Multidimensional signal representation by zero crossings and algebraic study
SIAM Journal on Applied Mathematics
Image Representation by Sign Information
IEEE Transactions on Pattern Analysis and Machine Intelligence
Topological Numbers and Singularities in Scalar Images: Scale-Space Evolution Properties
Journal of Mathematical Imaging and Vision
The Topological Structure of Scale-Space Images
Journal of Mathematical Imaging and Vision
Proceedings of the Third International Conference on Scale-Space and Morphology in Computer Vision
Scale-Space '01 Proceedings of the Third International Conference on Scale-Space and Morphology in Computer Vision
What Do Features Tell about Images?
Scale-Space '01 Proceedings of the Third International Conference on Scale-Space and Morphology in Computer Vision
Scale-Space '01 Proceedings of the Third International Conference on Scale-Space and Morphology in Computer Vision
A Linear Image Reconstruction Framework Based on Sobolev Type Inner Products
International Journal of Computer Vision
The Representation and Matching of Images Using Top Points
Journal of Mathematical Imaging and Vision
IEEE Transactions on Image Processing
Combining different types of scale space interest points using canonical sets
SSVM'07 Proceedings of the 1st international conference on Scale space and variational methods in computer vision
Towards a new paradigm for motion extraction
ICIAR'06 Proceedings of the Third international conference on Image Analysis and Recognition - Volume Part I
DSSCV'05 Proceedings of the First international conference on Deep Structure, Singularities, and Computer Vision
Discrete representation of top points via scale space tessellation
Scale-Space'05 Proceedings of the 5th international conference on Scale Space and PDE Methods in Computer Vision
A linear image reconstruction framework based on sobolev type inner products
Scale-Space'05 Proceedings of the 5th international conference on Scale Space and PDE Methods in Computer Vision
On image reconstruction from multiscale top points
Scale-Space'05 Proceedings of the 5th international conference on Scale Space and PDE Methods in Computer Vision
Uniqueness Results for Image Reconstruction from Features on Curves in α-Scale Spaces
Journal of Mathematical Imaging and Vision
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A minimal variance reconstruction scheme is derived using derivatives of the Gaussian as filters. A closed form mixed correlation matrix for reconstructions from multiscale points and their local derivatives up to the second order is presented. With the inverse of this mixed correlation matrix, a reconstruction of the image can be easily calculated. Some interesting results of reconstructions from multiscale critical points are presented. The influence of limited calculation precision is considered, using the condition number of the mixed correlation matrix.