IEEE Transactions on Pattern Analysis and Machine Intelligence
Regular Article: Computing Fourier Transforms and Convolutions on the 2-Sphere
Advances in Applied Mathematics
Spherical wavelets: efficiently representing functions on the sphere
SIGGRAPH '95 Proceedings of the 22nd annual conference on Computer graphics and interactive techniques
A critique of structure-from-motion algorithms
Computer Vision and Image Understanding
Catadioptric Projective Geometry
International Journal of Computer Vision
Scalable Extrinsic Calibration of Omni-Directional Image Networks
International Journal of Computer Vision
Lambertian Reflectance and Linear Subspaces
IEEE Transactions on Pattern Analysis and Machine Intelligence
Catadioptric Omnidirectional Camera
CVPR '97 Proceedings of the 1997 Conference on Computer Vision and Pattern Recognition (CVPR '97)
Direct Method for Visual Scene Reconstruction
VSR '95 Proceedings of the IEEE Workshop on Representation of Visual Scenes
ICPR '96 Proceedings of the 1996 International Conference on Pattern Recognition (ICPR '96) Volume I - Volume 7270
Motion Segmentation and Tracking Using Normalized Cuts
ICCV '98 Proceedings of the Sixth International Conference on Computer Vision
Distinctive Image Features from Scale-Invariant Keypoints
International Journal of Computer Vision
Rotation Estimation from Spherical Images
ICPR '04 Proceedings of the Pattern Recognition, 17th International Conference on (ICPR'04) Volume 3 - Volume 03
Radon-Based Structure from Motion without Correspondences
CVPR '05 Proceedings of the 2005 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR'05) - Volume 1 - Volume 01
A theory of spherical harmonic identities for BRDF/Lighting transfer and image consistency
ECCV'06 Proceedings of the 9th European conference on Computer Vision - Volume Part IV
Image-based Visual Servoing with Central Catadioptric Cameras
International Journal of Robotics Research
Motion estimation by decoupling rotation and translation in catadioptric vision
Computer Vision and Image Understanding
Omnidirectional image processing using geodesic metric
ICIP'09 Proceedings of the 16th IEEE international conference on Image processing
A Variational Framework for Structure from Motion in Omnidirectional Image Sequences
Journal of Mathematical Imaging and Vision
Central catadioptric image processing with geodesic metric
Image and Vision Computing
Simultaneous Camera Pose and Correspondence Estimation with Motion Coherence
International Journal of Computer Vision
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We present a novel approach for the estimation of 3D-motion directly from two images using the Radon transform. The feasibility of any camera motion is computed by integrating over all feature pairs that satisfy the epipolar constraint. This integration is equivalent to taking the inner product of a similarity function on feature pairs with a Dirac function embedding the epipolar constraint. The maxima in this five dimensional motion space will correspond to compatible rigid motions. The main novelty is in the realization that the Radon transform is a filtering operator: If we assume that the similarity and Dirac functions are defined on spheres and the epipolar constraint is a group action of rotations on spheres, then the Radon transform is a correlation integral. We propose a new algorithm to compute this integral from the spherical Fourier transform of the similarity and Dirac functions. Generating the similarity function now becomes a preprocessing step which reduces the complexity of the Radon computation by a factor equal to the number of feature pairs processed. The strength of the algorithm is in avoiding a commitment to correspondences, thus being robust to erroneous feature detection, outliers, and multiple motions.