A Computational Approach to Edge Detection
IEEE Transactions on Pattern Analysis and Machine Intelligence
On the Localization Performance Measure and Optimal Edge Detection
IEEE Transactions on Pattern Analysis and Machine Intelligence
Optimal Edge Detectors for Ramp Edges
IEEE Transactions on Pattern Analysis and Machine Intelligence
The Design and Use of Steerable Filters
IEEE Transactions on Pattern Analysis and Machine Intelligence
Optimal infinite impulse response zero crossing based edge detectors
CVGIP: Image Understanding
On Optimal Infinite Impulse Response Edge Detection Filters
IEEE Transactions on Pattern Analysis and Machine Intelligence
An optimal linear operator for step edge detection
CVGIP: Graphical Models and Image Processing
Optimal Edge Detection using Expansion Matching and Restoration
IEEE Transactions on Pattern Analysis and Machine Intelligence
Optimal Ramp Edge Detection Using Expansion Matching
IEEE Transactions on Pattern Analysis and Machine Intelligence
Linear Time Euclidean Distance Algorithms
IEEE Transactions on Pattern Analysis and Machine Intelligence
Canny Edge Detection Enhancement by Scale Multiplication
IEEE Transactions on Pattern Analysis and Machine Intelligence
Digital Image Processing: PIKS Scientific Inside
Digital Image Processing: PIKS Scientific Inside
Scale space smoothing, image feature extraction and bessel filters
SCIA'11 Proceedings of the 17th Scandinavian conference on Image analysis
Design of steerable filters for feature detection using canny-like criteria
IEEE Transactions on Pattern Analysis and Machine Intelligence
On optimal linear filtering for edge detection
IEEE Transactions on Image Processing
Quantitative error measures for edge detection
Pattern Recognition
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In this paper, we propose an edge detection algorithm based on the Green function associated with the Mumford-Shah segmentation model. This Green function has a singularity at its center. A regularization method is therefore proposed here to obtain an edge detection filter known here as the Bessel filter. This filter is robust in the presence of noise, and its implementation is simple. It is demonstrated here that this filter is scale invariant. A mathematical argument is also provided to prove that the gradient magnitude of the convolved image with this filter has local maxima in discontinuities of the original image. The Bessel filter enjoys better overall performance (the product of the detection performance and localization indices) in Canny-like criteria than the state-of-the-art filters in the literature. Quantitative and qualitative evaluations of the edge detection algorithms investigated in this paper on synthetic and real world benchmark images confirm the theoretical results presented here, indicating the scale invariant property of the Bessel filter. The numerical complexity of the algorithm proposed here is as low as any convolution-based edge detection algorithm.