The use of statistical analysis in line detection is necessary because of the noises induced by signal amplification and the random variations due to the microtexture of the object surface. Hunt et al. [5] have shown that the method derived from statistical signal detection theory has better performance than the Hough transform both in line detection and estimation. In this paper, we first derive two likelihood ratio tests for detecting a line in both gray level and binary images. These tests have some invariance properties. We also present some experimental results of detecting a line in the simulated image and also an edge line in the real image to demonstrate the usefulness of the tests. Then extensions of these tests to detect a parametric curve or a general shape or multiple curves are discussed in detail. Finally, a complete analysis of the Bayesian approach to line detection, particularly in the normal distributed case, is carried out successfully, and practical considerations of the whole theory are discussed with a conclusion that the theory is realistic and can be applied in many practical situations, and in some cases better than the Hough transform.