Uniform converting matrix in photometric stereo shape reconstruction method

We present an improvement in accuracy and stability of the method that reconstructs shape from photometric stereo. Our previous method applies the Jacobi's iterative method to the reflectance map equation. In this method the sparse matrix that converts the shading into depth has non-negative diagonal terms, assuring numerical stability for most cases. An extended numerical examination of the method, however, reveals two problems. One is associated with numerical instability and the other is with inaccuracy of the shape. In this paper, the matrix is modified so that all the diagonal terms have three non-negative terms for each of the two lighting directions. It is shown that the modification not only makes it possible to reconstruct shapes for certain bad lighting conditions, but it also significantly improves the accuracy over the entire shape.