MPEG-4 Toward Solid
Representation
Alain Mignot and Pierre Garneau
IEEE Trans. on Circuits and Systems for Video Tech.,
Vol. 14, NO. 7, JULY 2004, pp. 967-974.
Presented by:
Reza Aghaee
Multimedia Course(CMPT820)
Simon Fraser University
March.2005
Agenda

Introduction

Future of 3D Standards

Solid Representation: MPEG-4’s Answer to
3D Challenge

Implications of Rendering Mechanisms

Impacts on Applications

Conclusion
2
Introduction

Traditional 3D Image Creation
1.
Tessellation
–
2.
Geometry
–
3.
Models are created of individual objects
using link points that are made into a
number of individual polygons
Polygons are transformed in various
ways and lighting effects are applied
Rendering
–
Transformed images are rendered into
objects with very fine details
3
Introduction (cntd.)

Performance is the number of polygons
processed per second.

MPEG-4 is introducing a new and
different approach.

This method can be used in various 3D
applications. (Games/CAD/CAM/CAE)
4
Future of 3D Standards

3D Technology is at a Turning Point
–
–
–
10 years old OpenGL is reaching its
limits.
It’s confirmed by user-programmable
parts of the pipeline.
This limited programming capability, in
the form of vertex and pixel shaders,
appears to be the easiest solution.
5
Future of 3D Standards

Shader Programs May Not Be the
Solution
–
–
–
It is actually a step backward, in the
opposite direction of the beneficial
standardization process.
Graphic APIs display 3D scenes on
almost any device.
Drivers take care of hardware
differences other than performance.
6
Future of 3D Standards

Shader Programs May Not Be the
Solution (cntd.)
–
–
–
A software driver can not simulate
most shader programs.
Developers should provide different
versions for different graphic boards.
Shader Programs do not bring any
additional information to the rendering
process concerning the scene itself.
7
Future of 3D Standards

Historical Considerations
–
–
–
Higher performance was often
achieved by including parts of pipeline
into dedicated hardware.
First, later stages of the pipeline were
performed in hardware and front
portion in software driver.
3D technology should extend its
domain on functionalities performed by
application.
8
Future of 3D Standards

Limitations of the 3D Pipeline
Common to OpenGL and DirectX
–
–
–
Algorithms designed to create the
illusion of depth and continuity.
3D rendering is a set of techniques that
have nothing to do with geometric
objects.
In real 3D space, objects may
influence each other even if invisible.
9
Future of 3D Standards

Limitations of the 3D Pipeline Common
to OpenGL and DirectX (cntd.)
–
Two parallel data structures needed
•
•
–
–
One for describing the scene ( objects with
geometric attributes)
One for the set of polygons (each object in its
position relative to observer)
First structure for managing interactions
Second structure only for rendering
10
Future of 3D Standards
Traditional 3D Game Production
11
Future of 3D Standards
Traditional CAD rendering
12
Projected Evolution of 3D
standards
Data structure of geometric objects
and their attributes is common in
most applications.
 Most applications share a common
framework based on geometrical
and physical properties of objects.
 By including this framework in the
rendering engine the whole process
is well improved.

13
Solid Representation in
MPEG-4
MPEG-4 introduces the purely
mathematical definition of shapes.
 These shapes are based on
algebraic shapes combined with
arithmetic shapes.
 These shapes are completely
independent of rendering process.
 These functionalities are referred to
as “Solid Representation”.

14
Solid Representation in
MPEG-4

In MPEG-4, solid representation
functionalities deal with:
–
–
–
Reducing the size of files to be transmitted or
shared by transmitting constructive
commands rather than results.
Increasing the geometrical precision of
rendered objects by managing a polynomial
representation of volumes.
Manipulating complex objects combined by
solid operations.
15
Solid Representation in
MPEG-4

Solid Primitives
–
–
–
–
Any solid object has a
3-D form defined by a
skin, which delimits the
inside from the outside.
Figure 3
If equation of surface is
unknown the volume will be divided into
simpler pieces until they have known forms.
These primitives will then be assembled in
order to constitute the original complex shape.
Figure 3 is a complex shape made of a set of
solid primitives.
16
Solid Representation in
MPEG-4

There are two approaches to define a
surface:
–
–

Implicit Equation of a Sphere
–

A Parametric Equation giving spatial
coordinates of each surface point.
Implicit Equation of algebraic surfaces.
(Px – Cx ) 2 + ( Py – Cy ) 2 + (Pz - Cz) 2 - R2 = 0
Eq=0 means point is on the surface,
for Eq<0 point is inside and for Eq>0
point is outside the volume.
17
Solid Representation in
MPEG-4

A quadratic equation (second-degree equation)
allows to define the entire quadrics family:

An equation of the fourth degree allows to define
the quartics family:
18
Solid Representation in
MPEG-4

