Discretization errors in particle tracking

G. Carmon; N. Mamman; M. Feingold

doi:10.1016/j.physa.2006.10.048

Discretization errors in particle tracking

G. Carmon, N. Mamman, M. Feingold

Department of Physics

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

Abstract

High precision video tracking of microscopic particles is limited by systematic and random errors. Systematic errors are partly due to the discretization process both in position and in intensity. We study the behavior of such errors in a simple tracking algorithm designed for the case of symmetric particles. This symmetry algorithm uses interpolation to estimate the value of the intensity at arbitrary points in the image plane. We show that the discretization error is composed of two parts: (1) the error due to the discretization of the intensity, b_D and (2) that due to interpolation, b_I. While b_D behaves asymptotically like N^{- 1} where N is the number of intensity gray levels, b_I is small when using cubic spline interpolation.

Original language	English
Pages (from-to)	117-132
Number of pages	16
Journal	Physica A: Statistical Mechanics and its Applications
Volume	376
Issue number	1-2
DOIs	https://doi.org/10.1016/j.physa.2006.10.048
State	Published - 15 Mar 2007

Keywords

Discretization errors
Microbeads
Particle tracking

ASJC Scopus subject areas

Statistics and Probability
Condensed Matter Physics

Access to Document

10.1016/j.physa.2006.10.048

Cite this

@article{78847976a8be4ab78e2c018c0f525e21,

title = "Discretization errors in particle tracking",

abstract = "High precision video tracking of microscopic particles is limited by systematic and random errors. Systematic errors are partly due to the discretization process both in position and in intensity. We study the behavior of such errors in a simple tracking algorithm designed for the case of symmetric particles. This symmetry algorithm uses interpolation to estimate the value of the intensity at arbitrary points in the image plane. We show that the discretization error is composed of two parts: (1) the error due to the discretization of the intensity, bD and (2) that due to interpolation, bI. While bD behaves asymptotically like N- 1 where N is the number of intensity gray levels, bI is small when using cubic spline interpolation.",

keywords = "Discretization errors, Microbeads, Particle tracking",

author = "G. Carmon and N. Mamman and M. Feingold",

note = "Funding Information: We thank I. Abdulhalim, J. Bechhoefer, I. Dinstein, L. Gheber and C. Kedem for useful discussions and suggestions. This research was supported in part by the Israel Academy of Science and Humanities (Grant no. 263/00).",

year = "2007",

month = mar,

day = "15",

doi = "10.1016/j.physa.2006.10.048",

language = "English",

volume = "376",

pages = "117--132",

journal = "Physica A: Statistical Mechanics and its Applications",

issn = "0378-4371",

publisher = "Elsevier B.V.",

number = "1-2",

}

TY - JOUR

T1 - Discretization errors in particle tracking

AU - Carmon, G.

AU - Mamman, N.

AU - Feingold, M.

N1 - Funding Information: We thank I. Abdulhalim, J. Bechhoefer, I. Dinstein, L. Gheber and C. Kedem for useful discussions and suggestions. This research was supported in part by the Israel Academy of Science and Humanities (Grant no. 263/00).

PY - 2007/3/15

Y1 - 2007/3/15

N2 - High precision video tracking of microscopic particles is limited by systematic and random errors. Systematic errors are partly due to the discretization process both in position and in intensity. We study the behavior of such errors in a simple tracking algorithm designed for the case of symmetric particles. This symmetry algorithm uses interpolation to estimate the value of the intensity at arbitrary points in the image plane. We show that the discretization error is composed of two parts: (1) the error due to the discretization of the intensity, bD and (2) that due to interpolation, bI. While bD behaves asymptotically like N- 1 where N is the number of intensity gray levels, bI is small when using cubic spline interpolation.

AB - High precision video tracking of microscopic particles is limited by systematic and random errors. Systematic errors are partly due to the discretization process both in position and in intensity. We study the behavior of such errors in a simple tracking algorithm designed for the case of symmetric particles. This symmetry algorithm uses interpolation to estimate the value of the intensity at arbitrary points in the image plane. We show that the discretization error is composed of two parts: (1) the error due to the discretization of the intensity, bD and (2) that due to interpolation, bI. While bD behaves asymptotically like N- 1 where N is the number of intensity gray levels, bI is small when using cubic spline interpolation.

KW - Discretization errors

KW - Microbeads

KW - Particle tracking

UR - http://www.scopus.com/inward/record.url?scp=33846141225&partnerID=8YFLogxK

U2 - 10.1016/j.physa.2006.10.048

DO - 10.1016/j.physa.2006.10.048

M3 - Article

AN - SCOPUS:33846141225

SN - 0378-4371

VL - 376

SP - 117

EP - 132

JO - Physica A: Statistical Mechanics and its Applications

JF - Physica A: Statistical Mechanics and its Applications

IS - 1-2

ER -

Discretization errors in particle tracking

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this