Intensity-based 3-D Reconstruction with Non-linear Optimization

Image-based rendering methods such as light fields are used in computer graphics for the computation of new views of a scene out of a set of recorded images with known camera positions. The quality of the rendered images depends on the accuracy of information about the structure of the scene, consisting of a geometric 3-D model. In order to accurately reconstruct and optimize such a 3-D model, we define a residual function which represents the difference between an image rendered with the light field from a known viewpoint, and the original image at the same position. In order to get optimal results, we minimize this particular function by defining a non-linear least-squares problem which is solved by an appropriate optimization method. Here, we use a largely unknown, non-monotone variant of the Levenberg- Marquardt method. Thus, starting from a flat 3-D model in our experiments the non-monotone variant decreases the error by a factor of up to 3 in comparison to the monotone variant.