Cs 6825 motion part 2 optical flow
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CS 6825: Motion Part 2 – Optical Flow PowerPoint PPT Presentation


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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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Cs 6825 motion part 2 optical flow

CS 6825: Motion Part 2 – Optical Flow


Recall 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.

  • Hence we are seeing the projection of the 3D moving points onto the image plane.


Motion field and optical flow field

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


Brightness constancy equation

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.


Brightness constancy equation1

Brightness Constancy Equation

Taking derivative wrt time:


Brightness constancy equation2

Brightness Constancy Equation

Let

(Frame spatial gradient)

(optical flow)

(derivative across frames)

and


Brightness constancy equation3

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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