Heat Diffusion Long-Short Term Memory Learning for 3D Shape Analysis

Figure 1: Illustration of the heat diffusion kernel distribution of a 3D shape. (Color figure online)

Figure 2: Learning domain-invariant representations for sketch-based 3D shape retrieval using the CDHD-LSTM architecture. CDHD-LSTM is constructed by connecting a 3-layer neural network to HD-LSTM at the output ends, where the connection is established by sharing identical discriminative random vectors for sketches and 3D shapes that come from the same category.


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 cross-domain 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.

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