Scale-Based Description and Recognition of Planar Curves and Two-Dimensional Shapes
IEEE Transactions on Pattern Analysis and Machine Intelligence
Biological Cybernetics
Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations
Journal of Computational Physics
Fundamentals of digital image processing
Fundamentals of digital image processing
Solid shape
Scale-Space for Discrete Signals
IEEE Transactions on Pattern Analysis and Machine Intelligence
IAPR Proceedings of the international workshop on Visual form: analysis and recognition
Radiometry
A Theory of Multiscale, Curvature-Based Shape Representation for Planar Curves
IEEE Transactions on Pattern Analysis and Machine Intelligence
Three-dimensional computer vision: a geometric viewpoint
Three-dimensional computer vision: a geometric viewpoint
International Journal of Computer Vision
Area and Length Preserving Geometric Invariant Scale-Spaces
IEEE Transactions on Pattern Analysis and Machine Intelligence
International Journal of Computer Vision
Geometric methods for analysis of ridges in n-dimensional images
Geometric methods for analysis of ridges in n-dimensional images
On Projective Invariant Smoothing and Evolutions of PlanarCurves and Polygons
Journal of Mathematical Imaging and Vision
Differential and Integral Geometry of Linear Scale-Spaces
Journal of Mathematical Imaging and Vision
Linear Scale-Space Theory from Physical Principles
Journal of Mathematical Imaging and Vision
Topological Numbers and Singularities in Scalar Images: Scale-Space Evolution Properties
Journal of Mathematical Imaging and Vision
Geometry-Driven Diffusion in Computer Vision
Geometry-Driven Diffusion in Computer Vision
Scale-Space Theory in Computer Vision
Scale-Space Theory in Computer Vision
A Dynamic Scale–Space Paradigm
Journal of Mathematical Imaging and Vision
ICIAP '97 Proceedings of the 9th International Conference on Image Analysis and Processing-Volume I - Volume I
Fundamentals of Bicentric Perspective
Proceedings of the International Conference on Future Tendencies in Computer Science, Control and Applied Mathematics
SCALE-SPACE '97 Proceedings of the First International Conference on Scale-Space Theory in Computer Vision
Euclidean Invariants of Linear Scale-Spaces
ACCV '98 Proceedings of the Third Asian Conference on Computer Vision-Volume II
Line-finding in 2-D and 3-D by Multi-valued Non-linear Diffusion of Feature Maps
Mustererkennung 1993, Mustererkennung im Dienste der Gesundheit, 15. DAGM-Symposium
A Dynamic Scale–Space Paradigm
Journal of Mathematical Imaging and Vision
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The geometry of a space curve is described in terms of a Euclidean invariant frame field, metric, connection, torsion and curvature. Herethe torsion and curvature of the connection quantify the curve geometry. In order to retain a stable and reproducible descriptionof that geometry, such that it is slightly affected by non-uniform protrusions of the curve, a linearised Euclidean shortening flow is proposed. (Semi)-discretised versions of the flow subsequently physically realise a concise and exact (semi-)discrete curve geometry. Imposing special ordering relations the torsion and curvature in the curve geometry can be retrieved on a multi-scale basis not only for simply closed planar curves but also for open, branching, intersecting and space curves of non-trivial knot type. In the context of the shortening flows we revisit the maximum principle, the semi-group property and the comparison principle normally required in scale-space theories. We show that our linearised flow satisfies an adapted maximum principle, and that its Green‘s functions possess a semi-group property. We argue that the comparison principle in the case of knots can obstruct topological changes being in contradiction with the required curve simplification principle.Our linearised flow paradigm is not hampered by this drawback; allnon-symmetric knots tend to trivial ones being infinitely small circles in a plane. Finally, the differential and integral geometry of the multi-scale representation of the curve geometry under the flow is quantified by endowing the scale-space of curves with an appropriate connection, and calculating related torsion and curvature aspects. This multi-scale modern geometric analysis forms therewith an alternative for curve description methods based on entropy scale-space theories.