# Estimating Three-Dimensional Motion Parameters of a Rigid Planar Patch

Roger Y. Tsai, Thomas S Huang

Research output: Contribution to journalArticle

### Abstract

We present a new direct method of estimating the three-dimensional motion parameters of a rigid planar patch from two time-sequential perspective views (image frames). First, a set of eight pure parameters are defined. These parameters can be determined uniquely from the two given image frames by solving a set of linear equations. Then, the actual motion parameters are determined from these pure parameters by a method which requires the solution of a sixth-order polynomial of one variable only, and there exists a certain efficient algorithm for solving a sixth-order polynomial. Aside from a scale factor for the translation parameters, the number of real solutions never exceeds two. In the special case of three-dimensional translation, the motion parameters can be expressed directly as some simple functions of the eight pure parameters Thus, only a few arithmetic operations are needed.

Original language English (US) 1147-1152 6 IEEE Transactions on Acoustics, Speech, and Signal Processing 29 6 https://doi.org/10.1109/TASSP.1981.1163710 Published - Dec 1981

Polynomials
Linear equations

### ASJC Scopus subject areas

• Signal Processing

### Cite this

In: IEEE Transactions on Acoustics, Speech, and Signal Processing, Vol. 29, No. 6, 12.1981, p. 1147-1152.

Research output: Contribution to journalArticle

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