Research On Geometric Shape Representation For Deep Geometric Learning

In the 3D geometry research area,the geometric representation is an important research topic.For 3D geometric objects,the 3D representations suitable for different tasks may be different;conversely,each task also needs its appropriate geometric representation.First,for a single object,there are sever ways to represent its 3D shape,such as meshes,point clouds,voxels,multi-view images,depth images,etc.Second,for multiple 3D objects with potential correspondences,representing the deformations between them for reasonable registration is an important issue,which is critical for many downstream tasks,such as tracking,reconstruction,etc.For the above two cases of a single object and multi-object registration,this paper proposes a series of 3D geometric representations suitable for deep neural networks,mainly including the following aspects:·Neural field based local implicit representation of point cloud;·Radial basis function based local shape representation;·Non-rigid deformation representation based on point-wise weighted combination of rigid transformations;·Differentiable deformation graph based non-rigid deformation represention.In addition,this paper also conducts experiments on corresponding tasks to explore the superiority of the proposed geometric representations above.Neural field based local implicit representation of point cloud:Traditional point cloud only represents each point as a position or a local plane in the 3D space.In this paper,we propose a local implicit point cloud representation,namely Neural Points,.where each point represents a local continuous geometric shape via neural fields.Neural Points is trained with surfaces containing rich geometric details,such that the trained model has enough expression ability for various shapes.Specifically,we extract deep local features on the points and construct neural fields through the local isomorphism between the 2D parametric domain and the 3D local patch.In the final,local neural fields are integrated together to form the global surface.Experimental results show that Neural Points has powerful representation ability and demonstrate excellent robustness and generalization ability.In this manner,we can resample point cloud with arbitrary resolutions,and it outperforms state-of-the-art point cloud upsampling methods by a large margin.Radial basis function based local shape representation:The traditional 3D geometric representations in the deep learning pipeline face some challenges for complex 3D models,in which non-regularity and high complexity are essential difficulties.This paper focuses on the detail recovery task of 3D models so that geometric details that are not well represented in low-resolution models can be recovered and well represented in the result high-quality models.To this end,this paper proposes a local shape representation based on radial basis functions and designs a deep network to solve this problem and overcome the above challenges.We apply the implicit representation and the divide-and-conquer strategies to overcome the non-regularity and high complexity,respectively.To train the network,we constructed a dataset consisting of real and synthetic scan models,including high/low-quality pairs.Experimental results show that our proposed representation and network are suitable for general models and outperform previous methods in recovering geometric details.Non-rigid deformation representation based on point-wise weighted combination of rigid transformations:Learning non-rigid registration in an end-to-end manner is challenging due to the inherent high degrees of freedom and the lack of labeled training data.In this paper,we resolve these two challenges simultaneously.First,we propose to represent the non-rigid transformation with a point-wise combination of several rigid transformations.This representation not only makes the solution space well-constrained but also enables our method to be solved iteratively with a recurrent framework,which greatly reduces the difficulty of learning.Second,we introduce a differentiable loss function that measures the 3D shape similarity on the projected multiview 2D depth images so that our full framework can be trained end-to-end without ground truth supervision.Extensive experiments on several different datasets demonstrate that our proposed method outperforms the previous state-of-the-art by a large margin.Differentiable deformation graph based non-rigid deformation represention:The traditional pipeline for non-rigid registration is to iteratively update the correspondence and alignment such that the transformed source surface aligns well with the target surface.Among the pipeline,the correspondence construction and iterative manner are key to the results,while existing strategies might result in local optima.In this paper,we adopt the widely used deformation graph based representation,while replacing some key modules with neural learning based strategies.Specifically,we design a neural network to predict the correspondence and its reliability confidence rather than the strategies like nearest neighbor search and pair rejection.Besides,we adopt the GRU-based recurrent network for iterative refinement,which is more robust than the traditional strategy.The model is trained in a self-supervised manner,and thus can be used for arbitrary datasets without ground-truth.Extensive experiments demonstrate that our proposed method outperforms the state-of-the-art methods by a large margin.To sum up,we propose four different geometric representations,all of which are suitable for deep geometric learning,and have achieved better results than previous methods on the related tasks.Specific related tasks include:point cloud upsampling,geometric detail recovery of 3D models,and non-rigid registration of 3D surfaces.