Information processor

• US 7,030,880 B2
• Filed: 06/20/2002
• Issued: 04/18/2006
• Est. Priority Date: 06/21/2001
• Status: Active Grant

• Current Assignee: HI Corporation (Micware Co., Ltd.)
• Original Assignee: HI Corporation (Micware Co., Ltd.)
• Inventors: Tsutsumi, Junya, Kawabata, Kazuo, Oda, Kazutoshi, Tanioka, Yasuhisa
• Primary Examiner(s): Nguyen, Kimbinh T.
• Application Number:
  US10/344,452
• Publication Number:
  US 20030185460A1
• Time in Patent Office: 1,398 Days
• Field of Search: 345/419, 345/422, 345/427, 345/582, 345/586, 345/643, 345/644, 345/648, 382/251, 382/276
• US Class Current: 345/427
• CPC Class Codes: G06T 3/02 Affine transformations for image registration G06T3/147; for image mosaicing G06T3/4038

Abstract

In an information processing apparatus for conducting an affine transformation representative of $\left(\begin{array}{c}{x}^{\prime }\\ y^{\prime }\\ z^{\prime }\end{array}\right)=A\left(\begin{array}{c}x\\ y\\ z\end{array}\right)+\left(\begin{array}{c}{t}_1\\ t_2\\ t_3\end{array}\right),a\mathrm{matrix}$$A^{\prime }=\left(\begin{array}{ccc}{a}_{11}^{\prime }& a_{12}^{\prime }& a_{13}^{\prime }\\ a_{21}^{\prime }& a_{22}^{\prime }& a_{23}^{\prime }\\ a_{31}^{\prime }& a_{32}^{\prime }& a_{33}^{\prime }\end{array}\right)=\lambda A=\left(\begin{array}{ccc}\lambda a_{11}& \lambda a_{12}& \lambda a_{13}\\ \lambda a_{21}& \lambda a_{22}& \lambda a_{23}\\ \lambda a_{31}& \lambda a_{32}& \lambda a_{33}\end{array}\right)$
obtained by multiplying a matrix A for the affine transformation by λ(≠0) is stored in a memory section in advance. In case of conducting calculation processing for transforming coordinates (x,y,z)^t into coordinates (x′,y′,z′)^t by means of the affine transformation, A′ and a matrix (t₁,t₂,t₃)^t are read from the memory section,
x′=(a′₁₁*x+a′₁₂*y+a′₁₃*z)/λ+t₁;
y′=(a′₂₁*x+a′₂₂*y+a′₂₃*z)/λ+t₂;
z′=(a′₃₁*x+a′₃₂*y+a′₃₃*z)/λ+t₃;
are calculated, and the coordinates (x′,y′,z′)^t are obtained.

Claims

1. An information processing apparatus for, in conducting Rasterize processing of imaging of a three-dimensional image, calculating a quantity of a change of x coordinates $\Delta$

⁢

⁢

x=x2-x1y2-y1

to y coordinates of a straight line passing through a point P₁(x₁,y₁) and a point P₂(x₂,y₂) on a two-dimensional plain, characterized in that the apparatus comprises;

a memory in which a constant μ

representative of $\mathrm{\mu <br><br>}=\frac{\mathrm{\lambda <br><br>}}{y_2-y_1}$

is stored in association with the quantity of the change of the y coordinates; and

calculation means for, in calculating Δ

x, reading μ

corresponding to the quantity of the change of said y coordinates from said memory, and calculating

Δ

x′

=μ

*(x₂−

x₁);

by means of multiplication, and calculating this result as Δ

x.

2. An information processing apparatus recited in claim 1, characterized in that said λ

is limited to 2ⁿ(n≧

1), and the apparatus further comprises means for calculating Δ

x by right-shifting said calculated Δ

x′

by n digits.

