text: The design, analysis and application of a volumetric convolutional neural network (VCNN) are studied in this work. Although many CNNs have been proposed in the literature, their design is empirical. In the design of the VCNN, we propose a feed-forward K-means clustering algorithm to determine the filter number and size at each convolutional layer systematically. For the analysis of the VCNN, the cause of confusing classes in the output of the VCNN is explained by analyzing the relationship between the filter weights (also known as anchor vectors) from the last fully-connected layer to the output. Furthermore, a hierarchical clustering method followed by a random forest classification method is proposed to boost the classification performance among confusing classes. For the application of the VCNN, we examine the 3D shape classification problem and conduct experiments on a popular ModelNet40 dataset. The proposed VCNN offers the state-of-the-art performance among all volume-based CNN methods.
  @cite_18: 3D shape models are becoming widely available and easier to capture, making available 3D information crucial for progress in object classification. Current state-of-the-art 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 multi-resolution 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.
  @cite_21: 3D shape is a crucial but heavily underutilized cue in today's computer vision systems, mostly due to the lack of a good generic shape representation. With the recent availability of inexpensive 2.5D depth sensors (e.g. Microsoft Kinect), it is becoming increasingly important to have a powerful 3D shape representation in the loop. Apart from category recognition, recovering full 3D shapes from view-based 2.5D depth maps is also a critical part of visual understanding. To this end, we propose to represent a geometric 3D shape as a probability distribution of binary variables on a 3D voxel grid, using a Convolutional Deep Belief Network. Our model, 3D ShapeNets, learns the distribution of complex 3D shapes across different object categories and arbitrary poses from raw CAD data, and discovers hierarchical compositional part representation automatically. It naturally supports joint object recognition and shape completion from 2.5D depth maps, and it enables active object recognition through view planning. To train our 3D deep learning model, we construct ModelNet - a large-scale 3D CAD model dataset. Extensive experiments show that our 3D deep representation enables significant performance improvement over the-state-of-the-arts in a variety of tasks.
  @cite_26: Robust object recognition is a crucial skill for robots operating autonomously in real world environments. Range sensors such as LiDAR and RGBD cameras are increasingly found in modern robotic systems, providing a rich source of 3D information that can aid in this task. However, many current systems do not fully utilize this information and have trouble efficiently dealing with large amounts of point cloud data. In this paper, we propose VoxNet, an architecture to tackle this problem by integrating a volumetric Occupancy Grid representation with a supervised 3D Convolutional Neural Network (3D CNN). We evaluate our approach on publicly available benchmarks using LiDAR, RGBD, and CAD data. VoxNet achieves accuracy beyond the state of the art while labeling hundreds of instances per second.
summary: The volume-based approach voxelizes a 3D mesh model for a 3D representation. Several CNN networks have been proposed to classify the 3D shapes directly. Examples include the 3D ShapeNet @cite_21 , the VoxNet @cite_26 and the SubVolume supervision method @cite_18 . Although the network architectures of volume-based methods are typically shallow (e.g., the VoxNet model consists of two convolutional layers and one fully connected layer), they strike a balance between the number of available training samples and the network model complexity. Volume-based methods have two drawbacks. First, to control computational complexity, the resolution of a 3D voxel model is much lower than that of its corresponding 2D view-based representation. As a result, high frequency components of the original 3D mesh are sacrificed. Second, there are few pretrained CNN models on 3D data, volume-based networks have to be trained from scratch. Although a volumetric representation preserves the 3D structural information of an object, the performance of classifying 3D mesh models directly is still lower than that of classifying the corresponding view-based 2D models.