We describe a new method that interactively extracts salient object surfaces from 3D medical volume data. Isosurface extraction has been one of the most popular methods for 3D volume visualization. A contour, a connected component of an isosurface, often represents the boundary surface of an independent object in an image. However, an infinite number of isosurfaces are defined in an image and even one single isosurface may have many contours. Therefore, the problem of effectively finding a contour that represents a region of interest becomes important. Our method uses a contour tree as a user interface for extracting salient contours. The contour tree represents all possible contours and their topological structures. Geometric properties of each contour are computed and used to label the contour tree as the width and color of branches. The topological and geometric properties guide users to select salient contour surfaces which are then extracted using the propagation of seed cells derived from the tree. We fully utilize multicore CPUs and manycore GPUs during the extraction process to obtain enough interactivity. Our method was applied to various medical data sets. The results showed that our method is up to seven times faster than previous methods and that it interactively visualizes salient contour surfaces representing important features in the data.