Algorithm for 3D point cloud steganalysis based on composite operator feature enhancement

Abstract

Three-dimensional (3D) point cloud information hiding algorithms are mainly concentrated in the spatial domain. Existing spatial domain steganalysis algorithms are subject to more disturbing factors during the analysis and detection process, and can only be applied to 3D mesh objects, so there is a lack of steganalysis algorithms for 3D point cloud objects. To change the fact that steganalysis is limited to 3D mesh and eliminate the redundant features in the 3D mesh steganalysis feature set, we propose a 3D point cloud steganalysis algorithm based on composite operator feature enhancement. First, the 3D point cloud is normalized and smoothed. Second, the feature points that may contain secret information in 3D point clouds and their neighboring points are extracted as the feature enhancement region by the improved 3DHarris-ISS composite operator. Feature enhancement is performed in the feature enhancement region to form a feature-enhanced 3D point cloud, which highlights the feature points while suppressing the interference created by the rest of the vertices. Third, the existing 3D mesh feature set is screened to reduce the data redundancy of more relevant features, and the newly proposed local neighborhood feature set is added to the screened feature set to form the 3D point cloud steganography feature set POINT72. Finally, the steganographic features are extracted from the enhanced 3D point cloud using the POINT72 feature set, and steganalysis experiments are carried out. Experimental analysis shows that the algorithm can accurately analyze the 3D point cloud’s spatial steganography and determine whether the 3D point cloud contains hidden information, so the accuracy of 3D point cloud steganalysis, under the prerequisite of missing edge and face information, is close to that of the existing 3D mesh steganalysis algorithms.

1. Introduction

Three-dimensional (3D) models are widely used as multimedia communication carriers due to their complex structural characteristics and various forms of expression, which have attracted the attention of scholars in the field of information hiding. Information hiding of 3D models can be effectively realized by encoding the secret information and expressing the encoded secret information by modifying the structure of some areas in 3D models. Compared with traditional methods of hiding information in two-dimensional (2D) images, 3D models have a larger capacity and more areas for information hiding.

With the development of 3D model information steganography field, some miscreants began to use 3D model information steganography algorithms to carry out illegal activities, which leads to a series of security and privacy issues. To prevent 3D model steganography from being used maliciously, 3D model steganography analysis algorithms have been proposed. The spatial domain steganalysis method YANG208 for 3D mesh was first proposed in 2014, and feature detection and steganalysis were achieved by analyzing the coordinate changes under Cartesian and Laplace coordinate systems (Yang and Ivrissimtzis, 2014). Since then, 3D model steganalysis has been continuously studied with the goal of proposing new feature sets. Based on YANG208, further analysis and screening of features were carried out. Part of the feature set was retained, and vertex Euclidean distances and dihedral angle offsets were added to form the YANG40 feature set, which reduces the feature dimension under the premise of guaranteeing the accuracy. Based on the vertex normal vector and curvature, the detection ability of feature set LFS52 was significantly improved compared with that of the YANG40 feature set (Li and Bors, 2016). Based on LFS52, the spherical coordinate system and the edge pinch angle features were added to form the LFS76 feature set (Li and Bors, 2017), and the new edge vector features were added to form the ELFS124 feature set based on LFS76, which leads to a significant increase in the steganography analysis accuracy (Li et al., 2018a, 2018b; Li and Bors, 2020a). In addition to the spatial domain steganalysis algorithms, some studies have proposed the NVT+ steganalysis features based on the tensor matrix eigenroot (Zhou et al., 2021) and the WFS228 dataset based on the 3D wavelet decomposition which effectively expands the range of steganalysis in the transform domain (Li and Bors, 2020b). All the above 3D model steganalysis algorithms use 3D mesh as the carrier, which can effectively perform steganalysis on most of existing steganography algorithms. However, in reality, 3D mesh is difficult to obtain, and 3D point clouds are more readily available, motivating the need for point cloud steganalysis methods.