Curvature analysis and visualization for functions defined on Euclidean spaces or surfaces
Computer Aided Geometric Design
Scale-Space Theory in Computer Vision
Scale-Space Theory in Computer Vision
Applications of Locally Orderless Images
SCALE-SPACE '99 Proceedings of the Second International Conference on Scale-Space Theories in Computer Vision
State of the art on automatic road extraction for GIS update: a novel classification
Pattern Recognition Letters
The Second Order Local-Image-Structure Solid
IEEE Transactions on Pattern Analysis and Machine Intelligence
Journal of Mathematical Imaging and Vision
Exploring and exploiting the structure of saddle points in Gaussian scale space
Computer Vision and Image Understanding
Image and Vision Computing
Symmetries of 2-D Images: Cases without Periodic Translations
Journal of Mathematical Imaging and Vision
Basic Image Features (BIFs) Arising from Approximate Symmetry Type
SSVM '09 Proceedings of the Second International Conference on Scale Space and Variational Methods in Computer Vision
SSVM '09 Proceedings of the Second International Conference on Scale Space and Variational Methods in Computer Vision
General Geometric Good Continuation: From Taylor to Laplace via Level Sets
International Journal of Computer Vision
Discrete surfaces in isotropic geometry
Proceedings of the 12th IMA international conference on Mathematics of surfaces XII
Membrane nonrigid image registration
ECCV'10 Proceedings of the 11th European conference on Computer vision: Part II
Separable linear classifiers for online learning in appearance based object detection
CAIP'05 Proceedings of the 11th international conference on Computer Analysis of Images and Patterns
Covariant derivatives and vision
ECCV'06 Proceedings of the 9th European conference on Computer Vision - Volume Part IV
Image space I3 and eigen curvature for illumination insensitive face detection
ICIAR'05 Proceedings of the Second international conference on Image Analysis and Recognition
On α kernels, Lévy processes, and natural image statistics
Scale-Space'05 Proceedings of the 5th international conference on Scale Space and PDE Methods in Computer Vision
Greyscale photograph geometry informed by dodging and burning
ICVGIP'06 Proceedings of the 5th Indian conference on Computer Vision, Graphics and Image Processing
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A large part of "image processing" involves the computation of significant points, curves and areas ("features"). These can be defined as loci where absolute differential invariants of the image assume fiducial values, taking spatial scale and intensity (in a generic sense) scale into account. "Differential invariance" implies a group of "similarities" or "congruences". These "motions" define the geometrical structure of image space. Classical Euclidian invariants don't apply to images because image space is non-Euclidian. We analyze image structure from first principles and construct the fundamental group of image space motions. Image space is a Cayley-Klein geometry with one isotropic dimension. The analysis leads to a principled definition of "features" and the operators that define them.