# A Structured Dictionary Perspective on Implicit Neural Representations

@article{Yce2021ASD, title={A Structured Dictionary Perspective on Implicit Neural Representations}, author={Gizem Y{\"u}ce and Guillermo Ortiz-Jim{\'e}nez and Beril Besbinar and Pascal Frossard}, journal={2022 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR)}, year={2021}, pages={19206-19216} }

Implicit neural representations (INRs) have recently emerged as a promising alternative to classical discretized representations of signals. Nevertheless, despite their practical success, we still do not understand how INRs represent signals. We propose a novel unified perspective to theoretically analyse INRs. Leveraging results from harmonic analysis and deep learning theory, we show that most INR families are analogous to structured signal dictionaries whose atoms are integer harmonics of…

## 16 Citations

### Deep Learning on Implicit Neural Representations of Shapes

- Computer ScienceArXiv
- 2023

It is verified that inr2vec can embed effectively the 3D shapes represented by the input INRs and shown how the produced embeddings can be fed into deep learning pipelines to solve several tasks by processing exclusively INRs.

### DINER: Disorder-Invariant Implicit Neural Representation

- Computer ScienceArXiv
- 2022

It is found that a frequency-related problem could be largely solved by re-arranging the coordinates of the input signal, for which the disorder-invariant implicit neural representation (DINER) is proposed by augmenting a hash-table to a traditional INR backbone.

### Frequency-Modulated Point Cloud Rendering with Easy Editing

- Computer ScienceArXiv
- 2023

An effective point cloud rendering pipeline for novel view synthesis, which enables high fidelity local detail reconstruction, real-time rendering and user-friendly editing and high-fidelity interactive editing based on point cloud manipulation is developed.

### SplineCam: Exact Visualization and Characterization of Deep Network Geometry and Decision Boundaries

- Computer ScienceArXiv
- 2023

This paper develops the first provably exact method for computing the geometry of a DN's mapping - including its decision boundary - over a specified region of the data space by leveraging the theory of Continuous Piece-Wise Linear spline DNs.

### WIRE: Wavelet Implicit Neural Representations

- Computer ScienceArXiv
- 2023

Wavelet Implicit neural REpresentation (WIRE) uses a continuous complex Gabor wavelet activation function that is well-known to be optimally concentrated in space-frequency and to have excellent biases for representing images.

### Deformable Surface Reconstruction via Riemannian Metric Preservation

- MathematicsArXiv
- 2022

Estimating the pose of an object from a monocular image is an inverse problem fundamental in computer vision. The ill-posed nature of this problem requires incorporating deformation priors to solve…

### StegaNeRF: Embedding Invisible Information within Neural Radiance Fields

- Computer ScienceArXiv
- 2022

StegaNeRF is an initial exploration into the novel problem of instilling customizable, imperceptible, and recoverable information to NeRF renderings, with minimal impact to rendered images.

### TITAN: Bringing The Deep Image Prior to Implicit Representations

- Computer Science
- 2022

This paper proposes to address and improve INRs’ interpolation capabilities by explicitly inte-grating image prior information into the INR architecture via deep decoder, a speciﬁc implementation of the deep image prior (DIP).

### Continuous conditional video synthesis by neural processes

- Computer ScienceArXiv
- 2022

It is shown that conditional video synthesis can be formulated as a neural process, which maps input spatio-temporal coordinates to target pixel values given context spatio’s temporal coordinates and pixels values, and is able to interpolate or predict with an arbitrary high frame rate.

### Sobolev Training for Implicit Neural Representations with Approximated Image Derivatives

- Computer ScienceECCV
- 2022

This paper proposes a training paradigm for INRs whose target output is image pixels, to encode image derivatives in addition to image values in the neural network, and uses finite differences to approximate image derivatives.

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