Shape completion

Rutkowski, Wallace S.

doi:10.1016/0146-664x(79)90086-8

Cited by 31 publications

(7 citation statements)

References 0 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Here we want to solve the minimization problem (7). We wrote another Maple program to solve the corresponding system (8) for a wide range of parameter values.…”

Section: "Similarity Invariant" Turn-limited Elasticamentioning

confidence: 99%

Discrete elastica

Bruckstein¹,

Holt²,

Netravali³

1996

Discrete Geometry for Computer Imagery

View full text Add to dashboard Cite

show abstract

“…Here we want to solve the minimization problem (7). We wrote another Maple program to solve the corresponding system (8) for a wide range of parameter values.…”

Section: "Similarity Invariant" Turn-limited Elasticamentioning

confidence: 99%

Discrete elastica

Bruckstein¹,

Holt²,

Netravali³

1996

Discrete Geometry for Computer Imagery

View full text Add to dashboard Cite

show abstract

“…The authors use a clothoid for the curve and a system of nonlinear equations must be solved to find the curve. A biarc, which can also be used for curve completion, was thought to be not as pleasing as a smoother curve [13]. However, biarcs have the advantage that they are given by explicit formula.…”

Section: Introductionmentioning

confidence: 99%

A two-point G1 Hermite interpolating family of spirals

Meek

Walton

2009

Journal of Computational and Applied Mathematics

View full text Add to dashboard Cite

A one-parameter family of spirals that can match planar, two-point G 1 Hermite data is presented. These spirals can be used as an alternative to the biarc, which is also a one-parameter family of curves that can match two-point G 1 Hermite data. Some suggestions on choosing the free parameter of the family of spirals is given. It is shown that there is a unique G 1 Hermite interpolating spiral that passes through a given point in an allowable region. Three examples of the use of these spirals are given: curve completion with spirals, design with spirals, and approximation of the clothoid by spirals.

show abstract

“…While the biarc model was designed to satisfy the four original axioms, it violates smoothness (in the strict sense, since it is differentiable only once), it does not minimize total curvature in general (it does so only within the family of biarc curves), and it was also shown to violate extensibility in some cases [6]. While Ullman did not present a closed-form solution to his biarc model, a mathematical solution based on a one-dimensional nonlinear optimization was introduced later by Rutkowski [42] (see Figs. 3D, 3E, 3F, 3G, and 3H for our own implementation).…”

Section: Computational Studiesmentioning

confidence: 99%

“…(C) An example of an Euler spiral curve, whose curvature changes linearly with arclength, i.e., ðsÞ ¼ a Á s þ b, for some constants a and b. (D)-(H) Results of our own MATLAB implementation to previous popular curve completion algorithms, given the position and orientation of two inducers: The Biarc model [42], [51] is plotted in green, the Cubic interpolation model [6] is plotted in red, the Elastica model [21] is plotted in blue, and the Euler spiral model [27] is plotted in cyan. Please use the electronic version to zoom in for a better view.…”

Section: Computational Studiesmentioning

confidence: 99%

A Tangent Bundle Theory for Visual Curve Completion

Ben-Yosef

Ben-Shahar

2012

IEEE Trans. Pattern Anal. Mach. Intell.

View full text Add to dashboard Cite

Abstract-Visual curve completion is a fundamental perceptual mechanism that completes the missing parts (e.g., due to occlusion) between observed contour fragments. Previous research into the shape of completed curves has generally followed an "axiomatic" approach, where desired perceptual/geometrical properties are first defined as axioms, followed by mathematical investigation into curves that satisfy them. However, determining psychophysically such desired properties is difficult and researchers still debate what they should be in the first place. Instead, here we exploit the observation that curve completion is an early visual process to formalize the problem in the unit tangent bundle R 2 Â S 1 , which abstracts the primary visual cortex (V1) and facilitates exploration of basic principles from which perceptual properties are later derived rather than imposed. Exploring here the elementary principle of least action in V1, we show how the problem becomes one of finding minimum-length admissible curves in R 2 Â S 1 . We formalize the problem in variational terms, we analyze it theoretically, and we formulate practical algorithms for the reconstruction of these completed curves. We then explore their induced visual properties vis-à -vis popular perceptual axioms and show how our theory predicts many perceptual properties reported in the corresponding perceptual literature. Finally, we demonstrate a variety of curve completions and report comparisons to psychophysical data and other completion models.

show abstract

Shape completion

Cited by 31 publications

References 0 publications

Discrete elastica

Discrete elastica

A two-point G1 Hermite interpolating family of spirals

A Tangent Bundle Theory for Visual Curve Completion

Contact Info

Product

Resources

About