Abstract: To improve the retrieval precision of 3D model with the complex surface, a new method based on curvedness feature was proposed. First, the sample points were obtained on the 3D model surface. The curvedness of these points was obtained by computing Gauss curvature and Mean curvature. The curvedness values showed properties of 3D model surface. Secondly, the centroid of the model was set as the center. The coordinate system in which two coordinate axes were the curvedness value and the Euclid distance between the random point and the center was constructed. The distribution matrix of curvedness feature was obtained by computing the statistical number of the sample points in the different Euclid distance. This distribution matrix was the feature descriptor of the 3D model. This descriptor had the property of rotation invariance and translation invariance, which could well reflect the geometric characteristics of complex surfaces. Finally, the similarity between different models was given by comparing the curvedness distribution matrix. The experimental results show that the proposed method can effectively improve the accuracy of the 3D model retrieval, especially suitable for those models with complex surfaces.

Key words: feature extraction, curvedness, Gaussian curvature, mean curvature, 3D model retrieval

摘要： 针对如何提高复杂曲面的三维模型的检索精度的问题，提出了一种基于曲度特征的三维模型检索算法。首先，在模型表面选取随机采样点，计算点所在局部曲面的高斯曲率和平均曲率，通过高斯曲率和平均曲率求出随机点的曲度值，曲度值表明了曲面的凹凸属性。然后，以模型的质心为球心，以随机点与质心距离和曲度值为坐标轴建立坐标系，统计出一定距离范围内曲度值分布的概率，构建距离与曲度的分布矩阵，以此分布矩阵作为三维模型特征描述符。该特征描述符具有旋转不变性和平移不变性，能够很好地反映复杂曲面的几何特征。最后，通过比较分布矩阵给出不同模型间的相似度。实验结果表明，该方法相比形状分布算法的检索性能有较大提高，尤其适用于具有复杂曲面的三维模型检索。

关键词: 特征提取, 曲度, 高斯曲率, 平均曲率, 三维模型检索