Projectively invariant representations using implicit algebraic curves
ECCV 90 Proceedings of the first european conference on Computer vision
On Recognizing and Positioning Curved 3-D Objects from Image Contours
IEEE Transactions on Pattern Analysis and Machine Intelligence
IEEE Transactions on Pattern Analysis and Machine Intelligence
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
Similarity-invariant signatures for partially occluded planar shapes
International Journal of Computer Vision
Computing stable poses of piecewise smooth objects
CVGIP: Image Understanding - Special issue on directions in CAD-based vision
Geometric invariance in computer vision
Geometric invariance in computer vision
Higher-order interpolation and least-squares approximation using implicit algebraic surfaces
ACM Transactions on Graphics (TOG)
Geometric invariants and object recognition
International Journal of Computer Vision
Invariant signatures for planar shape recognition under partial occlusion
CVGIP: Image Understanding
Describing Complicated Objects by Implicit Polynomials
IEEE Transactions on Pattern Analysis and Machine Intelligence
Projective invariants for planar contour recognition
ECCV '94 Proceedings of the third European conference on Computer vision (vol. 1)
Using Geometric Distance Fits for 3-D Object Modeling and Recognition
IEEE Transactions on Pattern Analysis and Machine Intelligence
Foundations of semi-differential invariants
International Journal of Computer Vision
IEEE Transactions on Pattern Analysis and Machine Intelligence
Determining the Axis of a Surface of Revolution Using Tactile Sensing
IEEE Transactions on Pattern Analysis and Machine Intelligence
Parameterized Families of Polynomials for Bounded Algebraic Curve and Surface Fitting
IEEE Transactions on Pattern Analysis and Machine Intelligence
High-Order Differentiation Filters that Work
IEEE Transactions on Pattern Analysis and Machine Intelligence
Using Symbolic Computation to Find Algebraic Invariants
IEEE Transactions on Pattern Analysis and Machine Intelligence
Matching of 3-D curves using semi-differential invariants
ICCV '95 Proceedings of the Fifth International Conference on Computer Vision
The Use of Size Functions for Comparison of Shapes Through Differential Invariants
Journal of Mathematical Imaging and Vision
Recognizing Articulated Objects Using a Region-Based Invariant Transform
IEEE Transactions on Pattern Analysis and Machine Intelligence
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A general paradigm for recognizing 3D objectsis offered, and applied to some geometric primitives (spheres, cylinders, cones, and tori). The assumption is that a curve onthe surface, or a pair of intersecting curves, was measuredwith high accuracy (for instance, by a sensory robot).Differential invariants of the curve(s) are then usedto recognize the surface. The motivation is twofold:the output of some devices is not surface range data, butsuch curves. Also, a considerablespeedup is obtained by using curve data, as opposed tosurface data which usually contains a much higher numberof points.We survey global, algebraic methods for recognizingsurfaces, and point out their limitations. Afterintroducing some notions from differential geometry and eliminationtheory, the differential and “semi-differential”approaches to the problem are described, and novelinvariants which are based on the curve's curvature andtorsion are derived.