IEEE Transactions on Pattern Analysis and Machine Intelligence
Scaling Theorems for Zero Crossings
IEEE Transactions on Pattern Analysis and Machine Intelligence
Uniqueness of the Gaussian Kernel for Scale-Space Filtering
IEEE Transactions on Pattern Analysis and Machine Intelligence
Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations
Journal of Computational Physics
Image selective smoothing and edge detection by nonlinear diffusion. II
SIAM Journal on Numerical Analysis
A Theory of Multiscale, Curvature-Based Shape Representation for Planar Curves
IEEE Transactions on Pattern Analysis and Machine Intelligence
International Journal of Computer Vision
International Journal of Computer Vision
Invariant geometric evolutions of surfaces and volumetric smoothing
SIAM Journal on Applied Mathematics
Geometry-Driven Diffusion in Computer Vision
Geometry-Driven Diffusion in Computer Vision
Local Reproducible Smoothing Without Shrinkage
IEEE Transactions on Pattern Analysis and Machine Intelligence
Iterative Smoothed Residuals: A Low-Pass Filter for Smoothing With Controlled Shrinkage
IEEE Transactions on Pattern Analysis and Machine Intelligence
International Journal of Computer Vision
On Projective Invariant Smoothing and Evolutions of PlanarCurves and Polygons
Journal of Mathematical Imaging and Vision
Analyzing and Synthesizing Images by Evolving Curves with theOsher-Sethian Method
International Journal of Computer Vision
Migration Processes I: The Continuous Case
Journal of Mathematical Imaging and Vision
Migration Processes II: The Discrete Case
Journal of Mathematical Imaging and Vision
Linearised Euclidean Shortening Flow of Curve Geometry
International Journal of Computer Vision
A Dynamic Scale–Space Paradigm
Journal of Mathematical Imaging and Vision
Unfolding the Cerebral Cortex Using Level Set Methods
SCALE-SPACE '99 Proceedings of the Second International Conference on Scale-Space Theories in Computer Vision
Area preserving deformation of multiresolution curves
Computer Aided Geometric Design
Curvature-Driven PDE Methods for Matrix-Valued Images
International Journal of Computer Vision
Integral Invariants for Shape Matching
IEEE Transactions on Pattern Analysis and Machine Intelligence
New Possibilities with Sobolev Active Contours
International Journal of Computer Vision
3D Topology Preserving Flows for Viewpoint-Based Cortical Unfolding
International Journal of Computer Vision
Area preserving deformation of multiresolution curves
Computer Aided Geometric Design
New possibilities with Sobolev active contours
SSVM'07 Proceedings of the 1st international conference on Scale space and variational methods in computer vision
Vesicles and Amoebae: On Globally Constrained Shape Deformation
Journal of Mathematical Imaging and Vision
Corner cutting and augmentation: An area-preserving method for smoothing polygons and polylines
Computer Aided Geometric Design
Invariant geometric motions of space curves
IWMM'04/GIAE'04 Proceedings of the 6th international conference on Computer Algebra and Geometric Algebra with Applications
Construction of subdivision surfaces by fourth-order geometric flows with G1 boundary conditions
GMP'10 Proceedings of the 6th international conference on Advances in Geometric Modeling and Processing
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In this paper, area preserving multi-scale representations of planar curves are described. This allows smoothing without shrinkage at the same time preserving all the scale-space properties. The representations are obtained deforming the curve via geometric heat flows while simultaneously magnifying the plane by a homethety which keeps the enclosed area constant. When the Euclidean geometric heat flow is used, the resulting representation is Euclidean invariant, and similarly it is affine invariant when the affine one is used. The flows are geometrically intrinsic to the curve, and exactly satisfy all the basic requirements of scale-space representations. In the case of the Euclidean heat flow, it is completely local as well. The same approach is used to define length preserving geometric flows. A similarity (scale) invariant geometric heat flow is studied as well in this work.