3D image processing is an important problem in computer vision and pattern recognition fields. Compared with 2D image processing, its computation difficulty and cost are much higher due to the extra dimension. To fundamentally address this problem, we propose to embed the essential information in a 3D object into 2D space via spectral layout. Specifically, we construct a 3D adjacency graph to capture spatial structure of the 3D voxel grid. Then we calculate the eigenvectors corresponding to the second and third smallest eigenvalues of its graph Laplacian and perform spectral layout to map each voxel into a pixel in 2D Cartesian coordinate plane. The proposed method can achieve high quality 2D representations for 3D objects, which enables to use 2D-based methods to process 3D objects. The experimental results demonstrate the effectiveness and efficiency of our method.
翻译:3D 图像处理是计算机视觉和模式识别字段中的一个重要问题。 与 2D 图像处理相比, 其计算难度和成本因额外维度而高得多。 为了从根本上解决这一问题, 我们提议通过光谱布局将3D 对象中的基本信息嵌入 2D 空间。 具体地说, 我们建造一个 3D 相邻图, 以捕捉 3D voxel 网格的空间结构。 然后我们计算与其图解 Laplacian 的第二和第三个最小电子值相对应的二次和第三次电子元值, 并进行光谱布局, 将每个 voxel 绘制成 2D Cartesian 坐标平面中的像素。 拟议的方法可以实现3D 对象的高质量 2D 表示, 从而能够使用 2D 基方法处理 3D 对象。 实验结果显示了我们方法的有效性和效率 。