Graph-based Geometry Processing Techniques for 3D Meshes

Abstract

The first study is saliency detection on 3D surface geometry using random walk. A unified detection algorithm of view-independent and view-dependent saliency for 3D mesh models is proposed. While conventional techniques use irregular meshes, we adopt the semi-regular meshes to overcome the drawback of irregular connectivity for saliency computation. We employ the angular deviation of normal vectors between neighboring faces as geometric curvature features, which are evaluated at hierarchically structured triangle faces. We construct a fully-connected graph at each level of semi-regular mesh, where the face patches serve as graph nodes. At the base mesh level, we estimate the saliency as the stationary distribution of random walk. At the higher level meshes, we take the maximum value between the stationary distribution of random walk at the current level and an upsampled saliency map from the previous coarser scale. Moreover, we also propose a view-dependent saliency detection method , which employs the visibility feature in addition to geometric features to estimate the saliency with respect to a selected viewpoint. Experimental results demonstrate that the proposed saliency detection algorithm captures global conspicuous regions reliably and detects locally detailed geometric features faithfully, compared with conventional techniques. The second study is mesh compression. We propose a geometry compression algorithm for dynamic mesh sequences with varying connectivity. We partition each mesh frame into multiple segments, and investigate a segment-wise predictive coding framework. Generally, it is difficult to find the temporal correlation between two meshes in the spatial domain due to different connectivity. However, we observe that the corresponding frequency components capture similar geometric patterns regardless of mesh connectivity. Therefore, we extract the frequency domain signals by performing graph Fourier transform to the vertex coordinates in each mesh segment, and predict the frequency domain signals of the current frame using that of the previous frame. We adaptively select an optimal number of low-frequency components used for prediction according to mesh segments. We encode the prediction residuals of the selected low-frequency components and the remaining high-frequency components separately using different contexts of arithmetic coding. Experimental results demonstrate that the proposed algorithm achieves much higher coding gains compared with the conventional methods in terms of rate and distortion. The third study is mesh denoising. We propose a denoising algorithm for 3D meshes using graph spectral filter. While most of the conventional filtering methods apply weighted average of normal of neighboring faces, we propose a novel graph filtering method using the smoothness of the graph signal. We first analyze the smoothness of the graph signal using Rayleigh quotient and its correlation to energy concentration in the frequency domain. We then construct a weighted graph where each face of the input mesh is defined as a node. We then design an exponentialshaped filter whose shape is determined by the smoothness of the graph signal, and perform graph filter to the face normal. We finally update the vertex position iteratively using the filtered normal. Experimental results demonstrate that the proposed algorithm reliably remove noises while retaining sharp features with low computational complexity.