以圖神經網路將二維樂高建構映射至平鋪問題之方法

Abstract

樂高積木因積木種類的多樣性而被人們喜愛，且常被創作者們用在模型的設計上。近年來，出現許多樂高研究去探討如何以電腦計算建構出二維或三維的樂高模型，然而這些研究主要以長方體狀的基本磚來建構模型，使得外觀上雖然相似，但仍保有基本磚的稜角。此外，隨著用於建構的樂高磚種類和所要建構的模型大小增加，其搜索空間及運算時間也會大幅增加。\n為了克服以上問題，本研究首先嘗試將GNN與二維樂高建構做結合。以樂高磚中的基本磚和斜磚作為輸入，並透過給定樂高損失函數，將現有的圖神經網路研究，從平鋪問題擴展至樂高組合問題。同時，我們也針對輸入圖形進行變形和使用分治法，來提升組裝結果的覆蓋率和相似度。綜上所述，我們提出一套系統流程，在使用者給定輸入圖形後，訓練完成的GNN模型便能輸出符合樂高建構的平鋪結果，再經過量化分析、合併和顏色抓取等操作，便能產生所要的樂高組裝結果。

Lego bricks are loved by people because of the variety of building blocks, and are often used by creators in the design of models. Recently, there have been many LEGO researches to explore how to construct 2D or 3D LEGO models by computer. However, these researches mainly build models with normal bricks. Although the appearance is similar, it still retains the edges and corners of normal bricks. Furthermore, as the types of Lego bricks used for construction and the size of the model to be constructed increase, the search space and computation time will also increase significantly.\nIn order to overcome the above problems, our research first attempts to combine the graph neural network with the 2D Lego construction problem. Taking normal bricks and slope bricks in LEGO bricks as input, and by giving the Lego loss function, the existing graph neural network research is extended from the tiling problem to the Lego combinatorial problem. At the same time, we also deform the input shapes and use the divide-and-conquer method to improve the coverage and similarity of the assembly results. To sum up, we propose a Lego system building. The trained GNN model can output tiling results that conform to the LEGO construction after the user gives the input shapes. Then, through quantitative analysis, merging and color mapping, the desired LEGO brick sculptures can be generated.