Using Symbolic Computation to Find Algebraic Invariants

Authors:
D. Keren
Affiliations:
-
Venue:
IEEE Transactions on Pattern Analysis and Machine Intelligence
Year:
1994

Citing 9
Cited 9

Mathematica: a system for doing mathematics by computer

Mathematica: a system for doing mathematics by computer
On Recognizing and Positioning Curved 3-D Objects from Image Contours

IEEE Transactions on Pattern Analysis and Machine Intelligence
Polynomial Methods for Structure from Motion

IEEE Transactions on Pattern Analysis and Machine Intelligence
Estimation of Planar Curves, Surfaces, and Nonplanar Space Curves Defined by Implicit Equations with Applications to Edge and Range Image Segmentation

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
Geometric invariance in computer vision

Geometric invariance in computer vision
Geometric invariants and object recognition

International Journal of Computer Vision
Describing Complicated Objects by Implicit Polynomials

IEEE Transactions on Pattern Analysis and Machine Intelligence
Proceedings of the Second Joint European - US Workshop on Applications of Invariance in Computer Vision

Proceedings of the Second Joint European - US Workshop on Applications of Invariance in Computer Vision

Fitting Curves and Surfaces With Constrained Implicit Polynomials

IEEE Transactions on Pattern Analysis and Machine Intelligence
Recognizing 3D Objects Using Tactile Sensing and Curve Invariants

Journal of Mathematical Imaging and Vision
Hand Recognition Using Implicit Polynomials and Geometric Features

AVBPA '01 Proceedings of the Third International Conference on Audio- and Video-Based Biometric Person Authentication
Combining implicit polynomials and geometric features for hand recognition

Pattern Recognition Letters - Special issue: Audio- and video-based biometric person authentication (AVBPA 2001)
The Classical Theory of Invariants and Object Recognition Using Algebraic Curve and Surfaces

Journal of Mathematical Imaging and Vision
Topologically Faithful Fitting of Simple Closed Curves

IEEE Transactions on Pattern Analysis and Machine Intelligence
A Generalization of Moment Invariants on 2D Vector Fields to Tensor Fields of Arbitrary Order and Dimension

ISVC '09 Proceedings of the 5th International Symposium on Advances in Visual Computing: Part II
A complete system of measurement invariants for Abelian lie transformation groups

Scale Space'03 Proceedings of the 4th international conference on Scale space methods in computer vision
Multilevel algebraic invariants extraction by incremental fitting scheme

ACCV'09 Proceedings of the 9th Asian conference on Computer Vision - Volume Part I

Quantified Score

Hi-index	0.14

Visualization

Abstract

Implicit polynomials have proved themselves as having excellent representation power for complicated objects, and there is growing use of them in computer vision, graphics, and CAD. A must for every system that tries to recognize objects based on their representation by implicit polynomials are invariants, which are quantities assigned to polynomials that do not change under coordinate transformations. In the recognition system developed at the Laboratory for Engineering Man-Machine Studies in Brown University (LEMS), it became necessary to use invariants which are explicit and simple functions of the polynomial coefficients. A method to find such invariants is described and the new invariants presented. This work addresses only the problem of finding the invariants; their stability is studied in another paper.