4.8 SHREC 2021 Object Retrieval Challenge 93 regularly spaced variables in the orientation space S1 and decoded. In the case of the traditional disentanglement methods we cannot produce a latent variable representing an object’s identity, so there is no clear traversal between objects. In this case, we calculate a linear interpolation between the latent variables corresponding to an image from the start object and from the end object, after which we decode the intermediate latent variables, see Figure 4.12b. Notice that we cannot easily produce an image of an object with an arbitrary orientation, since we do not know the shape of the loop in the latent space representing a single object under different orientations. Figure 4.13 shows the generated images obtained by interpolating between two objects. We only show cc-VAE to represent the traditional models, since that method attained the best DLSBD score. A particularly interesting interpolation is between the wooden object and the orange cat figure. The interpolation of cc-VAE shows how a green object also shows up in between, while LSBD-VAE shows a consistent transition between the objects. A visual explanation of this observation is presented in Figure 4.12b. 4.8 SHREC 2021 Object Retrieval Challenge It is shown that data representations obtained from encoding functions that are equivariant with respect to rotations can be useful for shape retrieval (Esteves et al., 2017). Motivated by this, and to further investigate the applicability of our LSBD-VAE method, we participated in the SHREC 2021 3D Object Retrieval Challenge (Sipiran et al., 2021), which involves a dataset of 3D scanned models from cultural heritage objects. This allows to render multiple 2D images from the same model under different orientations, making it a suitable setting for our LSBD-VAE model to disentangle 2D rotations (modelled with anSO(2) group) from variability due to the object shape, similar to our experiments on COIL-100 and ModelNet40. In this section we briefly describe the challenge, as well as our submitted approaches and their results in this challenge. To accommodate the retrieval task, we incorporate a triplet loss (Schroff et al., 2015) into our LSBD-VAE formulation. Furthermore, we experiment with simpler models that omit some of the LSBD-VAE loss components.
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