# Non-linear Motion Estimation for Video Frame Interpolation using Space-time Convolutions

arXiv: https://arxiv.org/abs/2201.11407 · HTML: https://mlsanity.com/paper/2201.11407/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 40 of its 55 references that are in the map.
- First posted on arXiv 27 Jan 2022.

## Builds on (most cited first, 30 of 40)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [Perceptual Losses for Real-Time Style Transfer and Super-Resolution](https://mlsanity.com/paper/1603.08155/) (2016)
- [3D U-Net: Learning Dense Volumetric Segmentation from Sparse Annotation](https://mlsanity.com/paper/1606.06650/) (2016)
- [Spatial Transformer Networks](https://mlsanity.com/paper/1506.02025/) (2015)
- [A Closer Look at Spatiotemporal Convolutions for Action Recognition](https://mlsanity.com/paper/1711.11248/) (2017)
- [PWC-Net: CNNs for Optical Flow Using Pyramid, Warping, and Cost Volume](https://mlsanity.com/paper/1709.02371/) (2017)
- [The 2017 DAVIS Challenge on Video Object Segmentation](https://mlsanity.com/paper/1704.00675/) (2017)
- [FlowNet 2.0: Evolution of Optical Flow Estimation with Deep Networks](https://mlsanity.com/paper/1612.01925/) (2016)
- [Deep Multi-scale Convolutional Neural Network for Dynamic Scene Deblurring](https://mlsanity.com/paper/1612.02177/) (2016)
- [Video Enhancement with Task-Oriented Flow](https://mlsanity.com/paper/1711.09078/) (2017)
- [Can Spatiotemporal 3D CNNs Retrace the History of 2D CNNs and ImageNet?](https://mlsanity.com/paper/1711.09577/) (2017)
- [Optical Flow Estimation using a Spatial Pyramid Network](https://mlsanity.com/paper/1611.00850/) (2016)
- [Super SloMo: High Quality Estimation of Multiple Intermediate Frames for Video Interpolation](https://mlsanity.com/paper/1712.00080/) (2017)
- [Softmax Splatting for Video Frame Interpolation](https://mlsanity.com/paper/2003.05534/) (2020)
- [Depth-Aware Video Frame Interpolation](https://mlsanity.com/paper/1904.00830/) (2019)
- [Video Frame Interpolation via Adaptive Separable Convolution](https://mlsanity.com/paper/1708.01692/) (2017)
- [Video Frame Synthesis using Deep Voxel Flow](https://mlsanity.com/paper/1702.02463/) (2017)
- [UnFlow: Unsupervised Learning of Optical Flow with a Bidirectional Census Loss](https://mlsanity.com/paper/1711.07837/) (2017)
- [DeepStereo: Learning to Predict New Views from the World's Imagery](https://mlsanity.com/paper/1506.06825/) (2015)
- [Learning Spatio-Temporal Features with 3D Residual Networks for Action Recognition](https://mlsanity.com/paper/1708.07632/) (2017)
- [Video Frame Interpolation via Adaptive Convolution](https://mlsanity.com/paper/1703.07514/) (2017)
- [Context-aware Synthesis for Video Frame Interpolation](https://mlsanity.com/paper/1803.10967/) (2018)
- [Quadratic video interpolation](https://mlsanity.com/paper/1911.00627/) (2019)
- [Video Compression through Image Interpolation](https://mlsanity.com/paper/1804.06919/) (2018)
- [AdaCoF: Adaptive Collaboration of Flows for Video Frame Interpolation](https://mlsanity.com/paper/1907.10244/) (2019)
- [Iterative Residual Refinement for Joint Optical Flow and Occlusion Estimation](https://mlsanity.com/paper/1904.05290/) (2019)
- [BMBC:Bilateral Motion Estimation with Bilateral Cost Volume for Video Interpolation](https://mlsanity.com/paper/2007.12622/) (2020)
- [MEMC-Net: Motion Estimation and Motion Compensation Driven Neural Network for Video Interpolation and Enhancement](https://mlsanity.com/paper/1810.08768/) (2018)

## Built on by (most cited first, 3 of 3)

- [NeuralPCI: Spatio-temporal Neural Field for 3D Point Cloud Multi-frame Non-linear Interpolation](https://mlsanity.com/paper/2303.15126/) (2023)
- [JNMR: Joint Non-linear Motion Regression for Video Frame Interpolation](https://mlsanity.com/paper/2206.04231/) (2022)
- [TLB-VFI: Temporal-Aware Latent Brownian Bridge Diffusion for Video Frame Interpolation](https://mlsanity.com/paper/2507.04984/) (2025)

## Abstract (arXiv)

Video frame interpolation aims to synthesize one or multiple frames between two consecutive frames in a video. It has a wide range of applications including slow-motion video generation, frame-rate up-scaling and developing video codecs. Some older works tackled this problem by assuming per-pixel linear motion between video frames. However, objects often follow a non-linear motion pattern in the real domain and some recent methods attempt to model per-pixel motion by non-linear models (e.g., quadratic). A quadratic model can also be inaccurate, especially in the case of motion discontinuities over time (i.e. sudden jerks) and occlusions, where some of the flow information may be invalid or inaccurate. In our paper, we propose to approximate the per-pixel motion using a space-time convolution network that is able to adaptively select the motion model to be used. Specifically, we are able to softly switch between a linear and a quadratic model. Towards this end, we use an end-to-end 3D CNN encoder-decoder architecture over bidirectional optical flows and occlusion maps to estimate the non-linear motion model of each pixel. Further, a motion refinement module is employed to refine the non-linear motion and the interpolated frames are estimated by a simple warping of the neighboring frames with the estimated per-pixel motion. Through a set of comprehensive experiments, we validate the effectiveness of our model and show that our method outperforms state-of-the-art algorithms on four datasets (Vimeo, DAVIS, HD and GoPro).