Image-Based OA-Style Paper Pop-Up Design via Mixed-Integer Programming.

Origami architecture (OA) is a fascinating papercraft that involves only a piece of paper with cuts and folds. Interesting geometric structures 'pop up' when the paper is opened. However, manually designing such a physically valid 2D paper pop-up plan is challenging since fold lines must jointly satisfy hard spatial constraints. Existing works on automatic OA-style paper pop-up design all focused on how to generate a pop-up structure that approximates a given target 3D model. This article presents the first OA-style paper pop-up design framework that takes 2D images instead of 3D models as input. Our work is inspired by the fact that artists often use 2D profiles to guide the design process, thus benefited from the high availability of 2D image resources. Due to the lack of 3D geometry information, we perform novel theoretic analysis to ensure the foldability and stability of the resultant design. Based on a novel graph representation of the paper pop-up plan, we further propose a practical optimization algorithm via mixed-integer programming that jointly optimizes the topology and geometry of the 2D plan. We also allow the user to interactively explore the design space by specifying constraints on fold lines. Finally, we evaluate our framework on various images with interesting 2D shapes. Experiments and comparisons exhibit both the efficacy and efficiency of our framework.

Generating Ambiguous Figure-Ground Images.

Ambiguous figure-ground images, mostly represented as binary images, are fascinating as they present viewers a visual phenomena of perceiving multiple interpretations from a single image. In one possible interpretation, the white region is seen as a foreground figure while the black region is treated as shapeless background. Such perception can reverse instantly at any moment. In this paper, we investigate the theory behind this ambiguous perception and present an automatic algorithm to generate such images. We model the problem as a binary image composition using two object contours and approach it through a three-stage pipeline. The algorithm first performs a partial shape matching to find a good partial contour matching between objects. This matching is based on a content-aware shape matching metric, which captures features of ambiguous figure-ground images. Then we combine matched contours into a compound contour using an adaptive contour deformation, followed by computing an optimal cropping window and image binarization for the compound contour that maximize the completeness of object contours in the final composition. We have tested our system using a wide range of input objects and generated a large number of convincing examples with or without user guidance. The efficiency of our system and quality of results are verified through an extensive experimental study.