3. An information processing apparatus recited in claim 1 or claim 2, wherein coordinate values are limited to integers, and transformation processing is applied to coordinates (x,y,z)^t to create coordinates (x′

,y′

,z′

)^t by means of an affine transformation representative of $\left(\begin{array}{c}{x}^{\mathrm{\prime <br><br>}}\\ y^{\mathrm{\prime <br><br>}}\\ z^{\mathrm{\prime <br><br>}}\end{array}\right)=A<br><br>\left(\begin{array}{c}x\\ y\\ z\end{array}\right)+\left(\begin{array}{c}{t}_1\\ t_2\\ t_3\end{array}\right),$

characterized in that the apparatus further comprises;

a memory in which a matrix $A^{\mathrm{\prime <br><br>}}=\left(\begin{array}{ccc}{a}_{11}^{\mathrm{\prime <br><br>}}& a_{12}^{\mathrm{\prime <br><br>}}& a_{13}^{\mathrm{\prime <br><br>}}\\ a_{21}^{\mathrm{\prime <br><br>}}& a_{22}^{\mathrm{\prime <br><br>}}& a_{23}^{\mathrm{\prime <br><br>}}\\ a_{31}^{\mathrm{\prime <br><br>}}& a_{32}^{\mathrm{\prime <br><br>}}& a_{33}^{\mathrm{\prime <br><br>}}\end{array}\right)=\mathrm{\lambda <br><br>}<br><br><br><br>A=\left(\begin{array}{ccc}\mathrm{\lambda <br><br>}<br><br><br><br>a_{11}& \mathrm{\lambda <br><br>}<br><br><br><br>a_{12}& \mathrm{\lambda <br><br>}<br><br><br><br>a_{13}\\ \mathrm{\lambda <br><br>}<br><br><br><br>a_{21}& \mathrm{\lambda <br><br>}<br><br><br><br>a_{22}& \mathrm{\lambda <br><br>}<br><br><br><br>a_{23}\\ \mathrm{\lambda <br><br>}<br><br><br><br>a_{31}& \mathrm{\lambda <br><br>}<br><br><br><br>a_{32}& \mathrm{\lambda <br><br>}<br><br><br><br>a_{33}\end{array}\right)$

that is obtained by multiplying an affine transformation matrix $A=\left(\begin{array}{ccc}{a}_{11}& a_{12}& a_{13}\\ a_{21}& a_{22}& a_{23}\\ a_{31}& a_{32}& a_{33}\end{array}\right)$

by λ

(≠

0), a matrix (t₁,t₂,t₃)^t, and a shape data are stored; and

calculation means for, in transforming the coordinates (x,y,z)^t of said shape data into the coordinates (x′

,y′

,z′

)^t by means of an affine transformation of the matrix A and the matrix (t₁,t₂,t₃)^t, reading the matrix A′ and

the matrix (t₁,t₂,t₃)^t from said memory, and calculating

x′

=(a′

₁₁*x+a′

₁₂*y+a′

₁₃*z)/λ

+t₁;

y′

=(a′

₂₁*x+a′

₂₂*y+a′

₂₃*z)/λ

+t₂;

z′

=(a′

₃₁*x+a′

₃₂*y+a′

₃₃*z)/λ

+t₃;

to calculate the coordinates (x′

,y′

,z′

)^t.

4. An information processing apparatus recited in claim 3, characterized in that said λ

is limited to 2ⁿ(n≧

1), and

said calculation means is means for calculating divisional calculation of

x′

=(a′

₁₁*x+a′

₁₂*y+a′

₁₃*z)/λ

+t₁;

y′

=(a′

₂₁*x+a′

₂₂*y+a′

₂₃*z)/λ

+t₂;

z′

=(a′

₃₁*x+a′

₃₂*y+a′

₃₃*z)/λ

+t₃;

by conducting right-shifting by n digits.

5. An information processing apparatus recited in claim 4, characterized in that said calculation means is means for conducting the calculation by conducting right-shifting by n digits after adding a constant λ

/2 to each number to be divided.

6. An information processing apparatus recited in claim 3, characterized in that the apparatus comprises synthesis means for synthesizing two or more parameters that are multiplied by λ

(≠

0) in advance.

7. An information processing apparatus recited in claim 4, characterized in that the apparatus comprises synthesis means for synthesizing two or more parameters that are multiplied by λ

(≠

0) in advance.

