Page 61 - Dynamic Vision for Perception and Control of Motion

2.2 Objects 45

model both with respect to shape and to motion is not given but has to be inferred
from the visual appearance in the image sequence. This makes the use of complex
shape models with a large number of tesselated surface elements (e.g., triangles)
obsolete; instead, simple encasing shapes like rectangular boxes, cylinders, poly-
hedra, or convex hulls are preferred. Deviations from these idealized shapes such
as rounded edges or corners are summarized in fuzzy symbolic statements (like
“rounded”) and are taken into account by avoiding measurement of features in
these regions.

2.2.4 Shape and Feature Description

With respect to shape, objects and subjects are treated in the same fashion. Only
rigid objects and objects consisting of several rigid parts linked by joints are
treated here; for elastic and plastic modeling see, e.g., [Metaxas, Terzepoulos 1993].
Since objects may be seen at different distances, the appearance in the image may
vary considerably in size. At large distances, the 3-D shape of the object, usually,
is of no importance to the observer, and the cross section seen contains most of the
information for tracking. However, this cross section may depend on the angular
aspect conditions; therefore, both coarse-to-fine and aspect-dependent modeling of
shape is necessary for efficient dynamic vision. This will be discussed for simple
rods and for the task of perceiving road vehicles as they appear in normal road traf-
fic.

2.2.4.1 Rods
An idealized rod (like a geometric line) is an object with an extension in just one
direction; the cross section is small compared to its length, ideally zero. To exist in
the real 3-D world, there has to be matter in the second and third dimensions. The
simplest shapes for the cross section in these dimensions are circles (yielding a thin
cylinder for a constant radius along the main axis) and rectangles, with the square
as a special case. Arbitrary cross sections and arbitrary changes along the main axis
yield generalized cylinders, discussed in [Nevatia, Binford 1977] as a flexible generic
3-D-shape (sections of branches or twigs from trees may be modeled this way). In
many parts of the world, these “sticks” are used for marking the road in winter
when snow may eliminate the ordinary painted markings. With constant
crossísections as circles and triangles, they are often encountered in road traffic
also: Poles carrying traffic signs (at about 2 m elevation above the ground) very of-
ten have circular cross sections. Special poles with cross sections as rounded trian-
gles (often with reflecting glass inserts of different shapes and colors near the top
at about 1 m) are in use for alleviating driving at night and under foggy conditions.
Figure 2.12 shows some shapes of rods as used in road traffic. No matter what the
shape, the rod will appear in an image as a line with intensity edges, in general.
Depending on the shape of the cross section, different shading patterns may occur.
Moving around a pole with cross section (b) or (c) at constant distance R, the width
of the line will change; in case (c), the diagonals will yield maximum line width
when looked at orthogonally.