4.8 SHREC 2021 Object Retrieval Challenge 97 End-to-end (variational) autoencoders with triplet loss While triplet loss originally only uses an encoder network, it can easily be applied in an autoencoder setting as well, where there is also a decoder network that attempts to reconstruct the encoded representations back to the data space. The reconstruction loss of a regular autoencoder can be used simultaneously with the triplet loss in an end-to-end training procedure. Similarly, we can add a triplet loss to augment VAE-based models, in particular also our own LSBD-VAE. We implement a number of variants combining triplet loss with a (variational) autoencoder-based model. In each of the variants, the triplets used during training are created at object level, i.e. grouping all images of a particular object (from different orientations) together. The triplet creation is done via semi-hard online learning as described by Schroff et al. (2015). The general loss function for our variants looks as follows: L(xa,xp, xn,θxa,θxp,θxn)= λTLLTL(za, zp, zn) +λRE 1 M MX m=1 LRE(x (m) a )+LRE(x (m) n )+LRE(x (m) p ) +λKL 1 M MX m=1 LKL(x (m) a )+LKL(x (m) n )+LKL(x (m) p ) +λLSBD LLSBD(xa,θxa)+LLSBD(xn,θxn)+LLSBD(xp,θxp) . (4.27) Here, eachλ≥0 acts as a weight hyperparameter for the contribution of each loss term. The inputs xa, xp, xn actually represent batches of Mimages showing the same object from different angles, we writexa =(x (1) a , . . . ,x (M) a ). The inputs θxa,θxp,θxn represent the transformation labels for each batch, which are only required if λLSBD̸ = 0. The triplet loss is computed as in Equation 4.26, by first averaging over the encodings of all images of a particular object; we write za := 1 MP M m=1 h(x (m) a ), where h is the encoder. The reconstruction loss LRE andKL loss LKL are computed for each images individually and then averages over the batch. The LSBD loss LLSBD is computed over a full batch as described in Section 4.5.3. For the SHREC 2021 3D object retrieval challenge, we implemented the following five variants:
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