8. An information processing apparatus recited in claim 5, characterized in that the apparatus comprises synthesis means for synthesizing two or more parameters that are multiplied by λ

(≠

0) in advance.

9. An imaging processing method of, in conducting Rasterize processing of imaging of a three-dimensional image, calculating a quantity of a change of x coordinates $\Delta$

⁢

⁢

x=x2-x1y2-y1

to y coordinates of a straight line passing through a point P₁(x₁,y₁) and a point P₂(x₂,y₂) on a two-dimensional plain, characterized in that said method comprises steps of;

in calculating Δ

x, reading μ

corresponding to a quantity of a change of y coordinates of Δ

x to be calculated, from a memory in which the constant μ

representative of $\mathrm{\mu <br><br>}=\frac{\mathrm{\lambda <br><br>}}{y_2-y_1}$

is stored in association with the quantity of the change of the y coordinates; and

based on said μ

that was read, calculating

Δ

x′

=μ

*(x₂−

x₁);

by means of multiplication, and calculating this result as Δ

x.

10. An imaging processing method recited in claim 9, characterized in that, said λ

is limited to 2ⁿ(n≧

1), and the method further comprises a step of calculating Δ

x by right-shifting said calculated Δ

x′

by n digits.

11. An imaging processing method recited in claim 9 or claim 10, in which coordinate values are limited to integers, and transformation processing is applied to coordinates (x,y,z)^t to create coordinates (x′

,y′

,z′

)^t by means of an affine transformation representative of $\left(\begin{array}{c}{x}^{\mathrm{\prime <br><br>}}\\ y^{\mathrm{\prime <br><br>}}\\ z^{\mathrm{\prime <br><br>}}\end{array}\right)=A<br><br>\left(\begin{array}{c}x\\ y\\ z\end{array}\right)+\left(\begin{array}{c}{t}_1\\ t_2\\ t_3\end{array}\right),$

characterized in that the method comprises steps of;

in transforming the coordinates (x,y,z)^t of a shape data into the coordinates (x′

,y′

,z′

)^t by means of an affine transformation of a matrix A and a matrix (t₁,t₂,t₃)^t, reading a parameter A′

$A^{\mathrm{\prime <br><br>}}=\left(\begin{array}{ccc}{a}_{11}^{\mathrm{\prime <br><br>}}& a_{12}^{\mathrm{\prime <br><br>}}& a_{13}^{\mathrm{\prime <br><br>}}\\ a_{21}^{\mathrm{\prime <br><br>}}& a_{22}^{\mathrm{\prime <br><br>}}& a_{23}^{\mathrm{\prime <br><br>}}\\ a_{31}^{\mathrm{\prime <br><br>}}& a_{32}^{\mathrm{\prime <br><br>}}& a_{33}^{\mathrm{\prime <br><br>}}\end{array}\right)=\mathrm{\lambda <br><br>}<br><br><br><br>A=\left(\begin{array}{ccc}\mathrm{\lambda <br><br>}<br><br><br><br>a_{11}& \mathrm{\lambda <br><br>}<br><br><br><br>a_{12}& \mathrm{\lambda <br><br>}<br><br><br><br>a_{13}\\ \mathrm{\lambda <br><br>}<br><br><br><br>a_{21}& \mathrm{\lambda <br><br>}<br><br><br><br>a_{22}& \mathrm{\lambda <br><br>}<br><br><br><br>a_{23}\\ \mathrm{\lambda <br><br>}<br><br><br><br>a_{31}& \mathrm{\lambda <br><br>}<br><br><br><br>a_{32}& \mathrm{\lambda <br><br>}<br><br><br><br>a_{33}\end{array}\right)$

that is obtained by multiplying the matrix A by λ

(≠

0), and the matrix (t₁,t₂,t₃)^t, which are stored in a memory; and

based on said read matrix A′ and

matrix (t₁,t₂,t₃)^t, calculating

x′

=(a′

₁₁*x+a′

₁₂*y+a′

₁₃*z)/λ

+t₁;

y′

=(a′

₂₁*x+a′

₂₂*y+a′

₂₃*z)/λ

+t₂;

z′

=(a′

₃₁*x+a′

₃₂*y+a′

₃₃*z)/λ

+t₃;

and calculating the coordinates (x′

,y′

,z′

)^t.

