Research On Non-rigid 3D Shape Retrieval Method Based On Spectral Analysis

With the rapid development of 3D scanning and acquisition technology,it is of great significance to research how to retrieve 3D shape effectively.For the shape retrieval task,the key problem is how to construct a compact and stable shape descriptor and select an effective similarity measure method.In recent years,non-rigid 3D shape descriptors based on spectral analysis have attracted much attention due to their simplicity,high efficiency and good stability to various complex non-rigid transformations.Under the framework of Riemannian geometry,this thesis focus on the feature extraction and similarity measurement in non-rigid 3D shape retrieval,and analyze the disadvantages of current methods.For 3D shape with different geometric structures and deformation types,four non-rigid 3D shape retrieval methods based on spectral analysis are proposed from the perspectives of shape descriptor range(local and global)and retrieval accuracy range(coarse retrieval and fine retrieval),and the main research work and innovations are listed below:(1)A non-rigid 3D shape retrieval method based on scale-invariant Mexican hat wavelet is proposed,which solves the problem of unstable shape feature extraction in scaling transformation.This method is based on the Mexican hat wavelet signature on the manifold,using the logarithm sampling space transform and the Fourier transform the scaling transformation into the time domain into a time shift operation in the frequency domain,eliminating the sensitivity of the operator to the shape of the scaling transformation,and achieving more stable and more robust feature extraction;Furthermore,by calculating the modified Hausdorff distance between feature vectors,the accuracy of shape similarity calculation is improved,the problem of feature alignment is effectively avoided.The proposed method has good robustness for shapes with global and local scaling transformation,and the regions with the same shape have consistent feature representation,which can effectively realize local rough retrieval of non-rigid 3D shapes.(2)A non-rigid 3D shape retrieval method based on average incremental scale-invariant heat kernel signature is proposed,which solves the problem that the performance of heat kernel signature description depends on the selection of time parameters and the computational complexity of similarity is high.This method embeds the average heat kernel increment between adjacent frequency domains in the whole time scale into the scale-invariant heat kernel,and effectively extracts the global and local heat kernel information under all time parameters.This method can effectively describe the geometric features of similar shapes,enhance the ability of fine description of local details of shapes,and reduce the dependence of operators on time parameters.The feature truncation method greatly reduces the complexity of feature calculation while retaining all the attribute features of the shape,and further improves the stability of shape feature expression with different sampling accuracy and the efficiency of local rough retrieval of non-rigid shapes.(3)A non-rigid 3D shape retrieval method based on spectral feature fusion is proposed,which solves the problem that the heat kernel operator can only extract the global geometric structure from a macro perspective and lose the high-frequency local information of the shape.This method uses the scale-invariant heat mean signature as a weight assignment to the average incremental scale-invariant heat kernel,which enhances the detailed information description of the feature salient points.By fusing the scale-invariant harmonic kernel signature and using Bo F feature coding method,the global and local geometric information of the shape at different frequencies can be effectively extracted.It has good robustness and strong discrimination for shapes with holes and partial structure,and can achieve global fine retrieval of non-rigid 3D shapes more stably and effectively.(4)A non-rigid 3D shape retrieval method based on improved biharmonic kernel signature is proposed,which solves the problems of poor feature description and high computational complexity.This method improves the feature representation of biharmonic kernel signature,and combines it with Gaussian curvature information to obtain a descriptor that contains both shape intrinsic attributes and shape geometric information.By using the Bo F coding technology,the similarity calculation problem caused by the inconsistency of feature dimension is eliminated.The features extracted by this method have good global perception of the shape,and can organize the shape information efficiently and compactly,which greatly reduces the time complexity of shape feature extraction and similarity calculation,and can accurately and stably achieve global fine retrieval of shapes with more joint structures.