Object recognition by computer: the role of geometric constraints
Object recognition by computer: the role of geometric constraints
Shape from texture: estimation, isotropy and moments
Artificial Intelligence
Projectively invariant decomposition of planar shapes
Geometric invariance in computer vision
Fast recognition using algebraic invariants
Geometric invariance in computer vision
An efficiently computable metric for comparing polygonal shapes
SODA '90 Proceedings of the first annual ACM-SIAM symposium on Discrete algorithms
Robot Vision
Projectively Invariant Representations Using Implicit Algebraic Curves
ECCV '90 Proceedings of the First European Conference on Computer Vision
Canonical Frames for Planar Object Recognition
ECCV '92 Proceedings of the Second European Conference on Computer Vision
Fundamental Limitations on Projective Invariants of Planar Curves
IEEE Transactions on Pattern Analysis and Machine Intelligence
The Method of Normalization to Determine Invariants
IEEE Transactions on Pattern Analysis and Machine Intelligence
Invariant Fitting of Planar Objects by Primitives
IEEE Transactions on Pattern Analysis and Machine Intelligence
Robust Watermarking and Affine Registration of 3D Meshes
IH '02 Revised Papers from the 5th International Workshop on Information Hiding
Evaluating a Visualization of Image Similarity as a Tool for Image Browsing
INFOVIS '99 Proceedings of the 1999 IEEE Symposium on Information Visualization
On the choice of consistent canonical form during moment normalization
Pattern Recognition Letters
Drums, curve descriptors and affine invariant region matching
Image and Vision Computing
An approach to perceptual shape matching
VISUAL'05 Proceedings of the 8th international conference on Visual Information and Information Systems
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This paper presents an algorithm for transforming closed planar curves into a canonical form, independent of the viewpoint from which the original image of the contour was taken. The transformation that takes the contour to its canonical form is a member of the projective group PGL(2), chosen because PGL(2) contains all possible transformations of a plane curve under central projection onto another plane. The scheme relies on solving computationally an "isoperimetric" problem in which a transformation is sought which maximises the area of a curve given unit perimeter. In the case that the transformation is restricted to the affine subgroup there is a unique extremising transformation for any piecewise smooth closed curve. Uniqueness holds, almost always, even for curves that are not closed. In the full projective case, isoperimetric normalization is well-defined only for closed curves. We have found computational counterexamples for which there is more than one extremal transformation. Numerical algorithms are described and demonstrated both for the affine and the projective cases. Once a canonical curve is obtained, its isoperimetric area can be regarded as an invariant descriptor of shape.