3D surface reconstruction from contour line image by a regularization method

The regularization method, which is performed by minimizing an energy functional of the image, has recently been applied to many ill-posed problems in computer vision. Notably, Grimson(1983) developed a regularization method for surface reconstruction which used a sparse set of known elevation data. We have developed an approach to surface reconstruction using both contour image data and a sparse set of known elevation values. We define a new energy functional which integrates three kinds of constraints : smoothness, fitness, and contour line constraint. These constraints seek to ensure that the reconstructed surface smoothly approximates the known elevation values and has the same height value for all points on a contour line. The energy functional can be minimized by solving a large linear system of simultaneous equations. We have successfully reconstructed a detailed 3D topography by applying this method to contour lines and known sparse elevation data extracted from moire images and topographic maps.