Determining Optical Flow

By Berthold K. P. Horn, B. G. Schunck. 1981

Optical flow cannot be computed locally, since only one independent measurement is available from the image sequence at a point, while the flow velocity has two components. A second constraint is needed. A method for finding the optical flow pattern is presented which assumes that the apparent velocity of the brightness pattern varies smoothly almost everywhere in the image. An iterative implementation is shown which successfully computes the optical flow for a number of synthetic image sequences. The algorithm is robust in that it can handle image sequences that are quantized rather coarsely in space and time. It is also insensitive to quantization of brightness levels and additive noise. Examples are included where the assumption of smoothness is violated at singular points or along lines in the image.

Subfields: Computer Vision and Pattern Recognition

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Citations in the corpus

Perceiver IO: A General Architecture for Structured Inputs & Outputs (2021, background): “Optical flow is a decades-old open problem in computer vision [49, 33].”
FlowNet: Learning Optical Flow with Convolutional Networks (2015, methodology): “Variational approaches have dominated optical flow estimation since the work of Horn and Schunck [19].”
Playing for Data: Ground Truth from Computer Games (2016, background): “The use of synthetic data has been particularly significant in evaluating optical flow estimation due to the difficulty of obtaining accurate ground-truth flow measurements for real-world scenes [6, 7, 18, 32].”
Unsupervised Learning of Edges (2015, background): “Optical Flow: The estimation of optical flow is a classic problem in computer vision [18, 24].”
SIFT Flow: Dense Correspondence across Scenes and Its Applications (2011, methodology): “In stereo [26] and optical flow [ 29 ], [38], the brightness constancy assumption was often made for building the correspondence between two images.”
Temporal Segment Networks for Action Recognition in Videos (2017, background): “Recalling the seminal work on dense optical flow in [63], the partial derivatives of pixel intensities with respect to time play critical roles in computing optical flow.”
Unsupervised CNN for Single View Depth Estimation: Geometry to the Rescue (2016, methodology): “Our loss function as described in (3) is similar to the standard Horn and Schunck optic flow cost [17] for every frame.”
Optical Flow Estimation Using a Spatial Pyramid Network (2016, background): “com/anuragranj/spynet the sum of a data term based on brightness constancy and a spatial smoothness term [25].”
A Vision-Based Learning Method for Pushing Manipulation (1993, methodology): “The figure ground segmentation was accomplished by computing the optical flow [Horn and Schunk, 1981] with Fig.”
Digital Image Correlation: from Displacement Measurement to Identification of Elastic Properties – a Review (2006, background): “As such, the problem is ill-posed, unless additional assumptions are made on the regularity of the displacement field so that the information is sufficient to determine u with a reasonable accuracy [30].”
Learning Optical Flow (2008, methodology): “Various parametric forms have been used to model the potential function φ (or its negative log): Horn and Schunck [9] used”
Introduction to Autonomous Mobile Robots (2004, methodology): “For more details on this and other methods refer to [41, 77, 146].”
Stress Intensity Factor Gauging by Digital Image Correlation: Application in Cyclic Fatigue (2007, unknown): “As such, the problem is ill-posed, unless additional assumptions are made on the regularity of the displacement field so that the information is sufficient to determine u with a reasonable accuracy [27].”
Video Processing From Electro-Optical Sensors for Object Detection and Tracking in a Maritime Environment: A Survey (2016, methodology): “Optical flow of the segmented regions was computed using an energy minimization approach [130].”
PatchBatch: A Batch Augmented Loss for Optical Flow (2015, methodology): “Dense optical flow methods have been the subject of research for the past 35 years, starting with the work of Horn and Schunk [20].”
STEPS: A probabilistic precipitation forecasting scheme which merges an extrapolation nowcast with downscaled NWP (2006, background): “Optic flow theory (also known as optical flow) has developed for determining the motion of objects identified within an image (Horn and Schunck 1981).”
TAP-Vid: A Benchmark for Tracking Any Point in a Video (2022, unknown): “Optical Flow estimates dense motion, but only between image pairs [22, 40]; modern approaches [13, 25, 51, 63, 66] train and evaluate on synthetic scenes [6, 13, 46, 62], though depth scanners provide limited real data [16].”