We present a semi-supervised technique of object extraction for natural image matting. At first, we present a novel unsupervised graph-spectral algorithm for extraction of homogeneous regions in an image. We next derive a semi-supervised scheme from this unsupervised algorithm. In our method, it is sufficient for users to draw strokes only in one of object and background regions. The semi-supervised optimization problem is solved with an iterative method where memberships are propagated from strokes to their surroundings. We suggest a guideline for placement of strokes by exploiting the same iterative solution process in the unsupervised algorithm. We project the color vectors with the linear discriminant analysis to improve the color discriminability and speed up the convergence of the iterative method. Performance of the proposed method is examined for some images and the results are compared with other methods and ground truth mattes.