Heat Diffusion Long-Short Term Memory Learning for 3D Shape Analysis
The heat kernel is a fundamental solution in mathematical physics to distribution measurement of heat energy within a fixed region over time, and due to its unique property of being invariant to isometric transformations, the heat kernel has been an effec
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Abstract. The heat kernel is a fundamental solution in mathematical physics to distribution measurement of heat energy within a fixed region over time, and due to its unique property of being invariant to isometric transformations, the heat kernel has been an effective feature descriptor for spectral shape analysis. The majority of prior heat kernel-based strategies of building 3D shape representations fail to investigate the temporal dynamics of heat flows on 3D shape surfaces over time. In this work, we address the temporal dynamics of heat flows on 3D shapes using the long-short term memory (LSTM). We guide 3D shape descriptors toward discriminative representations by feeding heat distributions throughout time as inputs to units of heat diffusion LSTM (HD-LSTM) blocks with a supervised learning structure. We further extend HD-LSTM to a crossdomain structure (CDHD-LSTM) for learning domain-invariant representations of multi-view data. We evaluate the effectiveness of both HD-LSTM and CDHD-LSTM on 3D shape retrieval and sketch-based 3D shape retrieval tasks respectively. Experimental results on McGill dataset and SHREC 2014 dataset suggest that both methods can achieve state-of-the-art performance. Keywords: 3D shape retrieval · Recurrent neural network · Long-short term memory · Heat kernel signature
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Introduction
Researches on 3D-meshed surface models have been receiving exponentially increasing attentions with the sustainability growing expectations on virtual reality, which is believed to be the revolutionary technology that can completely reshape our lives. In fact, virtual reality isn’t exclusive for gaming anymore, it has already sprawled into many areas. For example, virtual reality movies are becoming the mainstream with Hollywood directors. Since the virtual world is established in a 3D space, researchers have been paying efforts to the development of multiple areas of 3D computer vision, which covers 3D correspondence, 3D shape retrieval, 3D segmentation, etc. The performance of these 3D analysis systems heavily rely on the quality of 3D shape representations, thus how to c Springer International Publishing AG 2016 B. Leibe et al. (Eds.): ECCV 2016, Part VII, LNCS 9911, pp. 305–321, 2016. DOI: 10.1007/978-3-319-46478-7 19
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effectively describe a 3D shape in machine language is of premier importance for 3D shape analysis. Popular strategies of building 3D shape representations mainly include the projection-based approaches and the heat kernel-based approach. Intuitively, the projection-based approaches aim to transform the 3D shape representation problem into a well developed-image representation problem by projecting a 3D shape from multiple viewpoints and consequently obtaining multiple projection images, where either handcrafted features (e.g., scale invariant feature transform (SIFT) [25]) or deep learning features (e.g., convolutional neural networks (CNN) [22]) are used to represent these projection images. On the other hand, the heat kernel-based approach estimates geometrical rel
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