General methods for determining projective invariants in imagery
CVGIP: Image Understanding
Invariant Descriptors for 3D Object Recognition and Pose
IEEE Transactions on Pattern Analysis and Machine Intelligence - Special issue on interpretation of 3-D scenes—part I
Geometric invariance in computer vision
Geometric invariance in computer vision
Geometric invariants and object recognition
International Journal of Computer Vision
Model-based invariants for 3-D vision
International Journal of Computer Vision
Invariants of Six Points and Projective Reconstruction From Three Uncalibrated Images
IEEE Transactions on Pattern Analysis and Machine Intelligence
Projectively invariant decomposition and recognition of planar shapes
International Journal of Computer Vision - Special issue: machine vision research at the Royal Institute of Technology
View Variation of Point-Set and Line-Segment Features
IEEE Transactions on Pattern Analysis and Machine Intelligence
Noise-Resistant Invariants of Curves
IEEE Transactions on Pattern Analysis and Machine Intelligence
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In this paper, we derive new geometric invariants for structured 3D points and lines from single image under projective transform, and we propose a novel model-based 3D object recognition algorithm using them. Based on the matrix representation of the transformation between space features (points and lines) and the corresponding projected image features, new geometric invariants are derived via the determinant ratio technique. First, an invariant for six points on two adjacent planes is derived, which is shown to be equivalent to Zhu's result [1], but in simpler formulation. Then, two new geometric invariants for structured lines are investigated: one for five lines on two adjacent planes and the other for six lines on four planes. By using the derived invariants, a novel 3D object recognition algorithm is developed, in which a hashing technique with thresholds and multiple invariants for a model are employed to overcome the over-invariant and false alarm problems. Simulation results on real images show that the derived invariants remain stable even in a noisy environment, and the proposed 3D object recognition algorithm is quite robust and accurate.