# An efficient exact algorithm for the ''least squares'' image registration problems

## Abstract

Image registration involves estimating how one set of n-dimensional points is rotated, scaled, and translates into a second set of n- dimensional points. In practice, n is usually 2 or 3. We give an exact algorithm to solve the ''least-squares'' formulation of the two-dimensional registration problem. The algorithm, which is based on parametric linear programming, can be viewed as a refinement of the O(k/sup 3/) approximation method proposed by Zikan and Silberburg. The approach can be extended to handle registration of images of different cardinalities. 13 refs., 1 fig.

- Authors:

- Publication Date:

- Research Org.:
- Stanford Univ., CA (USA). Systems Optimization Lab.

- OSTI Identifier:
- 6125034

- Report Number(s):
- SOL-89-5

ON: DE89013116

- DOE Contract Number:
- FG03-87ER25028

- Resource Type:
- Technical Report

- Resource Relation:
- Other Information: Portions of this document are illegible in microfiche products

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 99 GENERAL AND MISCELLANEOUS//MATHEMATICS, COMPUTING, AND INFORMATION SCIENCE; DATA; TRANSFORMATIONS; ANALYTICAL SOLUTION; ALGORITHMS; LEAST SQUARE FIT; LINEAR PROGRAMMING; TWO-DIMENSIONAL CALCULATIONS; INFORMATION; MATHEMATICAL LOGIC; MAXIMUM-LIKELIHOOD FIT; NUMERICAL SOLUTION; PROGRAMMING; 990230* - Mathematics & Mathematical Models- (1987-1989)

### Citation Formats

```
Zikan, K.
```*An efficient exact algorithm for the ''least squares'' image registration problems*. United States: N. p., 1989.
Web.

```
Zikan, K.
```*An efficient exact algorithm for the ''least squares'' image registration problems*. United States.

```
Zikan, K. Mon .
"An efficient exact algorithm for the ''least squares'' image registration problems". United States.
doi:.
```

```
@article{osti_6125034,
```

title = {An efficient exact algorithm for the ''least squares'' image registration problems},

author = {Zikan, K.},

abstractNote = {Image registration involves estimating how one set of n-dimensional points is rotated, scaled, and translates into a second set of n- dimensional points. In practice, n is usually 2 or 3. We give an exact algorithm to solve the ''least-squares'' formulation of the two-dimensional registration problem. The algorithm, which is based on parametric linear programming, can be viewed as a refinement of the O(k/sup 3/) approximation method proposed by Zikan and Silberburg. The approach can be extended to handle registration of images of different cardinalities. 13 refs., 1 fig.},

doi = {},

journal = {},

number = ,

volume = ,

place = {United States},

year = {Mon May 01 00:00:00 EDT 1989},

month = {Mon May 01 00:00:00 EDT 1989}

}

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