An atlas of functions
3D shape representation by contours
Computer Vision, Graphics, and Image Processing
American Mathematical Monthly
Trace Inference, Curvature Consistency, and Curve Detection
IEEE Transactions on Pattern Analysis and Machine Intelligence
Integrability disambiguates surface recovery in two-image photometric stereo
International Journal of Computer Vision
Parts of Visual Form: Computational Aspects
IEEE Transactions on Pattern Analysis and Machine Intelligence
A Comparison of Measures for Detecting Natural Shapes in Cluttered Backgrounds
International Journal of Computer Vision - Special issue on computer vision research at NEC Research Institute
IEEE Transactions on Pattern Analysis and Machine Intelligence
ACM Transactions on Mathematical Software (TOMS)
Curves and Surfaces for Computer-Aided Geometric Design: A Practical Code
Curves and Surfaces for Computer-Aided Geometric Design: A Practical Code
Filtering, Segmentation, and Depth
Filtering, Segmentation, and Depth
Numerical Recipes in FORTRAN; The Art of Scientific Computing
Numerical Recipes in FORTRAN; The Art of Scientific Computing
Figure-Ground Discrimination: A Combinatorial Optimization Approach
IEEE Transactions on Pattern Analysis and Machine Intelligence
A Comparison of Measures for Detecting Natural Shapes in Cluttered Backgrounds
ECCV '98 Proceedings of the 5th European Conference on Computer Vision-Volume II - Volume II
Stochastic completion fields: a neural model of illusory contour shape and salience
ICCV '95 Proceedings of the Fifth International Conference on Computer Vision
Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,
Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,
Salient Closed Boundary Extraction with Ratio Contour
IEEE Transactions on Pattern Analysis and Machine Intelligence
Contour Inferences for Image Understanding
International Journal of Computer Vision
G1 interpolation with a single Cornu spiral segment
Journal of Computational and Applied Mathematics
A two-point G1 Hermite interpolating family of spirals
Journal of Computational and Applied Mathematics
Proceedings of Graphics Interface 2009
Sketch-Based Interfaces and Modeling (SBIM): Sketching piecewise clothoid curves
Computers and Graphics
Image and Vision Computing
Journal of Mathematical Imaging and Vision
Computing clothoid segments for trajectory generation
IROS'09 Proceedings of the 2009 IEEE/RSJ international conference on Intelligent robots and systems
Bayesian inference for layer representation with mixed Markov random field
EMMCVPR'07 Proceedings of the 6th international conference on Energy minimization methods in computer vision and pattern recognition
3D Euler spirals for 3D curve completion
Proceedings of the twenty-sixth annual symposium on Computational geometry
Proceedings of the 14th ACM Symposium on Solid and Physical Modeling
A biologically-inspired theory for non-axiomatic parametric curve completion
ACCV'10 Proceedings of the 10th Asian conference on Computer vision - Volume Part II
Skeleton Search: Category-Specific Object Recognition and Segmentation Using a Skeletal Shape Model
International Journal of Computer Vision
3D Euler spirals for 3D curve completion
Computational Geometry: Theory and Applications
High-Order differential geometry of curves for multiview reconstruction and matching
EMMCVPR'05 Proceedings of the 5th international conference on Energy Minimization Methods in 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
Multi-scale vessel boundary detection
CVBIA'05 Proceedings of the First international conference on Computer Vision for Biomedical Image Applications
Computer vision for fruit harvesting robots state of the art and challenges ahead
International Journal of Computational Vision and Robotics
Computer Graphics Forum
Geometrically Guided Exemplar-Based Inpainting
SIAM Journal on Imaging Sciences
Technical Section: Euler arc splines for curve completion
Computers and Graphics
Sketching piecewise clothoid curves
SBM'08 Proceedings of the Fifth Eurographics conference on Sketch-Based Interfaces and Modeling
Bottom-up perceptual organization of images into object part hypotheses
ECCV'12 Proceedings of the 12th European conference on Computer Vision - Volume Part I
Tangent bundle curve completion with locally connected parallel networks
Neural Computation
"Mind the gap": tele-registration for structure-driven image completion
ACM Transactions on Graphics (TOG)
Interpolation of two-dimensional curves with Euler spirals
Journal of Computational and Applied Mathematics
Hi-index | 0.00 |
In this paper we address the curve completion problem, e.g., the geometric continuation of boundaries of objects which are temporarily interrupted by occlusion. Also known as the gap completion or shape completion problem, this problem is a significant element of perceptual grouping of edge elements and has been approached by using cubic splines or biarcs which minimize total curvature squared (elastica), as motivated by a physical analogy. Our approach is motivated by railroad design methods of the early 1900's which connect two rail segments by “transition curves”, and by the work of Knuth on mathematical typography. We propose that in using an energy minimizing solution completion curves should not penalize curvature as in elastica but curvature variation. The minimization of total curvature variation leads to an Euler Spiral solution, a curve whose curvature varies linearly with arclength. The construction of this curve from a pair of points and tangents at these points is reduced to a nonlinear system of equations involving Fresnel Integrals, whose solution relies on optimization from a suitable initial condition constrained to satisfy given boundary conditions. Since the choice of an appropriate initial curve is critical in this optimization, we analytically derive an optimal solution in the class of biarc curves, which is then used as the initial curve. The resulting interpolations yield intuitive interpolation across gaps and occlusions, and are extensible, in contrast to scale invariant elastica. In addition, Euler Spiral segments can be used in other applications of curve completions, e.g., modeling boundary segments between curvature extrema or skeletal branch geometry.