Image analysis – Image transformation or preprocessing
Reexamination Certificate
1997-11-17
2001-11-20
Lee, Thomas D. (Department: 2624)
Image analysis
Image transformation or preprocessing
C345S418000, C345S473000, C345S474000
Reexamination Certificate
active
06320988
ABSTRACT:
BACKGROUND OF THE INVENTION
1. Field of the Invention
This invention relates to a method of transforming the shape of a skeleton model, an image synthesizing apparatus, and an information storage medium.
2. Description of Related Art
A technique called inverse kinematics is known in the art. With this technique, a skeleton model
20
such as that shown in
FIG. 22A
is created beforehand within a computer. The user then uses an input device such as a mouse to transform that skeleton model
20
while viewing the skeleton model
20
on a display device, such as a CRT, to create any motion or pose that the user desires. It should be noted that each of the joint or end points of the skeleton model
20
is called a “node” in the description that follows, and a linking “bone” that connects two nodes is called an arc.
Several methods of using this inverse kinematics technique are known in the art, such as is described in “Modeling and Animation Techniques for a Computer Generated Actor” (by Fukui Kazuo, reference material for a seminar on Human Modelling and Display Techniques, held in September 1991 by the Information Processing Society). With this prior-art technique, arc-to-arc angles &thgr;
1
, &thgr;
2
, and &thgr;
3
are used as basic variables representing the shape of a skeleton model, as shown in FIG.
22
B. One of the problems to be solved with this prior-art inverse kinematics method occurs when there is a straight-linked skeleton having a fixed node
40
and the location (x, y, z) of a node
42
at the other end thereof has been specified. The difficulty involves deriving the arc-to-arc angles &thgr;
1
, &thgr;
2
, and &thgr;
3
that implement this method. This problem is equivalent to obtaining an inverse function f
−1
(x, y, z) of a function f(&thgr;
1x
, &thgr;
1y
, &thgr;
1z
, &thgr;
2x
. . . ). However, since the function f is non-linear, it is not easy to obtain this inverse function. In this case, infinitesimal differentials &Dgr;x, &Dgr;y, and &Dgr;z in x, y, and z are approximated by linear expression involving infinitesimal differentials &Dgr;&thgr;
1x
, &Dgr;&thgr;
1y
, &Dgr;&thgr;
1z
, &Dgr;&thgr;
2x
. . . of the arc-to-arc angles. The problem to be solved thereby can be reduced to the solving of the set of simultaneous equations shown in FIG.
22
C. However, the matrix M in
FIG. 22C
is not square and the number of variables thereof is less than the number of equations, so there is an infinite number of solutions. In this case, by adding a condition that the sum of squares of variations in the arc-to-arc angles is a minimum, the set of simultaneous equations of
FIG. 22C
can be solved.
However, the above described prior-art technique applies to a straight-linked skeleton that has one end fixed wherein arc-to-arc angles are used as basic variables expressing the shape, so it involves the following problems:
1. It is Difficult to Handle a Multiple-branching Structure
With this prior-art technique, in order to handle a skeleton model of a multiple-branching structure (a structure in which three or more arcs are connected to one node), such as that shown for example in
FIG. 22C
, it is necessary to divide it into a plurality of directly linked structures
23
to
27
and then set parent-child relationships as shown in
FIGS. 23A and 23B
. To move one of the hands of the skeleton model
20
, for example, a node
30
is set as a root and a node
32
is moved as an effector, and to move the other hand, the node
30
is set as the root and a node
34
is moved as an effector. Similarly, to move one of the legs, a node
36
is set as a root in this case and a node
38
is moved as an effector. The user must therefore work while constantly being aware of which node acts as the root and which node acts as effector, which makes the work troublesome.
2. It is Difficult to Handle Complicated Restrictive Conditions
If restrictive conditions are set for a plurality of nodes, for example, it is necessary to divide the skeleton into suitable directly linked structures before handling it, so that the processing becomes complicated. These restrictive conditions are generally expressed as equations defining the node coordinates. If, for example, the node
38
in
FIG. 22A
is restricted to a polygon, an equation is used that always limits the node
38
to locations on that polygon. However, the basic variables used in the prior-art technique are the arc-to-arc angles, so it is difficult to use the above equations and thus restrictive conditions are difficult to handle.
3. It is Difficult to Move a Plurality of Nodes in Different Directions Simultaneously
In other words, if an attempt is made to move nodes
38
and
39
in different directions simultaneously, for example, with the prior-art technique, the processing is extremely complicated.
SUMMARY OF THE INVENTION
This invention was devised in order to solve the above-described technical problems and has as an objective thereof the provision of a method of transforming the shape of a skeleton model, an image synthesizing apparatus, and an information storage medium which can easily handle a skeleton model of a multiple-branching structure and which enable the simple setting of complicated restrictive conditions.
In order to solve the above technical problems, a first aspect of this invention relates to a method of transforming the shape of a skeleton model , comprising the steps of:
expressing the skeleton model by basic variables that comprise coordinates of at least one node of the skeleton model;
causing a change in at least one of a set of basic equations and an evaluation expression based on given information, the set of basic equations taking the basic variables as unknowns and comprising an equation that defines the length of a plurality of arcs of the skeleton model as given values, and the evaluation expression uniquely determining a solution for the basic variables of the set of basic equations;
obtaining the solution that substantially satisfies the set of basic equations and makes the value of the evaluation expression one of substantially a minimum, substantially a maximum, or substantially stationary; and
transforming the shape of the skeleton model, based on the thus obtained solution.
With this aspect of the invention, a skeleton model is expressed by basic variables comprising node coordinates. Furthermore, a solution that substantially satisfies the basic equations is uniquely specified by adding a condition such as one that makes the value of an evaluation expression substantially at minimum, to determine the shape of the skeleton model. Therefore, this aspect of the invention makes it possible to handle all nodes equally, making it easy to manipulate a skeleton model of a multiple-branching structure. Since it is often necessary to define a restrictive condition on the basis of node coordinates, this aspect of the invention enables the simple setting of complicated restrictive conditions.
The basic variables may comprise components of arc-normal vectors that are perpendicular to the arcs; and the set of basic equations may comprise an equation defining the length of the arc-normal vectors as given values and an equation specifying that the arc-normal vectors are perpendicular to the arcs.
The arc-normal vector is used as a basic variable, so that all arcs can be handled equally, making it easy to manipulate a skeleton model of a multiple-branching structure.
The basic variables may comprise components of arc-normal vectors that are perpendicular to the arcs; and a variation in the components of the arc-normal vectors may be expressed as a single given variable to obtain the solution for these basic variables.
Since a variation in the components of the arc-normal vectors can be expressed by a single given variable as mentioned above, the number of unknowns to be solved can be reduced, increasing the speed of processing. Note that it is particularly preferable to express the variation in the components of the arc-normal vectors as a linear expression involving a single given variable.
The basic vari
Baba Tetsuji
Yamaguchi Kentaro
Yoshida Hiroshi
Lee Thomas D.
Namco Ltd.
Oliff & Berridge PLC.
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