Image Features Based on a New Approach to 2D Rotation Invariant Quadrature Filters
ECCV '02 Proceedings of the 7th European Conference on Computer Vision-Part I
The Monogenic Scale-Space: A Unifying Approach to Phase-Based Image Processing in Scale-Space
Journal of Mathematical Imaging and Vision
Inferior Temporal Neurons Show Greater Sensitivity to Nonaccidental than to Metric Shape Differences
Journal of Cognitive Neuroscience
Signal modeling for two-dimensional image structures
Journal of Visual Communication and Image Representation
Estimating local multiple orientations
Signal Processing
Continuous dimensionality characterization of image structures
Image and Vision Computing
The monogenic wavelet transform
IEEE Transactions on Signal Processing
Optical flow estimation from monogenic phase
IWCM'04 Proceedings of the 1st international conference on Complex motion
GET: the connection between monogenic scale-space and gaussian derivatives
Scale-Space'05 Proceedings of the 5th international conference on Scale Space and PDE Methods in Computer Vision
Phase congruency induced local features for finger-knuckle-print recognition
Pattern Recognition
The monogenic curvature scale-space
IWCIA'06 Proceedings of the 11th international conference on Combinatorial Image Analysis
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Local intrinsic dimensionality is shown to be an elementary structural property of multidimensional signals that cannot be evaluated using linear filters. We derive a class of polynomial operators for the detection of intrinsically 2-D image features like curved edges and lines, junctions, line ends, etc. Although it is a deterministic concept, intrinsic dimensionality is closely related to signal redundancy since it measures how many of the degrees of freedom provided by a signal domain are in fact used by an actual signal. Furthermore, there is an intimate connection to multidimensional surface geometry and to the concept of `Gaussian curvature'. Nonlinear operators are inevitably required for the processing of intrinsic dimensionality since linear operators are, by the superposition principle, restricted to OR-combinations of their intrinsically 1-D eigenfunctions. The essential new feature provided by polynomial operators is their potential to act on multiplicative relations between frequency components. Therefore, such operators can provide the AND-combination of complex exponentials, which is required for the exploitation of intrinsic dimensionality. Using frequency design methods, we obtain a generalized class of quadratic Volterra operators that are selective to intrinsically 2-D signals. These operators can be adapted to the requirements of the signal processing task. For example, one can control the “curvature tuning” by adjusting the width of the stopband for intrinsically 1-D signals, or the operators can be provided in isotropic and in orientation-selective versions. We first derive the quadratic Volterra kernel involved in the computation of Gaussian curvature and then present examples of operators with other arrangements of stop and passbands. Some of the resulting operators show a close relationship to the end-stopped and dot-responsive neurons of the mammalian visual cortex