract:

    In our previous work, we developed a virtual colonoscopy system on a high-end 16-processor SGI Challenge with an expensive hardware graphics accelerator. The goal of this work is to port the system to a low cost PC in order to increase its availability for mass screening. Recently, Mitsubishi Electric has developed a volume-rendering PC board, called VolumePro, which includes 128 MB of RAM and vg500 rendering chip. The vg500 chip, based on Cube-4 technology, can render a 256 3 volume at 30 frames per second. High image quality of volume rendering inside the colon is guaranteed by the full lighting model and 3D interpolation supported by the vg500 chip. However, the VolumePro board is lacking some features required by our interactive colon navigation. First, VolumePro currently does not support Perspective Projection which is paramount for interior colon navigation. Second, the patient colon data is usually much larger than 256 3 and cannot be rendered in real-time. In this paper, we present our solutions to these problems, including simulated Perspective Projection and axis aligned boxing techniques, and demonstrate the high performance of our virtual colonoscopy system on low cost PCs.

  • a ray slice sweep volume rendering engine
    International Conference on Computer Graphics and Interactive Techniques, 1997
    Co-Authors: Ingmar Bitter, Arie E Kaufman
    Abstract:

    Ray-slice-sweeping is a plane sweep algorithm for volume rendering, The compositing buffer sweeps through the volume and combines the accumulated image with the new slice of just-projected voxels. The image combination is guided by sight rays from the view point through every voxel of the new slice. Cube-.#L is a volume rendering architecture which employs a ray-slice-sweeping algorithm. It improves the Cube-4 architecture in three ways. First, during Perspective Projection all voxels of the dataset contribute to the rendering. Second, it computes gradients at the voxel positions which improves accuracy and allows a more compact implementation, Third, Cube-AL has less control overhead than Cube-C