Phase unwrapping is an integral part of multiple imaging techniques, and as a result, a wide range of algorithms have been created to unwrap phases. One such algorithm is the minimum Lp-norm phase unwrapping algorithm. This algorithm transforms the phase unwrapping problem into a minimization problem of a certain functional, which it solves with an iterative method. However, the problem is usually not convex, and when there are many sharp edges in the data to be unwrapped, the algorithm often produces a local minimum with new discontinuities in originally smooth areas. To prioritize solutions which minimize the functional better in smooth areas, we use weights to deprioritize data lying along edges in the ground-truth image. This requires a method to find ground-truth edges using the wrapped image, which we describe. When using the modified algorithm, we generally obtain improved results on images with multiple edges (both lower errors and more correct edge placement).
Many image reproduction devices, such as printers, are limited to only a few numbers of printing inks. Halftoning, which is the process to convert a continuous-tone image into a binary one, is, therefore, an essential part of printing. An iterative halftoning method, called Iterative Halftoning Method Controlling the Dot Placement (IMCDP), which has already been introduced in the literature, generally results in halftones of good quality. In this paper, we propose a structure-based alternative to this algorithm that improves the halftone image quality in terms of sharpness, structural similarity, and tone preservation. By employing appropriate symmetrical and non-symmetrical Gaussian filters inside the proposed halftoning method, it is possible to adaptively change the degree of sharpening in different parts of the continuous-tone image. This is done by identifying a dominant line in the neighborhood of each pixel in the original image, utilizing the Hough Transform, and aligning the dots along the dominant line. The objective and subjective quality assessments verify that the proposed structure-based method not only results in sharper halftones, giving more three-dimensional impression, but also improves the structural similarity and tone preservation. The adaptive nature of the proposed halftoning method makes it an appropriate algorithm to be further developed to a 3D halftoning method, which could be adapted to different parts of a 3D object by exploiting both the structure of the images being mapped and the 3D geometrical structure of the underlying printed surface.