Finding the centerline of the tubular structure helps to segment or analyze the organs such as the vessels or neuron fibers in medical images. This paper described a semi-automatic method using the minimum cost path finding and Hessian matrix analysis in scale space to calculate the centerline of tubular structure organs. Unlike
previous approaches, exhaustive search for line-like shapes in every scale is prevent. Centerline pixels candidates and the width of the vessel are extracted by analyzing the intensity profile along the gradient vectors in the image. A verification procedure using Hassian matrix analysis with the scale obtained from the gradient analysis is applied to those candidates. Results obtained from the Hessian matrix analysis are used to construct a weighted graph. Finding the minimum cost path in the graph gives the centerline of the tubular structure. The method is applied to find the centerline of the vessels in the 2D angiogram and the neuron fibers in the 3D confocal microscopic images.