On geometric interpolation of circle-like curves

Jaklič, Gašper; Kozak, Jernej; Krajnc, Matjaž; Žagar, Emil

doi:10.1016/j.cagd.2007.03.002

Cited by 19 publications

(11 citation statements)

References 9 publications

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“…We would like to remark that a great deal of research has been done on the approximation of circular arcs and whole circles (see, e.g., [18] and the references therein). Since in our case the vesicle contour is known to have circular shape, special polynomial or spline approximations are not needed.…”

Section: Determining Vesicle Radius From a Videomicrographmentioning

confidence: 99%

Determining membrane permeability of giant phospholipid vesicles from a series of videomicroscopy images

Peterlin

Jaklič

Pisanski

2009

Meas. Sci. Technol.

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Abstract.A technique for determining the permeability of a phospholipid membrane on a single giant unilamellar vesicle (GUV) is described, which complements the existing methods utilizing either a planar black lipid membrane or sub-micrometre-sized liposomes.A single GUV is transferred using a micropipette from a solution of a nonpermeable solute into an iso-osmolar solution of a solute with a higher membrane permeability. Osmotical swelling of the vesicle is monitored with a CCD camera mounted on a phase contrast microscope, and a sequence of images is obtained. On each image, the points on the vesicle contour are determined using Sobel filtering with adaptive binarization threshold, and from these, the vesicle radius is calculated with a great accuracy. From the time-dependence of the vesicle radius, the membrane permeability is obtained. Using a test set of data, the method provided a consistent estimate of the POPC membrane permeability for glycerol, P = 1.7 × 10 −8 m/s, with individual samples ranging from 1.61 × 10 −8 m/s to 1.98 × 10 −8 m/s. This value is ≈ 40% lower than the one obtained on similar systems. Possible causes for this discrepancy are discussed.

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Section: Determining Vesicle Radius From a Videomicrographmentioning

confidence: 99%

Determining membrane permeability of giant phospholipid vesicles from a series of videomicroscopy images

Peterlin

Jaklič

Pisanski

2009

Meas. Sci. Technol.

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“…More general results concerning the Lagrange interpolation of 2 n points on a circle-like curve by a parametric polynomial curve of degree n and the same approximation error, i.e., 2 n, are in [2].…”

Section: Discussionmentioning

confidence: 99%

“…Note that (2.1) is a particular case of (2.3) where c = 0. The following theorem, which has already been considered in [2] in a different context, gives one of the solutions of the nonlinear system (1.8) for any n in a closed form.…”

Section: Solution Of the Problemmentioning

confidence: 96%

Approximation of circular arcs by parametric polynomial curves

et al. 2007

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“…In high order parametric polynomial approximation of circular arcs ( [4], for example), the coefficients of the optimal solution involve the number of restricted partitions of a natural number. Namely, the coefficients of the parametric polynomial approximant p(t) = (x(t), y(t)) T , where …”

Section: Examplesmentioning

confidence: 99%