Implicit second-degree equation defining
quadrics is:
c0 X 02  c1 X 0 X 1  c2 X 12  c3 X 0 X 2  c4 X 1 X 2 
c5 X 22  c6 X 0 X 3  c7 X 1 X 3  c8 X 2 X 3  c9 X 32  0
where for each point coordinates (X0…X3) the result
is:
F(X0,…,X3) < 0 ; F(X0,…,X3) = 0 ; F(X0,…,X3) > 0
whether the point is inside, on the surface or outside.
19
Solid Representation in
MPEG-4
The point coordinates are made
homogeneous by adding X3 .
 A surface of fourth-degree will have
35 coefficients.
 Unbound surfaces should be
bounded to be processed and
displayed.
 Cylinder equation is an example of
unbound volumes.

20
Solid Representation in
MPEG-4

In MPEG-4 the coefficients of the
quadric (second-degree implicit
surface) may be defined by six
geometric control points.
P0,P1 : 2 contact points on the quadric.
P2,P3 : 2 poles of the construction
tetrahedron.
P4,P5 : 2 passing points of the quadric.

Each point is defined using homogeneous
coordinates allowing the point to be
sent to infinity (affine geometry)
21
Solid Representation in
MPEG-4

In MPEG-4 two Geometry nodes
implement algebraic surfaces:
1.
Implicit Node:
Defines the surface by the coefficients of the
polynomial.
2.
Quadric Node:
Defines the surface by the six control points
explained in the previous slide.
22
Solid Representation in
MPEG-4
“Arithmetic of Forms” is a logical
modeling system for solid objects.
 Description of a solid object takes
the form of a solid tree made up of
operators and operands.
 Operands are primitives or more
complex solid objects.
 Operators are mostly union,
intersection and logical subtraction.

23
Solid Representation in
MPEG-4

Each basic geometric
primitive splits space into
three regions – external,
boundary, and internal –
coded by integers 0, 1, 2.

This ternary
coding of
space tells
us the
density of
every point
in space.
Constructive Solid Geometry (CGS) tree and
corresponding model 3D
24
Solid Representation in
MPEG-4

There are three basic sets of operators
1.
General Arithmetic Operators on Densities:
–
–
For instance, addition, multiplication, and
difference of densities of two volumes.
Below is multiplication of two forms F0 and F1.
25
Solid Representation in
MPEG-4

Three basic Sets of Operators (cntd.)
2.
Arithmetic Operators with Ternary Logic:
–
–
–
They use ternary logic only.
Examples are union and intersection.
Below is ternary intersection of F0 and F1.
26
Solid Representation in
MPEG-4

Three basic Sets of Operators (cntd.)
3.
Densities Filtering
–
–
In MPEG-4 a set of test functions is applied
on the root of the solid tree to filter densities
while keeping the filtering inside the tree.
Examples can be “Equality Filter” (F0==F1)
Results of Solid Operations
27
Implications of Rendering
Mechanisms


If the volumes must be displayed very precisely
some techniques can be used to render the output.
If one accepts less geometric precision, it is
possible to consider tessellation of implicit surfaces
before or after applying solid operation and
rendering.
28
Implications of Rendering
Mechanisms
The functionalities of solid
representation in MPEG-4 including
Implicit, Quadric and SoldRep
Nodes are completely independent
from the rendering method.
 All the solid operators are
independent from the rendering
process too.

29
Impacts on Applications

Compactness
–
–
Suitable for sophisticated web applications
including online gaming on small-constrained
devices mobile phones and PDAs.
Complete model of a historical castle with a
level of detail from roof frame to door openers
takes 50 Kb.
30
Impacts on Applications
The following example is a model
solely based on SolidRep geometry.
Details of the Leihorra villa’s model
Complete Solid Model of Leihorra villa 31
Impacts on Applications

Exact Geometry
–
–
–
The exact geometry is preserved up to the
decoder.
It allows very precise scientific applications as
CAD/CAM or simulations.
Below is the simulation of the Canadian
Space arm from Canadian Space Agency.
32
Impacts on Applications

Embedded Topology and 3D Properties
There is a wrap-up of the topology and 3D
solid properties (e.g. constituent matter and
physical properties)
– Local manipulation, exploration of the model
and very accurate collision detection is
allowed.
– The picture is
an inside view
of the villa as
the result of a
solid
Operation.
–
33
Impacts on Applications


There are many games claiming that the player
can destroy almost any object to find other
hidden spaces.
This model can help implement these models
without very heavy programming techniques.
Model cut with a laser beam
Complete Original Model
34
Conclusion





Polygonal pipelines can’t present the future of
3D standards.
Solid representation can transfer very complex
models in their most exact geometry and in a
very compact way.
Even without a dedicated hardware current
CPUs are powerful enough to provide real-time
processing.
Solid representation is now a part of the MPEG4 part-16.
New APIs will be developed including object
description to accelerate solid representation.
35