Trace Inference, Curvature Consistency, and Curve Detection
IEEE Transactions on Pattern Analysis and Machine Intelligence
Two stages of curve detection suggest two styles of visual computation
Neural Computation
Stochastic differential equations (3rd ed.): an introduction with applications
Stochastic differential equations (3rd ed.): an introduction with applications
An Active Testing Model for Tracking Roads in Satellite Images
IEEE Transactions on Pattern Analysis and Machine Intelligence
Embedding Gestalt Laws in Markov Random Fields
IEEE Transactions on Pattern Analysis and Machine Intelligence
Fundamental Limits of Bayesian Inference: Order Parameters and Phase Transitions for Road Tracking
IEEE Transactions on Pattern Analysis and Machine Intelligence
IEEE Transactions on Pattern Analysis and Machine Intelligence
ACM Transactions on Mathematical Software (TOMS)
Signal Processing for Computer Vision
Signal Processing for Computer Vision
Figure-Ground Discrimination: A Combinatorial Optimization Approach
IEEE Transactions on Pattern Analysis and Machine Intelligence
Logical/Linear Operators for Image Curves
IEEE Transactions on Pattern Analysis and Machine Intelligence
Parsing Images into Region and Curve Processes
ECCV '02 Proceedings of the 7th European Conference on Computer Vision-Part III
Invertible Orientation Bundles on 2D Scalar Images
SCALE-SPACE '97 Proceedings of the First International Conference on Scale-Space Theory in Computer Vision
Computing Stochastic Completion Fields in Linear-Time Using a Resolution Pyramid
CAIP '97 Proceedings of the 7th International Conference on Computer Analysis of Images and Patterns
Toward discrete geometric models for early vision
Toward discrete geometric models for early vision
The curve indicator random field
The curve indicator random field
Parsing Images into Regions, Curves, and Curve Groups
International Journal of Computer Vision
Shape Representation and Classification Using the Poisson Equation
IEEE Transactions on Pattern Analysis and Machine Intelligence
International Journal of Computer Vision
Shape representation and classification using the Poisson equation
CVPR'04 Proceedings of the 2004 IEEE computer society conference on Computer vision and pattern recognition
On similarity-invariant fairness measures
Scale-Space'05 Proceedings of the 5th international conference on Scale Space and PDE Methods in Computer Vision
Pen stroke extraction and refinement using learned models
SBM'04 Proceedings of the First Eurographics conference on Sketch-Based Interfaces and Modeling
Tangent bundle curve completion with locally connected parallel networks
Neural Computation
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While complaints about typical edge operators are common, proposals articulating a notion of the 驴perfect驴 edge map are comparatively rare, hindering the improvement of contour enhancement techniques. To address this situation, we suggest that one objective of visual contour computation is the estimation of a clean sketch from a corrupted rendition, the latter modeling noisy and low contrast edge or line operator responses to an image. Our formal model of this clean sketch is the curve indicator random field (CIRF), whose role is to provide a basis for defining edge likelihood models by eliminating the parameter along each curve to create an image of curves. For curves modeled with stationary Markov processes, this ideal edge prior is non-Gaussian and its moment generating functional has a form closely related to the Feynman-Kac formula. This sketch model leads to a nonlinear, minimum mean squared error contour enhancement filter that requires the solution of two elliptic partial differential equations. The framework is also independent of the order of the contour model, allowing us to introduce a Markov process model for contour curvature. We analyze the distribution of such curves and show that its mode is the Euler spiral, a curve minimizing changes in curvature. Example computations using the contour enhancement filter with the curvature-based contour model are provided, highlighting how the filter is curvature-selective even when curvature is absent in the input.