# 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

### 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: 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

• 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 Equation

Taking derivative wrt time:

### Brightness Constancy Equation

Let

(optical flow)

(derivative across frames)

and

### 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 !