Solving inverse problems in computer vision by scale space reconstruction
Alan G. Jones, Chris Taylor · Research Explorer (The University of Manchester) · 1994
Ill-posed inverse problems are widely encountered in computer vision. examples include shape from shading, surface reconstruction from sparse data and optic flow. Unique solutions to these problems are conventionally found by minimizing an objective function regularized by a smoothness constraint. However, objective functions of this form often contain many local minima, making it difficult to find an adequate solution by standard numerical methods. We describe an algorithm for solving inverse problems using scale space tracking which is robust, provably convergent and avoids local minima. The algorithm generates a hierarchy of solutions at different scales, forming a scale space from which a final solution can be selected at a later stage. We show how the use of gaussian basis functions to construct solutions can result in scale space behaviour without the need to blur the input data. Results are shown for shape from shading and surface reconstruction from stereo data, using both real and synthetic images.