Integrating Region Growing and Edge Detection
IEEE Transactions on Pattern Analysis and Machine Intelligence
Error estimation in automatic quadrature routines
ACM Transactions on Mathematical Software (TOMS)
Image selective smoothing and edge detection by nonlinear diffusion. II
SIAM Journal on Numerical Analysis
Image selective smoothing and edge detection by nonlinear diffusion
SIAM Journal on Numerical Analysis
On the Gibbs Phenomenon and Its Resolution
SIAM Review
Picture Segmentation by a Tree Traversal Algorithm
Journal of the ACM (JACM)
Detection of Edges in Spectral Data II. Nonlinear Enhancement
SIAM Journal on Numerical Analysis
Adaptive Split-and-Merge Segmentation Based on Piecewise Least-Square Approximation
IEEE Transactions on Pattern Analysis and Machine Intelligence
Partial Smoothing Splines for Noisy +Boundaries with Corners
IEEE Transactions on Pattern Analysis and Machine Intelligence
Quadratic Spline Wavelet Approach to Automatic Extraction of Baselines from Document Images
ICDAR '97 Proceedings of the 4th International Conference on Document Analysis and Recognition
Combining Region Splitting and Edge Detection through Guided Delaunay Image Subdivision
CVPR '97 Proceedings of the 1997 Conference on Computer Vision and Pattern Recognition (CVPR '97)
Lower Bounds for Simplicial Covers and Triangulations of Cubes
Discrete & Computational Geometry
Polynomial Fitting for Edge Detection in Irregularly Sampled Signals and Images
SIAM Journal on Numerical Analysis
Handbook of Mathematical Models in Computer Vision
Handbook of Mathematical Models in Computer Vision
Adaptive Edge Detectors for Piecewise Smooth Data Based on the minmod Limiter
Journal of Scientific Computing
Constructive Approximation of Discontinuous Functions by Neural Networks
Neural Processing Letters
Extracting Grain Boundaries and Macroscopic Deformations from Images on Atomic Scale
Journal of Scientific Computing
Detection of Edges in Spectral Data III--Refinement of the Concentration Method
Journal of Scientific Computing
Generating segmented meshes from textured color images
Journal of Visual Communication and Image Representation
3D Edge Detection by Selection of Level Surface Patches
Journal of Mathematical Imaging and Vision
Robust edge detection using mumford-shah model and binary level set method
SSVM'11 Proceedings of the Third international conference on Scale Space and Variational Methods in Computer Vision
Edge Detection by Adaptive Splitting II. The Three-Dimensional Case
Journal of Scientific Computing
The canny edge detection and its improvement
AICI'12 Proceedings of the 4th international conference on Artificial Intelligence and Computational Intelligence
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In this paper we propose an algorithm (EDAS-d) to approximate the jump discontinuity set of functions defined on subsets of 驴 d . We have limited our study to the 1D (EDAS-1) and 2D (EDAS-2) versions of the algorithm. Theoretical and computational results prove its effectiveness in the case of piecewise continuous 1D functions and piecewise constant 2D functions. The algorithm is based on adaptive splitting of the domain of the function guided by the value of an average integral. EDAS-d exhibits a number of attractive features: accurate determination of the jump points, fast processing, absence of oscillatory behavior, precise determination of the magnitude of the jumps, and ability to differentiate between real jumps (discontinuities) and steep gradients. Moreover, low-dimensional versions of EDAS-d can be used for solving higher dimensional problems. Computational experiments also show that EDAS-d can be applied to solve some problems involving general piecewise continuous functions. EDAS-1 and EDAS-2 have been used to determine edges in 2D-images. The results are quite satisfactory for practical purposes.