2016
DOI: 10.1016/j.amc.2015.06.127
|View full text |Cite
|
Sign up to set email alerts
|

A family of smooth and interpolatory basis functions for parametric curve and surface representation

Abstract: a b s t r a c tInterpolatory basis functions are helpful to specify parametric curves or surfaces that can be modified by simple user-interaction. Their main advantage is a characterization of the object by a set of control points that lie on the shape itself (i.e., curve or surface). In this paper, we characterize a new family of compactly supported piecewise-exponential basis functions that are smooth and satisfy the interpolation property. They can be seen as a generalization and extension of the Keys inter… Show more

Help me understand this report

Search citation statements

Order By: Relevance

Paper Sections

Select...
1
1
1
1

Citation Types

0
7
0

Year Published

2016
2016
2018
2018

Publication Types

Select...
4
1

Relationship

2
3

Authors

Journals

citations
Cited by 9 publications
(7 citation statements)
references
References 27 publications
0
7
0
Order By: Relevance
“…The outlining has been done by interpolating twelve landmarks on the contours of the chromosomes with the basis functions proposed in [39], [40]. This procedure allowed us to obtain a spline-based curve description of each chromosome with landmarks that are corresponding throughout the data set.…”
Section: ) Learning Shape Priorsmentioning
confidence: 99%
See 1 more Smart Citation
“…The outlining has been done by interpolating twelve landmarks on the contours of the chromosomes with the basis functions proposed in [39], [40]. This procedure allowed us to obtain a spline-based curve description of each chromosome with landmarks that are corresponding throughout the data set.…”
Section: ) Learning Shape Priorsmentioning
confidence: 99%
“…The PFH is outlined on a specific 2D section of the ultrasound volume using the following procedure: A clinician draws key points on the image which have particular anatomical meaning. Curves are then computed by interpolating the ordered set of key points using spline interpolators [39], [40], as shown in Figure 7 (top row).…”
Section: ) Classification In Medical Imagingmentioning
confidence: 99%
“…Parametric curves that are represented by compactly supported basis functions are often used to construct active-contour models [16], [17] and to segment bioimages [18]- [20]. More generally, the control-point-based nature of (4) makes this model particularly convenient in applications where user interaction is required [21], [22]. The reason is that the simple adjustment of one control point is enough to adjust the curve locally.…”
Section: A Periodic Signals and Closed Parametric Curvesmentioning
confidence: 99%
“…is finite, and ' and are spline basis functions that satisfy the Riesz basis condition [8]. For the explicit expressions of ' and to construct a cylindrical surface, we refer the reader to [9].…”
Section: Spline-based Implementationmentioning
confidence: 99%