Paper Reading AI Learner

On the Nonlinear Statistics of Optical Flow

2018-11-09 22:50:29
Henry Adams, Johnathan Bush, Brittany Carr, Lara Kassab, Joshua Mirth
arXiv_CV
   
Abstract

In "A naturalistic open source movie for optical flow evaluation," Butler et al. create a database of ground-truth optical flow from the computer-generated video Sintel. We study the high-contrast $3\times 3$ patches from this video, and provide evidence that this dataset is well-modeled by a torus (a nonlinear 2-dimensional manifold). Our main tools are persistent homology and zigzag persistence, which are popular techniques from the field of computational topology. We show that the optical flow torus model is naturally equipped with the structure of a fiber bundle, which is furthermore related to the statistics of range images.

Abstract (translated)

URL

https://arxiv.org/abs/1812.00875

PDF

https://arxiv.org/pdf/1812.00875.pdf

Tags
3D Action Action_Localization Action_Recognition Activity Adversarial Agent Attention Autonomous Bert Boundary_Detection Caption Chat Classification CNN Compressive_Sensing Contour Contrastive_Learning Deep_Learning Denoising Detection Dialog Diffusion Drone Dynamic_Memory_Network Edge_Detection Embedding Embodied Emotion Enhancement Face Face_Detection Face_Recognition Facial_Landmark Few-Shot Gait_Recognition GAN Gaze_Estimation Gesture Gradient_Descent Handwriting Human_Parsing Image_Caption Image_Classification Image_Compression Image_Enhancement Image_Generation Image_Matting Image_Retrieval Inference Inpainting Intelligent_Chip Knowledge Knowledge_Graph Language_Model Matching Medical Memory_Networks Multi_Modal Multi_Task NAS NMT Object_Detection Object_Tracking OCR Ontology Optical_Character Optical_Flow Optimization Person_Re-identification Point_Cloud Portrait_Generation Pose Pose_Estimation Prediction QA Quantitative Quantitative_Finance Quantization Re-identification Recognition Recommendation Reconstruction Regularization Reinforcement_Learning Relation Relation_Extraction Represenation Represenation_Learning Restoration Review RNN Salient Scene_Classification Scene_Generation Scene_Parsing Scene_Text Segmentation Self-Supervised Semantic_Instance_Segmentation Semantic_Segmentation Semi_Global Semi_Supervised Sence_graph Sentiment Sentiment_Classification Sketch SLAM Sparse Speech Speech_Recognition Style_Transfer Summarization Super_Resolution Surveillance Survey Text_Classification Text_Generation Tracking Transfer_Learning Transformer Unsupervised Video_Caption Video_Classification Video_Indexing Video_Prediction Video_Retrieval Visual_Relation VQA Weakly_Supervised Zero-Shot