Sit Atilla, Shin Woong-Hee, Kihara Daisuke
Department of Mathematics and Statistics, Eastern Kentucky University, Richmond, KY, 40475 USA.
Department of Biological Sciences, Purdue University, West Lafayette, IN, 47907 USA.
Pattern Recognit. 2019 Sep;93:534-545. doi: 10.1016/j.patcog.2019.05.019. Epub 2019 May 8.
Direct comparison of three-dimensional (3D) objects is computationally expensive due to the need for translation, rotation, and scaling of the objects to evaluate their similarity. In applications of 3D object comparison, often identifying specific local regions of objects is of particular interest. We have recently developed a set of 2D moment invariants based on discrete orthogonal Krawtchouk polynomials for comparison of local image patches. In this work, we extend them to 3D and construct 3D Krawtchouk descriptors (3DKDs) that are invariant under translation, rotation, and scaling. The new descriptors have the ability to extract local features of a 3D surface from any region-of-interest. This property enables comparison of two arbitrary local surface regions from different 3D objects. We present the new formulation of 3DKDs and apply it to the local shape comparison of protein surfaces in order to predict ligand molecules that bind to query proteins.
由于需要对三维（3D）物体进行平移、旋转和缩放以评估其相似性，因此直接比较三维物体的计算成本很高。在三维物体比较的应用中，通常识别物体的特定局部区域特别重要。我们最近基于离散正交Krawtchouk多项式开发了一组二维矩不变量，用于比较局部图像块。在这项工作中，我们将其扩展到三维，并构建了在平移、旋转和缩放下不变的三维Krawtchouk描述符（3DKD）。新的描述符能够从任何感兴趣区域提取三维表面的局部特征。这一特性使得能够比较来自不同三维物体的两个任意局部表面区域。我们提出了3DKD的新公式，并将其应用于蛋白质表面的局部形状比较，以预测与查询蛋白质结合的配体分子。