12. An imaging processing method recited in claim 11, characterized in that said λ

is limited to 2ⁿ(n≧

1), and

said calculating step is a step of calculating division of

x′

=(a′

₁₁*x+a′

₁₂*y+a′

₁₃*z)/λ

+t₁;

y′

=(a′

₂₁*x+a′

₂₂*y+a′

₂₃*z)/λ

+t₂;

z′

=(a′

₃₁*x+a′

₃₂*y+a′

₃₃*z)/λ

+t₃;

by conducting right-shifting by n digits to calculate the coordinates (x′

,y′

,z′

)^t.

13. An imaging processing method recited in claim 12, characterized in that the method further comprises a step of adding a constant λ

/2 to each number to be divided before conducting said right-shifting by n digits.

14. An imaging processing method recited in claim 11, characterized in that the method further comprises a step of synthesizing two or more parameters that are multiplied by λ

(≠

0) in advance.

15. An imaging processing method recited in claim 12, characterized in that the method further comprises a step of synthesizing two or more parameters that are multiplied by λ

(≠

0) in advance.

16. An imaging processing method recited in claim 13, characterized in that the method further comprises a step of synthesizing two or more parameters that are multiplied by λ

(≠

0) in advance.

17. A program for, in conducting Rasterize processing of imaging of a three-dimensional image, making an information processing apparatus conduct calculation processing for calculating a quantity of a change of x coordinates $\Delta$

⁢

⁢

x=x2-x1y2-y1

to y coordinates of a straight line passing through a point P₁(x₁,y₁) and a point P₂(x₂,y₂) on a two-dimensional plain, characterized in that said program comprises steps of;

in calculating Δ

x, reading μ

corresponding to a quantity of a change of y coordinates of Δ

x to be calculated, from a memory in which the constant μ

representative of $\mathrm{\mu <br><br>}=\frac{\mathrm{\lambda <br><br>}}{y_2-y_1}$

is stored in association with the quantity of the change of the y coordinates; and

based on said μ

that was read, calculating

Δ

x′

=μ

*(x₂−

x₁);

by means of multiplication, and calculating this result as Δ

x.

18. A program recited in claim 17, characterized in that, in the information processing apparatus, said λ

is limited to 2ⁿ(n≧

1), and the program further comprises a step of calculating Δ

x by right-shifting said calculated Δ

x′

by n digits.

19. A program recited in claim 17 or claim 18, in making an information processing apparatus apply transformation processing to coordinates (x,y,z)^t to create coordinates (x′

,y′

,z′

)^t by means of an affine transformation representative of $\left(\begin{array}{c}{x}^{\mathrm{\prime <br><br>}}\\ y^{\mathrm{\prime <br><br>}}\\ z^{\mathrm{\prime <br><br>}}\end{array}\right)=A<br><br>\left(\begin{array}{c}x\\ y\\ z\end{array}\right)+\left(\begin{array}{c}{t}_1\\ t_2\\ t_3\end{array}\right),$

wherein coordinate values are limited to integers, characterized in that the program comprises steps of;

in transforming the coordinates (x,y,z)^t of the shape data into the coordinates (x′

,y′

,z′

)^t by means of an affine transformation of a matrix A and a matrix (t₁,t₂,t₃)^t, reading a parameter A′

