Optimal Estimation of Contour Properties by Cross-Validated Regularization
IEEE Transactions on Pattern Analysis and Machine Intelligence
Coping with Discontinuities in Computer Vision: Their Detection, Classification, and Measurement
IEEE Transactions on Pattern Analysis and Machine Intelligence
On Optimal Infinite Impulse Response Edge Detection Filters
IEEE Transactions on Pattern Analysis and Machine Intelligence
Adaptive Determination of Filter Scales for Edge Detection
IEEE Transactions on Pattern Analysis and Machine Intelligence
Regularization, Scale-Space, and Edge Detection Filters
Journal of Mathematical Imaging and Vision
Finite-Element Methods for Active Contour Models and Balloons for 2-D and 3-D Images
IEEE Transactions on Pattern Analysis and Machine Intelligence
Signal differentiation through a Green's function approach
Pattern Recognition Letters
Multi-scale binarization of images
Pattern Recognition Letters
On the Choice of Band-Pass Quadrature Filters
Journal of Mathematical Imaging and Vision
Efficient, recursively implemented differential operator, with application to edge detection
Pattern Recognition Letters
Neural Computation
An optimal scale for edge detection
IJCAI'87 Proceedings of the 10th international joint conference on Artificial intelligence - Volume 2
Multi objective optimization based fast motion detector
MMM'11 Proceedings of the 17th international conference on Advances in multimedia modeling - Volume Part I
"Influence areas" as a tool for testing of image restoration methods
AICT'11 Proceedings of the 2nd international conference on Applied informatics and computing theory
PReMI'05 Proceedings of the First international conference on Pattern Recognition and Machine Intelligence
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We consider edge detection as the problem of measuring and localizing changes of light intensity in the image. As discussed by Torre and Poggio (1984), edge detection, when defined in this way, is an ill-posed problem in the sense of Hadamard. The regularized solution that arises is then the solution to a variational principle. In the case of exact data, one of the standard regularization methods (see Poggio and Torre, 1984) leads to cubic spline interpolation before differentiation. We show that in the case of regularly-spaced data this solution corresponds to a convolution filter--- to be applied to the signal before differentiation -- which is a cubic spline. In the case of non-exact data, we use another regularization method that leads to a different variational principle. We prove (1) that this variational principle leads to a convolution filter for the problem of one- dimensional edge detection, (2) that the form of this filter is very similar to the Gaussian filter, and (3) that the regularizing parameter $\lambda$ in the variational principle effectively controls the scale of the filter.