### Abstract

A relatively simple mathematical procedure for the reconstruction of the 3-dimensional (3D) image of the left ventricle (LV) of the heart is presented. The method is based on the assumption that every ray whoch emanates from the midpoint of the long axis of the 3D body crosses the surface boundary of the ventricle at one and only one point. The coordinates r_{i}, φ_{i}, θ_{i} of the data points on, say, the outer boundary, (i.e., the epicardium) are calculated in a spherical coordinate system having its origin in the midpoint of the long axis. The problem of defining the coordinates of a prescribed grid point on the boundary is treated as an interpolation problem for the function r = r(φ, θ), defined in the rectangle 0 ≤ φ ≤ 2π; 0 ≤ θ ≤ π with r_{i} given in the points (φ_{i}, θ_{i}).

Original language | English (US) |
---|---|

Pages (from-to) | 420-427 |

Number of pages | 8 |

Journal | Computer Vision, Graphics and Image Processing |

Volume | 37 |

Issue number | 3 |

DOIs | |

State | Published - 1987 |

Externally published | Yes |

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### ASJC Scopus subject areas

- Engineering(all)

### Cite this

*Computer Vision, Graphics and Image Processing*,

*37*(3), 420-427. https://doi.org/10.1016/0734-189X(87)90046-6

**A simple approach to the problem of 3-D reconstruction.** / Brevdo, L.; Sideman, S.; Beyar, R.

Research output: Contribution to journal › Article

*Computer Vision, Graphics and Image Processing*, vol. 37, no. 3, pp. 420-427. https://doi.org/10.1016/0734-189X(87)90046-6

}

TY - JOUR

T1 - A simple approach to the problem of 3-D reconstruction

AU - Brevdo, L.

AU - Sideman, S.

AU - Beyar, R.

PY - 1987

Y1 - 1987

N2 - A relatively simple mathematical procedure for the reconstruction of the 3-dimensional (3D) image of the left ventricle (LV) of the heart is presented. The method is based on the assumption that every ray whoch emanates from the midpoint of the long axis of the 3D body crosses the surface boundary of the ventricle at one and only one point. The coordinates ri, φi, θi of the data points on, say, the outer boundary, (i.e., the epicardium) are calculated in a spherical coordinate system having its origin in the midpoint of the long axis. The problem of defining the coordinates of a prescribed grid point on the boundary is treated as an interpolation problem for the function r = r(φ, θ), defined in the rectangle 0 ≤ φ ≤ 2π; 0 ≤ θ ≤ π with ri given in the points (φi, θi).

AB - A relatively simple mathematical procedure for the reconstruction of the 3-dimensional (3D) image of the left ventricle (LV) of the heart is presented. The method is based on the assumption that every ray whoch emanates from the midpoint of the long axis of the 3D body crosses the surface boundary of the ventricle at one and only one point. The coordinates ri, φi, θi of the data points on, say, the outer boundary, (i.e., the epicardium) are calculated in a spherical coordinate system having its origin in the midpoint of the long axis. The problem of defining the coordinates of a prescribed grid point on the boundary is treated as an interpolation problem for the function r = r(φ, θ), defined in the rectangle 0 ≤ φ ≤ 2π; 0 ≤ θ ≤ π with ri given in the points (φi, θi).

UR - http://www.scopus.com/inward/record.url?scp=0023311642&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0023311642&partnerID=8YFLogxK

U2 - 10.1016/0734-189X(87)90046-6

DO - 10.1016/0734-189X(87)90046-6

M3 - Article

AN - SCOPUS:0023311642

VL - 37

SP - 420

EP - 427

JO - Computer Vision, Graphics, and Image Processing

JF - Computer Vision, Graphics, and Image Processing

SN - 0734-189X

IS - 3

ER -