Feature Extraction and Image Processing

150 Feature Extraction and Image Processing

Now by Equation 4.71 we can substitute for P(t + t)

x+ x,y+ y

to give

PP

PPP

() = () +

()

+

()

+

()

,,

,,,

ttx

t

x

y

t

y

t

t

t

xy xy

xy xy xy

(4.77)

which with some rearrangement gives the motion constraint equation

x

t

x

y

t

yt

+ = –

PPP

(4.78)

We can recognise some terms in this equation. P/ x and P/ y are the first-order differentials

of the image intensity along the two image axes. P/ t is the rate of change of image

intensity with time. The other two factors are the ones concerned with optical flow, as they

describe movement along the two image axes. Let us call

u

x

t

y

t

= and = v

These are the optical flow components: ...