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      NeRF
      ZERO-SHOT NeRF CLASSIFICATION
      NeRF RETRIEVAL FROM IMAGES
      NeRF GENERATION FROM IMAGES
      NeRF
      NeRF
      NeRF
      "a 3d model of a car"
      NeRF
      "a 3d model of a fighter jet"
      NeRF RETRIEVAL FROM TEXT
      NeRF
      NeRF
      NeRF
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      + +
      +

      + Connecting NeRFs, Images, and Text +
      + + INRV 2024 (CVPR 2024) + +

      +
      + + +
      +
      + +
      Department of Computer Science and Engineering (DISI) +
      University of Bologna, Italy +
      +
      + + + + + +
      +
      +

      + Abstract +

      + Applications of our framework +

      + Neural Radiance Fields (NeRFs) have emerged as a standard framework for representing 3D scenes and objects, introducing a novel data type for information exchange and storage. Concurrently, significant progress has been made in multimodal representation learning for text and image data. This paper explores a novel research direction that aims to connect the NeRF modality with other modalities, similar to established methodologies for images and text. To this end, we propose a simple framework that exploits pre-trained models for NeRF representations alongside multimodal models for text and image processing. Our framework learns a bidirectional mapping between NeRF embeddings and those obtained from corresponding images and text. This mapping unlocks several novel and useful applications, including NeRF zero-shot classification and NeRF retrieval from images or text. +

      +
      +
      + +
      +
      + + +
      +
      +

      + Method +

      + +

      + Our framework, dubbed \({\tt inr2vec}\), is composed of an encoder and a decoder. + The encoder is designed to take as input the weights of an INR and produce a + compact embedding that encodes all the relevant information of the input INR. A + first challenge in designing an encoder for INRs consists in defining how the + encoder should ingest the weights as input, since processing naively all the + weights would require a huge amount of memory. Following standard practice, we + consider INRs composed of several hidden layers, each one with \(H\) nodes, i.e., + the linear transformation between two consecutive layers is parameterized by a matrix + of weights \(\mathbf{W}_{i} \in \mathbb{R}^{H \times H}\) and a vector of biases + \(\mathbf{b}_{i} \in \mathbb{R}^{H \times 1}\). Thus, stacking \(\mathbf{W}_{i}\) + and \({\mathbf{b}_{i}}^T\), the mapping between two consecutive layers can be + represented by a single matrix \(\mathbf{P}_i \in \mathbb{R}^{(H+1) \times H}\). + For an INR composed of \(L + 1\) hidden layers, we consider the \(L\) linear + transformations between them. Hence, stacking all the \(L\) matrices \(\mathbf{P}_i + \in \mathbb{R}^{(H+1) \times H}, i=1,\dots,L\), between the hidden layers we obtain + a single matrix \(\mathbf{P}\in \mathbb{R}^{L(H+1) \times H}\), that we use to + represent the INR in input to \({\tt inr2vec}\) encoder. We discard the input and + output layers in our formulation as they feature different dimensionality and their + use does not change \({\tt inr2vec}\) performance (additional details in the + paper). The \({\tt inr2vec}\) encoder is designed with a simple architecture, consisting + of a series of linear layers with batch norm and ReLU non-linearity followed by + final max pooling. At each stage, the input matrix is transformed by one linear + layer, that applies the same weights to each row of the matrix. The final max + pooling compresses all the rows into a single one, obtaining the desired embedding. +

      + inr2vec encoder + +
      +
      + +

      + In order to guide the \({\tt inr2vec}\) encoder to produce meaningful embeddings, + we first note that we are not interested in encoding the values of the input weights + in the embeddings produced by our framework, but, rather, in storing information + about the 3D shape represented by the input INR. For this reason, we supervise + the decoder to replicate the function approximated by the input INR instead of + directly reproducing its weights, as it would be the case in a standard auto-encoder + formulation. In particular, during training, we adopt an implicit decoder which + takes in input the embeddings produced by the encoder and decodes the input INRs + from them. After the overall framework has been trained end to end, the frozen + encoder can be used to compute embeddings of unseen INRs with a single forward + pass while the implicit decoder can be used, if needed, to reconstruct the discrete + representation given an embedding. +

      + inr2vec framework + +
      +
      + +

      + In the following figure we compare 3D shapes reconstructed from INRs unseen during + training with those reconstructed by the \({\tt inr2vec}\) decoder starting from + the latent codes yielded by the encoder. We visualize point clouds with 8192 points, + meshes reconstructed by marching cubes from a grid with resolution \(128^3\) and + voxels with resolution \(64^3\). We note that, though our embedding is dramatically + more compact than the original INR, the reconstructed shape resembles the ground-truth + with a good level of detail. +

      + inr2vec reconstructions + +
      +
      + +

      + Moreover, we linearly interpolate between the embeddings produced by \({\tt inr2vec}\) + from two input shapes and show the shapes reconstructed from the interpolated + embeddings. The results presented in the next figure highlight that the latent + space learned by \({\tt inr2vec}\) enables smooth interpolations between shapes + represented as INRs. +

