Considering the special requirement of variable-diameter lumen volume measurement

and after analyzing the diameter-length volume detection method

we proposed a kind of high precision reconstruction method for variable-diameter 3D lumen surface

based on cubic spline inner radius parameter interpolation and the function after interpolation.In this method

a group of inner radius in various depths are measured and interpolated through a high precision cubic spline function.M-relation top-triangle diagonal equations are defined and solved in a stable and convergence way with a method named "pursue".Thus the method can obtain a precise inner radius function curve

and then the variable-diameter lumen volume 3D shape can be reconstructed with the interpolated inner radius curve.Test and simulation shows that the method can eliminate the unsmooth shortcoming caused by subsection low order interpolation with its inherent feature

and can meet the vision effect in inner capacity reconstruction.Further more the volume measurement error are reduced after interpolated by cubic spline without increasing any calculation

and the measurement relative error could reach 2‰ required by the system.