3D Skeleton-based Human
Modeling with Metaballs
18 April 2008
Donghun Kim
Robot Vision Lab
Contents
Motivation
 What is the Metaball?
 How can we visualize Metaballs?
 3D Skeleton Human Model
 Human model using Metaballs
 Examples
 Future Works

Motivation



Motion Analysis of Non-rigid Object
Motion Analysis of Articulated Object
Model based Pose Estimation and Tracking





3D Mesh Data by Visual Hall
3D Skeleton( Curve Skeleton by Thinning, DT,
Geometric or General Fields) - on going
3D Skeleton-based Motion tracking
Metaball Human Model for shape recovery
Motion Analysis by Skeleton-based Motion
and Shape Info. (i.e. Manifold learning)
Implicit Surfaces
Implicit Surfaces: Surfaces which are
contours(isosurface) through some
scalar field in 3D
 Different Field function: Metaball, Soft
Objects, Blobbies

What are isosurfaces?



Consider a function f(x,y,z) which define a
scalar field in 3D space.
Isosurface S is set of points for which
f(x,y,z) = const.
It can be thought as an Implicit function
relating x,y and z -> so called implicit
surface sometimes
Metaballs
x: a point in 3d space


A particularly interesting case
Use implicit equation of the form
N

i 1

ri
x  pi
2
1
pi : center position of
metaballs
ri : Metaball’s own density
field
Gradient can be computed directly
N
2  ri
i 1
x  pi
f  

2
N: num. of metaballs
2
4
 ( x  pi )
Soft/blobby objects that blend into each other
Field Functions

Blobby Molecules
r is distance of a point in
space to a particular
control point
br2
D(r)  ae

Metaballs

3r2
a(1  2 )
 3a b r

D(r )   (1  ) 2
b
 2
0



if 0  r 
b
3
b
r b
3
if b  r
if
Soft Objects

4r 6 17r 4 22r 2

D(r )  a (1  9b 6  9b 4  9b 2 )

0
Comparison of Field Functions
< Figure from [4]>
Examples
< Images from [4]>
Metaballs are cool! 
Marching Cubes
Well-known Method for scalr field
polygonizataion
 Sample f(x,y,z) on a cubic lattice
 For each cubic cell

Estimate where isosurface inetersects cell
edges by linear interpolation
 Tessellate depending on values of f() at
cell vertices

Marching Cubes



Algorithm for creating a polygonal surface
representation of an isosurface of a 3D scalar
field
Combine simplicity with high speed because
of using lookup tables
Application


Reconstruction of a surface from volumetric
datasets
Creating a 3D contour of a mathematical scalar
field
Marching Cubes


Each vertex can be either “inside” or “outside”
For each cube cell there are 256 ways for
isosurface to intersect it can be simplified
down to 15 unique
Marching Cubes

Example
cubeindex = 0; if (grid.val[0] < isolevel) cubeindex
|= 1; if (grid.val[1] < isolevel) cubeindex |= 2; if
(grid.val[2] < isolevel) cubeindex |= 4; if (grid.val[3
< isolevel) cubeindex |= 8; if (grid.val[4] < isolevel)
cubeindex |= 16; if (grid.val[5] < isolevel)
cubeindex |= 32; if (grid.val[6] < isolevel)
cubeindex |= 64; if (grid.val[7] < isolevel)
cubeindex |= 128;
< Images from [5]>
P = P1 + (isovalue - V1) (P2 - P1) / (V2 - V1)
Marching Cubes

Sampling Grid Resolution

Smoothness and Processing time to display
< Images from [5]>
Examples of Marching Cubes
• More Information about Marching Cubes is in [3].
3D Skeleton Human Model

Structure( 15 nodes, 14 metaballs)
7
12
8
3
2
6 11
1
0
4
9
13
5
10
14
15
Human Model using Metaballs

Head(1-2-7)
Human Model using Metaballs

Chest(0-1-2-3-6)
Human Model using Metaballs

Left Arm(1-2-3-8-12)
Human Model using Metaballs

Right Arm(1-2-5-11-15)
Human Model using Metaballs

Left Hip & Thigh(0-4-9)
Human Model using Metaballs

Right Hip & Thigh(0-5-10)
Human Model using Metaballs

Left Leg(4-9-13)
Human Model using Metaballs

Right leg(5-10-14)
Human Model using Metaballs

Result (Polygon Surface)
Human Model using Metaballs

Result (Filled surface)
Programming




3D cloud data and mesh data from Visual Hall(using
EPVH lib) as the input of 3D skeleton
3D Human Model Tool based on Jonney’s 3D Human
Model Frame (using Ellipsoid, Cylinder, Sphere)
OpenGL and FLTK GUI based tool
Functions

3D reconstruction by Visual hall






Obtain Multiple Camera-view point images in OpenGL Environment
Calculate Camera matrix by transforming the OpenGL representation to
Physical camera representation
Parameterized 3D Skeleton Human Model
3D Skeleton-based Metaball Model
Simple model size option (Height considering body ratio, fat-thin
option)
Image Saving with OpenCV in OpenGL
Modeling Tool
Made by Dave Kim and Thanks to Jonney
Modeling Tool
Made by Dave Kim and Thanks to Jonney
Data Comparison

Multi-View Silhouette Images of
Different Human Model


Ellipsoid, Cylinder and Sphere vs. Metaballs
3D cloud points and triangle meshes by
Visual hall
Example (I)
Example (I)
Example (II)

Metaball Human Model
Example (II)

Result by Visual Hall
Future Work

3D Curve skeleton Algorithm[2]

DT (fast) + General Field (robust)
3D skeleton human model fitting to
Curve Skeleton -> Pose Estimation
 Shape recovery using the information
from the skeletonization
 Motion Analysis

Reference
4.
Clement Menier, Bruno Raffin, “3D Skeleton-based Pose
Recovery,” The 3rd international Symposimum on 3D Data
Processing, Visualization and Transmission, 2006
Nicu D. Cormea etc at al., “Curve-Skeleton Application,” IEEE
Visualization 2005
T. S. Newman, H. Yi, “A survey of the marching cubes
algorithm,” Computers and Graphics, 2006
Implicit Surfaces written by Paul Bourke, June 1997,
5.
Polygonising A Scalar Field written by Paul Bourke, May 1994,
1.
2.
3.
http://local.wasp.uwa.edu.au/~pbourke/modelling_rendering/i
mplicitsurf/
http://local.wasp.uwa.edu.au/~pbourke/geometry/polygonise