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CS 6825: Motion Part 2 – Optical Flow

CS 6825: Motion Part 2 – Optical Flow. Recall: Optical Flow. is an approximation of the 2D motion field. Motion in the world usually occurs in 3D, but, we have a 2D image sensor. So, we see the results as movement across the 2D image plane.

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CS 6825: Motion Part 2 – Optical Flow

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  1. CS 6825: Motion Part 2 – Optical Flow

  2. Recall: Optical Flow • is an approximation of the 2D motion field. • Motion in the world usually occurs in 3D, but, we have a 2D image sensor. So, we see the results as movement across the 2D image plane. • Hence we are seeing the projection of the 3D moving points onto the image plane.

  3. Motion Field and Optical Flow Field • Motion field: projection of 3D motion vectors on image plane • Optical flow field: apparent motion of brightness patterns • We equate motion field with optical flow field

  4. Brightness Constancy Equation • Let P be a moving point in 3D: • At time t, P has coords (X(t),Y(t),Z(t)) • Let p=(x(t),y(t)) be the coords. of its image at time t. • Let E(x(t),y(t),t) be the brightness at p at time t. • Brightness Constancy Assumption: • As P moves over time, E(x(t),y(t),t) remains constant.

  5. Brightness Constancy Equation Taking derivative wrt time:

  6. Brightness Constancy Equation Let (Frame spatial gradient) (optical flow) (derivative across frames) and

  7. Brightness Constancy Equation We want to calculate v= [dx/dt dy/dt] Becomes: vy r E -Et/|r E| Can calculate these: Different techniques to figure these out. DE is the spatial change in brightness in image i Et is the difference in the brightness at (x,y) between image i and image i+1 vx The Optical Flow is CONSTRAINED to be on a line !

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