Recently, the estimation of the vessel diameter and cross-sectional are from the images of the coronary arteries has been considered, aiming at the quantitative diagnosis of the coronary artery stenoses. The edge detection of the vessel image is the clue to the estimation of the vessel diameter and the cross-sectional area. however, no method has been established with a sufficient accuracy. This paper proposes an adaptive Laplacian-Gaussian filter method for the accurate edge detection of the vessel image which is an improvement of the zero-crossing method. By the proposed method, it is shown that the edge is detected at the position corresponding to the vessel radius if the image of the vessel retains a similar shape even if the vessel diameter changes.