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We explore an approach to the unwrapping of two-dimensional phase functions using a robust extrapolation-projection algorithm. Phase unwrapping is essential for imaging systems that construct the image from phase information. Unlike some existing methods where unwrapping is performed locally on a pixel-by-pixel basis, this work approaches the unwrapping problem from a global point of view. The unwrapping is done iteratively by a modification of the Gerchberg-Papoulis extrapolation algorithm, and the solution is refined by projecting onto the available global data at each iteration. Robustness of the algorithm is demonstrated through its performance in a noisy environment, and in comparison with a least-squares algorithm well-known in the literature.

The reproduction of color images by color halftoning can be characterized by the Neugebauer model/equation. However, the Neugebauer equation is not easy to solve because of the highly nonlinear relationship between the underlying Neugebauer primaries and the colorants. We attempt to solve the Neugebauer equation by vector space methods. The proposed method of solution is applicable to any number of colorants, although our experimental results are confined to the CMY and CMYK cases. Among the constraints we consider are those related to a bound on the permissible amount of total ink and a bound on the total cost of applying colorants to achieve a satisfactory level of color reproduction. Our results demonstrate that the vector space method is a feasible approach for solving for the required amounts of colorants in the constrained color halftoning problem.

We consider the reproduction of color subject to material and neighborhood constraints. By "material constraints," we mean any constraints that are applied to the amount of ink, lights, voltages, and currents that are used in the generation of color. In the first instance we consider the problem of reproducing a target color constrained by maximum additive color signals, such as in the phosphorescence process in a cathode ray tube. In the second instance we consider the more difficult problem of reproducing color subject to constraints on the maximum primary color variations in a (spatial) neighborhood. We introduce the idea of adjacent color variance (ACV) and then attempt to reproduce colors subject to an upper bound on the ACV. An algorithm that is suitable for this task is the method of vector space projections (VSP). In order to use VSP for constrained color reproduction, we use a novel approach to linearize nonlinear CIE-Lab space constraints. Experimental results are furnished that demonstrate that using the ACV as a bound helps to reduce reproduction artifacts in a color image.