Abstract: It is well known that the performance of line (circle) extraction strongly depends on the used parameterization, however there exist few reports in the literature on the design of general line (circle) parameterization. In this paper, we present an approach for systematic design of general line (circle) parameterization. The paper consists of the following 6 parts. 1. The design of the line (circle) parameterizations satisfying purely the uniqueness condition is investigated. 2. The design of the line (circle) parameterizations possessing the enlarging property is investigated. 3. The design of the line parameterizations possessing the focusing property is investigated. 4. The design of the circle parameterizations possessing the focusing property is investigated. 5. The relationship between a specific parameterization with stretching or focusing property and filter theory is discussed. 6. Some simple experiments are presented to illustrate the usefulness of our theoretical results. This work could be used as a theoretical basis for the optimal design of line (circle) parameterizations.