Abstract: Traditional visualization approaches for volumetric data are not able to reflect clear interior structures of input data. We present a method to enhance volume rendering by topological features under a continuous framework. A continuous field is first reconstructed from discrete data by 7-directional box spline quasi-interpolation, and critical points are obtained from gradient polynomial systems. Then saddle-extremum arcs are computed from the continuous field, and the lengths of them are used to build a weighted critical value histogram, which helps to design a new transfer function. Compared with those existing discrete approaches, our method is easier to implement and the results are smoother and clearer.