Diffusion-on-Manifold Aggregation of Local Features for Shape-based 3D Model Retrieval

Aggregating a set of local features has become one of the most common approaches for representing a multi-media data such as 2D image and 3D model. The success of Bag-of-Features (BF) aggregation [2] prompted several extensions to BF, that are, VLAD [12], Fisher Vector (FV) coding [22] and Super Vector (SV) coding [34]. They all learn small number of codewords, or representative local features, by clustering a set of large number of local features. The set of local features extracted from a media data (e.g., an image) is encoded by considering distribution of features around the codewords; BF uses frequency, VLAD and FV uses displacement vector, and SV uses a combination of both. In doing so, these encoding algorithms assume linearity of feature space about a codeword. Consequently, even if the set of features form a non-linear manifold, its non-linearity would be ignored, potentially degrading quality of aggregated features. In this paper, we propose a novel feature aggregation algorithm called Diffusion-on-Manifold (DM) that tries to take into account, via diffusion distance, structure of non-linear manifold formed by the set of local features. In view of 3D shape retrieval, we also propose a local 3D shape feature defined for oriented point set. Experiments using shape-based 3D model retrieval scenario show that the DM aggregation results in better retrieval accuracy than the existing aggregation algorithms we've compared against, that are, VLAD, FV, and SV, etc..