      + inr2vec interpolations + +
      +
      + +
      +
      + + +
      +
      +

      + Results +

      + +

      + We first evaluate the feasibility of using \({\tt inr2vec}\) embeddings of INRs + to solve tasks usually tackled by representation learning, and we select 3D + retrieval as a benchmark. Quantitative results, reported in the following table, + show that, while there is an average gap of 1.8 mAP with PointNet++, \({\tt inr2vec}\) + is able to match, and in some cases even surpass, the performance of the other baselines. +

      + retrieval + +
      +
      + +

      + We then address the problem of classifying point clouds, meshes and voxel grids. + Despite the different nature of the discrete representations taken into account, + \({\tt inr2vec}\) allows us to perform shape classification on INRs embeddings by + the very same downstream network architecture, i.e., a simple fully connected + classifier consisting of three layers with 1024, 512 and 128 features. The results + reported in the next table show that \({\tt inr2vec}\) embeddings deliver + classification accuracy close to the specialized baselines across all the + considered datasets, regardless of the original discrete representation of the + shapes in each dataset. Remarkably, our framework allows us to apply the same + simple classification architecture on all the considered input modalities, in stark + contrast with all the baselines that are highly specialized for each modality, + exploit inductive biases specific to each such modality and cannot be deployed on + representations different from those they were designed for. +

      + classification + +
      +
      + +

      + While the tasks of retrieval and classification concern the possibility of using + \({\tt inr2vec}\) embeddings as a compact proxy for the global information of the + input shapes, with the task of point cloud part segmentation we aim at investigating + whether \({\tt inr2vec}\) embeddings can be used also to assess upon local properties + of shapes. The part segmentation task consists in predicting a semantic label for + each point of a given cloud. We tackle this problem by training a decoder similar + to that used to train our framework (see left part of the following figure). Such + decoder is fed with the \({\tt inr2vec}\) embedding of the INR representing the + input cloud, concatenated with the coordinate of a 3D query, and it is trained to + predict the label of the query point. Qualitative results reported in the right + part of the figure show the possibility of performing also a local discriminative + task as challenging as part segmentation based on the task-agnostic embeddings + produced by \({\tt inr2vec}\). +

      + part segmentation + +
      +
      + +

      + We also address the task of shape generation in an adversarial setting to investigate + whether the compact representations produced by our framework can be adopted also + as medium for the output of deep learning pipelines. For this purpose, as depicted + in the next figure, we train a Latent-GAN to generate embeddings indistinguishable + from those produced by \({\tt inr2vec}\) starting from random noise. The generated + embeddings can then be decoded into discrete representations with the implicit + decoder exploited during \({\tt inr2vec}\) training. Since our framework is agnostic + w.r.t. the original discrete representation of shapes used to fit INRs, we can + train Latent-GANs with embeddings representing point clouds or meshes based on the + same identical protocol and architecture (two simple fully connected networks as + generator and discriminator). In the following figure, we show some samples + generated with the described procedure, comparing them with SP-GAN for what concerns + point clouds and Occupancy Networks (VAE formulation) for meshes. The shapes generated + with our Latent-GAN trained only on \({\tt inr2vec}\) embeddings seem comparable + to those produced by the considered baselines, in terms of both diversity and richness of details. +

      + shape generation + +
      +
      + +

      + Finally we consider the possibility of learning a mapping between two distinct + latent spaces produced by our framework for two separate datasets of INRs, based + on a \(\textit{transfer}\) function designed to operate on \({\tt inr2vec}\) + embeddings as both input and output data. Such transfer function can be realized + by a simple fully connected network that maps the input embedding into the output + one and is trained by a standard MSE loss. Here, we apply this idea to two tasks. + Firstly, we address point cloud completion by learning a mapping from \({\tt inr2vec}\) + embeddings of INRs that represent incomplete clouds to embeddings associated with + complete clouds. Then, we tackle the task of surface reconstruction on ShapeNet cars, + training the transfer function to map \({\tt inr2vec}\) embeddings representing + point clouds into embeddings that can be decoded into meshes. As we can appreciate + from the samples reported in the figure, the transfer function can learn an effective + mapping between \({\tt inr2vec}\) latent spaces. Indeed, by processing exclusively + INRs embedding, we can obtain output shapes that are highly compatible with the + input ones whilst preserving the distinctive details, like the pointy wing of the + airplane or the flap of the first car. +

      + mapping + +
      +
      + +
      +
      + + +
      +
      +

      + Cite us +

      +
      +
      +@inproceedings{deluigi2023inr2vec,
      +    title = {Deep Learning on Implicit Neural Representations of Shapes},
      +    author = {De Luigi, Luca 
      +              and Cardace, Adriano 
      +              and Spezialetti, Riccardo 
      +              and Zama Ramirez, Pierluigi 
      +              and Salti, Samuele
      +              and Di Stefano, Luigi},
      +    booktitle = {International Conference on Learning Representations (ICLR)},
      +    year = {2023}
      +}
      +                    
      +
      +
      +
      + +
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