Abstract
Logos are one of the most important graphic design forms that use an abstracted shape to clearly represent the spirit of a community. Among various styles of abstraction, a particular golden-ratio design is frequently employed by designers to create a concise and regular logo. In this context, designers utilize a set of circular arcs with golden ratios (i.e., all arcs are taken from circles whose radii form a geometric series based on the golden ratio) as the design elements to manually approximate a target shape. This error-prone process requires a large amount of time and effort, posing a significant challenge for design space exploration. In this work, we present a novel computational framework that can automatically generate golden ratio logo abstractions from an input image. Our framework is based on a set of carefully identified design principles and a constrained optimization formulation respecting these principles. We also propose a progressive approach that can efficiently solve the optimization problem, resulting in a sequence of abstractions that approximate the input at decreasing levels of detail. We evaluate our work by testing on images with different formats including real photos, clip arts, and line drawings. We also extensively validate the key components and compare our results with manual results by designers to demonstrate the effectiveness of our framework. Moreover, our framework can largely benefit design space exploration via easy specification of design parameters such as abstraction levels, golden circle sizes, etc.