A Computational Approach to Edge Detection
IEEE Transactions on Pattern Analysis and Machine Intelligence
Trace Inference, Curvature Consistency, and Curve Detection
IEEE Transactions on Pattern Analysis and Machine Intelligence
Scale-Space and Edge Detection Using Anisotropic Diffusion
IEEE Transactions on Pattern Analysis and Machine Intelligence
Mean square estimation and projections
Signal Processing
Edge-Labeling Using Dictionary-Based Relaxation
IEEE Transactions on Pattern Analysis and Machine Intelligence
An Active Testing Model for Tracking Roads in Satellite Images
IEEE Transactions on Pattern Analysis and Machine Intelligence
ACM Transactions on Mathematical Software (TOMS)
A Probabilistic Interpretation of the Saliency Network
ECCV '00 Proceedings of the 6th European Conference on Computer Vision-Part II
A Markov Process Using Curvature for Filtering Curve Images
EMMCVPR '01 Proceedings of the Third International Workshop on Energy Minimization Methods in Computer Vision and Pattern Recognition
Invertible Orientation Bundles on 2D Scalar Images
SCALE-SPACE '97 Proceedings of the First International Conference on Scale-Space Theory in Computer Vision
Toward discrete geometric models for early vision
Toward discrete geometric models for early vision
The curve indicator random field
The curve indicator random field
The Volterra and Wiener Theories of Nonlinear Systems
The Volterra and Wiener Theories of Nonlinear Systems
Correction to "An Application of Relaxation Labeling to Line and Curve Enhancement"
IEEE Transactions on Computers
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How should one filter very noisy images of curves? While blurring with a Gaussian reduces noise, it also reduces contour contrast. Both non-homogeneous and anisotropic diffusion smooth images while preserving contours, but these methods assume a single local orientation and therefore they can merge or distort nearby or crossing contours. To avoid these difficulties, we view curve enhancement as a statistical estimation problem in the three-dimensional (x, y, 驴)-space of positions and directions, where our prior is a probabilistic model of an ideal edge/line map known as the curve indicator random field (CIRF). Technically, this random field is a superposition of local times of Markov processes that model the individual curves; intuitively, it is an idealized artist's sketch, where the value of the field is the amount of ink deposited by the artist's pen. After reviewing the CIRF framework and our earlier formulas for the CIRF cumulants, we compute the minimum mean squared error (MMSE) estimate of the CIRF embedded in large amounts of Gaussian white noise. The derivation involves a perturbation expansion in an infinite noise limit, and results in linear, quadratic, and cubic (Volterra) CIRF filters for enhancing images of contours. The self-avoidingness of smooth curves in (x, y, 驴) simplified our analysis and the resulting algorithms, which run in O(n log n) time, where n is the size of the input. This suggests that the Gestalt principle of good continuation may not only express the likely smoothness of contours, but it may have a computational basis as well.