SIGGRAPH Asia 2016 - Course notes directions in shape analysis towards functionality

The majority of man-made objects are designed to serve a certain function, and this is often reflected by the geometry of the objects, or the way that they are used or organized in an environment. In recent years, many efforts in shape analysis have developed methods that extract high-level structural and semantic information from geometric shapes and scenes, especially involving man-made objects. One can argue that the ultimate goal of some of these works is to understand the functionality of the objects. Moreover, there have also been works that explicitly model and incorporate functionality into the processing of shapes and scenes. Thus, functionality has been receiving increasingly more attention in shape analysis and geometric modeling, either directly or indirectly, since functionality considerations can aid in applications such as semantic classification, shape editing and synthesis, as well as product design, development, and fabrication. In this course, we discuss recent developments that incorporate functionality aspects into the analysis of 3D shapes and scenes, to provide a summary of the state-of-the-art in this area, including a discussion of key ideas and literature works. More specifically, we first discuss approaches that are precursors in this front, such as structure-aware and data-driven methods that learn relationships between shape parts or objects in scenes. Next, we cover works that more explicitly model the functionality of shapes and scenes, such as agent- and interaction-based methods. The course is structured in the form of talks given by four different speakers, aided by electronic slides that include notes for subsequent consultation

H-CNN: Spatial Hashing Based CNN for 3D Shape Analysis

We present a novel spatial hashing based data structure to facilitate 3D shape analysis using convolutional neural networks (CNNs). Our method builds hierarchical hash tables for an input model under different resolutions that leverage the sparse occupancy of 3D shape boundary. Based on this data structure, we design two efficient GPU algorithms namely hash2col and col2hash so that the CNN operations like convolution and pooling can be efficiently parallelized. The perfect spatial hashing is employed as our spatial hashing scheme, which is not only free of hash collision but also nearly minimal so that our data structure is almost of the same size as the raw input. Compared with existing 3D CNN methods, our data structure significantly reduces the memory footprint during the CNN training. As the input geometry features are more compactly packed, CNN operations also run faster with our data structure. The experiment shows that, under the same network structure, our method yields comparable or better benchmark results compared with the state-of-the-art while it has only one-third memory consumption when under high resolutions (i.e. 256 3)