3D object feature extraction and classification using 3D MF-DFA

In this study, we propose a three-dimensional (3D) object recognition method using multifractal properties. The proposed method is based on a 3D multifractal detrended fluctuation analysis (MF-DFA) using the voxel data of an object. We propose a 3D MF-DFA by extending a conventional MF-DFA, which is widely adopted for analyzing the time series. In the current study, the data processed by the model were changed from the time-series data in the original MF-DFA into the voxels of 3D objects. Thus, the steps in the original model were extended to a 3D processing structure. To voxelize the scatter point data, we apply a modified Allen–Cahn (AC) equation with the Neumann boundary condition to generate the object volume. Various 3D models after voxelization are used for the 3D MF-DFA to calculate the generalized Hurst exponents. The calculated generalized Hurst exponents of different categories show different distributions and are used as the training feature input vector into a multi-classification system, i.e., one-versus-one support vector machines (OvO-SVMs). The computational results show that the proposed method can effectively extract the features of an object. Metrics such as the accuracy, precision, and recall are utilized to measure the efficiency and robustness. When compared with state-of-art algorithms, our empirical tests show that the proposed 3D MF-DFA-OvO-SVM system is superior to most of the methods in terms of classification accuracy. In addition, we also confirm that our proposed model is applicable to object detection in 3D space. An efficient method may be useful for autonomous driving, robot cruises, and AR-based intelligent user interfaces.