Optical flow (motion vector) computation Course: Computer Graphics and Image Processing Semester:Fall 2002 Presenter:Nilesh Ghubade Advisor: Dr Longin Jan Latecki Dept:Computer and Information Science, Temple University, Philadelphia, PA-19122

Motion Analysis Three groups of motion-related problems: 1. Motion detection Registers any detected motion. Registers any detected motion. Single static camera. Single static camera. Used for security purposes. Used for security purposes. 2. Moving object detection and location Determination of object trajectory. Determination of object trajectory. Static camera, moving objects OR Moving camera, static objects OR Both camera and objects moving. Static camera, moving objects OR Moving camera, static objects OR Both camera and objects moving. 3. Deriving 3D properties Use of set of 2D projections acquired at different time instants of object motion. Use of set of 2D projections acquired at different time instants of object motion.

Object motion assumptions Maximum velocity. Maximum velocity. Small acceleration. Small acceleration. Common motion of object points. Common motion of object points. Mutual correspondence. Mutual correspondence. C max * dt t0t0 t1t1 t2t2

Differential motion analysis Simple subtraction of images acquired at different instants in time makes motion detection possible, assuming stationary camera position and constant illumination. Simple subtraction of images acquired at different instants in time makes motion detection possible, assuming stationary camera position and constant illumination. Difference image is a binary image  subtract two consecutive images. Difference image is a binary image  subtract two consecutive images. Cumulative difference image: Cumulative difference image: Reveals motion direction. Reveals motion direction. Time related motion properties. Time related motion properties. Slow motion and small object motion. Slow motion and small object motion. Constructed from sequence of ‘n’ images taking first image as the reference image.

Example Motion in front of a security camera. Sobel filter edge detection.

Motion Detection- Sobel filter 10 frames/second15 frames/second 25 frames/second

Optical Flow Optical Flow reflects the image changes due to motion during a time interval dt. Optical Flow reflects the image changes due to motion during a time interval dt. Optical flow field is the velocity field that represents the 3D motion of object points across a 2D image. Optical flow field is the velocity field that represents the 3D motion of object points across a 2D image. It should not be sensitive to illumination changes and motion of unimportant objects (e.g. shadows) It should not be sensitive to illumination changes and motion of unimportant objects (e.g. shadows) Exceptions: Exceptions: 1. Non-zero optical flow  fixed sphere illuminated by a moving source. 2. Zero optical flow  smooth sphere under constant illumination, although there is rotational motion and true non- zero motion field.

Optical Flow (continued…) Aim is to determine optical flow that corresponds with true motion field. Aim is to determine optical flow that corresponds with true motion field. Necessary pre-condition of subsequent higher level motion processing  stationary or moving camera. Necessary pre-condition of subsequent higher level motion processing  stationary or moving camera. Provides tools to determine motion parameters, relative distances of objects in the image etc.. Provides tools to determine motion parameters, relative distances of objects in the image etc.. Example: Example: t1 t2

Assumptions Optical flow computation is based on two assumptions: 1. The observed brightness of any object point is constant over time. 2. Nearby points in the image plane move in a similar manner (the velocity smoothness constraint).

Optical flow computation The optical flow field represented in the form of Velocity vector: Length of the vector determines the magnitude of velocity. Length of the vector determines the magnitude of velocity. Direction of the vector determines the direction of motion. Direction of the vector determines the direction of motion. Global optical flow estimation— Local constraints are propagated globally. Local constraints are propagated globally. But errors also propagate across the solution. But errors also propagate across the solution. Local optical flow estimation— Divide image into smaller regions. Divide image into smaller regions. But inefficient in the areas where spatial gradients change slowly  here use global method, neighboring image parts contribute. But inefficient in the areas where spatial gradients change slowly  here use global method, neighboring image parts contribute.

Forms of motion Translation at constant distance from the observer. Set of parallel motion vectors. Translation in depth relative to the observer. Set of vectors having common focus of expansion. Rotation at constant distance from view axis. Set of concentric motion vectors. Rotation of planar object perpendicular to the view axis. One or more sets of vectors starting from straight line segments.

Representation Locate the position of a pixel (row,col) in the current image by computing shortest Euclidean distance with respect to 5-by-5 neighborhood in the next consecutive frame

Experiments 3-by-3 neighborhood

Experiments (contd…) 5-by-5 neighborhood

Experiments (contd…)

Applications of optical flow Object motion detection. Object motion detection. Action recognition. Action recognition. Active vision or structure of motion – Active vision or structure of motion – Reconstruction of 3D object by computing depth information. Reconstruction of 3D object by computing depth information. If you have distance (depth) maps, you can reconstruct surface of the object. If you have distance (depth) maps, you can reconstruct surface of the object. Facial expression recognition: reference  Facial expression recognition: reference 

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