Deep learning has been used as a powerful tool for various tasks in computer vision, such as image segmentation, object recognition and data generation. A key part of end-to-end training is designing the appropriate encoder to extract specific features from the input data. However, few encoders maintain the topological properties of data, such as connection structures and global contours. In this paper, we introduce a Voronoi Diagram encoder based on convex set distance (CSVD) and apply it in edge encoding. The boundaries of Voronoi cells is related to detected edges of structures and contours. The CSVD model improves contour extraction in CNN and structure generation in GAN. We also show the experimental results and demonstrate that the proposed model has great potentiality in different visual problems where topology information should be involved.
3D shape models are becoming widely available and easier to capture, making available 3D information crucial for progress in object classification. Current state-of-theart methods rely on CNNs to address this problem. Recently, we witness two types of CNNs being developed: CNNs based upon volumetric representations versus CNNs based upon multi-view representations. Empirical results from these two types of CNNs exhibit a large gap, indicating that existing volumetric CNN architectures and approaches are unable to fully exploit the power of 3D representations. In this paper, we aim to improve both volumetric CNNs and multi-view CNNs according to extensive analysis of existing approaches. To this end, we introduce two distinct network architectures of volumetric CNNs. In addition, we examine multi-view CNNs, where we introduce multiresolution filtering in 3D. Overall, we are able to outperform current state-of-the-art methods for both volumetric CNNs and multi-view CNNs. We provide extensive experiments designed to evaluate underlying design choices, thus providing a better understanding of the space of methods available for object classification on 3D data. Contour detection serves as the basis of a variety of computer vision tasks such as image segmentation and object recognition. The mainstream works to address this problem focus on designing engineered gradient features. In this work, we show that contour detection accuracy can be improved by instead making the use of the deep features learned from convolutional neural networks (CNNs). While rather than using the networks as a blackbox feature extractor, we customize the training strategy by partitioning contour (positive) data into subclasses and fitting each subclass by different model parameters. A new loss function, named positive-sharing loss, in which each subclass shares the loss for the whole positive class, is proposed to learn the parameters. Compared to the sofmax loss function, the proposed one, introduces an extra regularizer to emphasizes the losses for the positive and negative classes, which facilitates to explore more discriminative features. Our experimental results demonstrate that learned deep features can achieve top performance on Berkeley Segmentation Dataset and Benchmark (BSDS500) and obtain competitive cross dataset generalization result on the NYUD dataset. We present OctNet, a representation for deep learning with sparse 3D data. In contrast to existing models, our representation enables 3D convolutional networks which are both deep and high resolution. Towards this goal, we exploit the sparsity in the input data to hierarchically partition the space using a set of unbalanced octrees where each leaf node stores a pooled feature representation. This allows to focus memory allocation and computation to the relevant dense regions and enables deeper networks without compromising resolution. We demonstrate the utility of our OctNet representation by analyzing the impact of resolution on several 3D tasks including 3D object classification, orientation estimation and point cloud labeling. This paper proposes a computationally efficient approach to detecting objects natively in 3D point clouds using convolutional neural networks (CNNs). In particular, this is achieved by leveraging a feature-centric voting scheme to implement novel convolutional layers which explicitly exploit the sparsity encountered in the input. To this end, we examine the trade-off between accuracy and speed for different architectures and additionally propose to use an L 1 penalty on the filter activations to further encourage sparsity in the intermediate representations. To the best of our knowledge, this is the first work to propose sparse convolutional layers and L 1 regularisation for efficient large-scale processing of 3D data. We demonstrate the efficacy of our approach on the KITTI object detection benchmark and show that VoteSDeep models with as few as three layers outperform the previous state of the art in both laser and laser-vision based approaches by margins of up to 40 while remaining highly competitive in terms of processing time. 