INTRODUCTION TO CONTENT-BASED VISUAL PROCESSING - Video Object Extraction and Representation: Theory and Applications - page 4

Figure 1.1. Physical Object vs. Video Object: a) a cube as a Physical Object moving
through time in the real world, translating with constant velocity in the y direction
from t=0 to t=1 and then translating in the z direction from t=1 to t=2 and b) its
corresponding Video Object through a projection onto the x-y plane. Note that the

time correspondence between two spaces.

physical object is a philosophical postulate that frames the topic. The
video object is a simple result of this postulate, and a simpler, interme-
diate representation of the physical object.
We now define the fundamental elements of this topic. We define the
physical world as the domain where the ground truth exists, the real
4-D physical space ( x phys ,y phys ,z phys ,t phys )(3-D space with time com-
ponent). Three dimensional objects that move around in physical space
(see Fig 1.1a) are called physical objects. Our own view of this world is
limited: from a single camera view, the physical world is projected onto
a3-D space ( x,y,t ) that we call the video space. The video sequence,
I ( x, y, t ), is a real-valued function over the video space that represents
a series of grayscale images that we see. A timeslice of a video sequence
( I ( x,y,t ) | t = t 0 ) is called a frame t 0 in this topic. For a given time in-
stant, each 3-D object in the physical world is projected as a flat 2-D
image. Moving through the physical world, a 3-D object is projected as
a time-indexed series of 2-D images. The X and Y dimensions of the

space are symmetric. Along the time dimension, there exists a strong

correspondence between images along the X-Y planes due to the fact

that physical objects either are stationary or must move away, but do

not suddenly appear and disappear.

P OSTULATE 1.1 ( O BJECT - O RIENTED D ECOMPOSITION ) The video se-
quence I ( x, y, t ) is a composition of projections of a number of physical
objects that exist in the physical world.

The video sequence may be parti-