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.
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.
@cite_18 @cite_21 @cite_26
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While deep convolutional neural networks (CNNs) have achieved remarkable success in 2D medical image segmentation, it is still a difficult task for CNNs to segment important organs or structures from 3D medical images owing to several mutually affected challenges, including the complicated anatomical environments in volumetric images, optimization difficulties of 3D networks and inadequacy of training samples. In this paper, we present a novel and efficient 3D fully convolutional network equipped with a 3D deep supervision mechanism to comprehensively address these challenges; we call it 3D DSN. Our proposed 3D DSN is capable of conducting volume-to-volume learning and inference, which can eliminate redundant computations and alleviate the risk of over-fitting on limited training data. More importantly, the 3D deep supervision mechanism can effectively cope with the optimization problem of gradients vanishing or exploding when training a 3D deep model, accelerating the convergence speed and simultaneously improving the discrimination capability. Such a mechanism is developed by deriving an objective function that directly guides the training of both lower and upper layers in the network, so that the adverse effects of unstable gradient changes can be counteracted during the training procedure. We also employ a fully connected conditional random field model as a post-processing step to refine the segmentation results. We have extensively validated the proposed 3D DSN on two typical yet challenging volumetric medical image segmentation tasks: (i) liver segmentation from 3D CT scans and (ii) whole heart and great vessels segmentation from 3D MR images, by participating two grand challenges held in conjunction with MICCAI. We have achieved competitive segmentation results to state-of-the-art approaches in both challenges with a much faster speed, corroborating the effectiveness of our proposed 3D DSN. Recent developments in techniques for modeling, digitizing and visualizing 3D shapes has led to an explosion in the number of available 3D models on the Internet and in domain-specific databases. This has led to the development of 3D shape retrieval systems that, given a query object, retrieve similar 3D objects. For visualization, 3D shapes are often represented as a surface, in particular polygonal meshes, for example in VRML format. Often these models contain holes, intersecting polygons, are not manifold, and do not enclose a volume unambiguously. On the contrary, 3D volume models, such as solid models produced by CAD systems, or voxels models, enclose a volume properly. This paper surveys the literature on methods for content based 3D retrieval, taking into account the applicability to surface models as well as to volume models. The methods are evaluated with respect to several requirements of content based 3D shape retrieval, such as: (1) shape representation requirements, (2) properties of dissimilarity measures, (3) efficiency, (4) discrimination abilities, (5) ability to perform partial matching, (6) robustness, and (7) necessity of pose normalization. Finally, the advantages and limitations of the several approaches in content based 3D shape retrieval are discussed. For modeling the 3D world behind 2D images, which 3D representation is most appropriate? A polygon mesh is a promising candidate for its compactness and geometric properties. However, it is not straightforward to model a polygon mesh from 2D images using neural networks because the conversion from a mesh to an image, or rendering, involves a discrete operation called rasterization, which prevents back-propagation. Therefore, in this work, we propose an approximate gradient for rasterization that enables the integration of rendering into neural networks. Using this renderer, we perform single-image 3D mesh reconstruction with silhouette image supervision and our system outperforms the existing voxel-based approach. Additionally, we perform gradient-based 3D mesh editing operations, such as 2D-to-3D style transfer and 3D DeepDream, with 2D supervision for the first time. These applications demonstrate the potential of the integration of a mesh renderer into neural networks and the effectiveness of our proposed renderer. A longstanding question in computer vision concerns the representation of 3D shapes for recognition: should 3D shapes be represented with descriptors operating on their native 3D formats, such as voxel grid or polygon mesh, or can they be effectively represented with view-based descriptors? We address this question in the context of learning to recognize 3D shapes from a collection of their rendered views on 2D images. We first present a standard CNN architecture trained to recognize the shapes' rendered views independently of each other, and show that a 3D shape can be recognized even from a single view at an accuracy far higher than using state-of-the-art 3D shape descriptors. Recognition rates further increase when multiple views of the shapes are provided. In addition, we present a novel CNN architecture that combines information from multiple views of a 3D shape into a single and compact shape descriptor offering even better recognition performance. The same architecture can be applied to accurately recognize human hand-drawn sketches of shapes. We conclude that a collection of 2D views can be highly informative for 3D shape recognition and is amenable to emerging CNN architectures and their derivatives.