A Robust Iterative Shape-From-Shading Algorithm with Modified Transforming Matrix

We present a new simple iterative shape-from-shading algorithm, which gives greater numerical stability and as a result more accurate shapes than the previous one. The Jacobi’s iterative method is applied to the difference between the image and the reflectance function of the three depth parameters to get an iterative relation, which is then modified so that all the eigenvalues of the inverting matrix consist of three squared terms. This prevents the determinant of the matrix from being null to a great degree, resulting in a more accuracy of the shape estimate. We also rotate the coordinates by an arbitrary angle, when needed, to improve the reconstruction with no such shape distortions as stripe-like ones and with a resolution enhancement. Computer experiments were made using several synthetic and real images to show its effectiveness.