Recovering solid geometric object from single line drawing image

Abstract

Many educational materials contain a lot of solid geometric figures. The solid geometric objects in these figures are usually drawn as 2D line drawings thus have lost their 3D information. This paper presents a method to recover the 3D information of the solid geometric object from single line drawing image taken from the geometric books, which would be used to help the users better present and understand the solid geometric object on their mobile devices. The main advantage of our method is the abilitYTo handle inaccurately processed sketches as opposed to the previous methods which require perfect line drawings as inputs. Our method consists of three main steps as follows. First, the sketch of the input line drawing image is automatically extracted and further represented as an undirected graph. Second, candidate 3D models from the pre-built 3D model database are found by graph similarity-based searching and sub-graph isomorphism matching. Third, for each candidate 3D model, the model parameters, the rotation and the translation aligning the model with the sketch are found by minimizing an objective function which is composed of the residuals between the vertices of the sketch and the 2D projections of the candidate model's vertices, and an optimal reconstruction solution is further selected as the final result. Extensive experimental results demonstrate the effectiveness and robustness of our method for recovering the solid geometric object from single line drawing image.