$A^{\mathrm{\prime <br><br>}}=\left(\begin{array}{ccc}{a}_{11}^{\mathrm{\prime <br><br>}}& a_{12}^{\mathrm{\prime <br><br>}}& a_{13}^{\mathrm{\prime <br><br>}}\\ a_{21}^{\mathrm{\prime <br><br>}}& a_{22}^{\mathrm{\prime <br><br>}}& a_{23}^{\mathrm{\prime <br><br>}}\\ a_{31}^{\mathrm{\prime <br><br>}}& a_{32}^{\mathrm{\prime <br><br>}}& a_{33}^{\mathrm{\prime <br><br>}}\end{array}\right)=\mathrm{\lambda <br><br>}<br><br><br><br>A=\left(\begin{array}{ccc}\mathrm{\lambda <br><br>}<br><br><br><br>a_{11}& \mathrm{\lambda <br><br>}<br><br><br><br>a_{12}& \mathrm{\lambda <br><br>}<br><br><br><br>a_{13}\\ \mathrm{\lambda <br><br>}<br><br><br><br>a_{21}& \mathrm{\lambda <br><br>}<br><br><br><br>a_{22}& \mathrm{\lambda <br><br>}<br><br><br><br>a_{23}\\ \mathrm{\lambda <br><br>}<br><br><br><br>a_{31}& \mathrm{\lambda <br><br>}<br><br><br><br>a_{32}& \mathrm{\lambda <br><br>}<br><br><br><br>a_{33}\end{array}\right)$

that is obtained by multiplying the matrix A by λ

(≠

0), and the matrix (t₁,t₂,t₃)^t, which are stored in a memory; and

based on said read matrix A′ and

matrix (t₁, t₂, t₃)^t, calculating

x′

=(a′

₁₁*x+a′

₁₂*y+a′

₁₃*z)/λ

+t₁;

y′

=(a′

₂₁*x+a′

₂₂*y+a′

₂₃*z)/λ

+t₂;

z′

=(a′

₃₁*x+a′

₃₂*y+a′

₃₃*z)/λ

+t₃;

to calculate the coordinates (x′

,y′

,z′

)^t.

20. A program recited in claim 19, characterized in that, in case that said λ

is limited to 2ⁿ(n≧

1), said calculating step in said program is a step of, in the information processing apparatus, calculating division of

x′

=(a′

₁₁*x+a′

₁₂*y+a′

₁₃*z)/λ

+t₁;

y′

=(a′

₂₁*x+a′

₂₂*y+a′

₂₃*z)/λ

+t₂;

z′

=(a′

₃₁*x+a′

₃₂*y+a′

₃₃*z)/λ

+t₃;

by conducting right-shifting by n digits to calculate the coordinates (x′

,y′

,z′

)^t.

21. A program recited in claim 20, characterized in that, in the information processing apparatus, the program further comprises a step of adding a constant λ

/2 to each number to be divided before conducting said right-shifting by n digits.

22. A program recited in claim 19, characterized in that, in the information processing apparatus, the program further comprises a step of synthesizing two or more parameters that are multiplied by λ

(≠

0) in advance.

23. A program recited in claim 20, characterized in that, in the information processing apparatus, the program further comprises a step of synthesizing two or more parameters that are multiplied by λ

(≠

0) in advance.

24. A program recited in claim 21, characterized in that, in the information processing apparatus, the program further comprises a step of synthesizing two or more parameters that are multiplied by λ

(≠

0) in advance.

25. A record medium in which a program for, in conducting Rasterize processing of imaging of a three-dimensional image, making an information processing apparatus conduct calculation processing for calculating a quantity of a change of x coordinates $\Delta$

⁢

⁢

x=x2-x1y2-y1

to y coordinates of a straight line passing through a point P₁(x₁,y₁) and a point P₂(x₂,y₂) on a two-dimensional plain, characterized in that said program comprises steps of;

in calculating Δ

x, reading μ

corresponding to a quantity of a change of y coordinates of Δ

x to be calculated, from a memory in which the constant μ

representative of $\mathrm{\mu <br><br>}=\frac{\mathrm{\lambda <br><br>}}{y_2-y_1}$

is stored in association with the quantity of the change of the y coordinates; and

based on said μ

that was read, calculating

Δ

x′

=μ

*(x₂−

x₁);

by means of multiplication, and calculating this result as Δ

x.

26. A record medium in which the program is stored recited in claim 25, characterized in that, in the information processing apparatus, said λ

is limited to 2ⁿ(n≧

1), and the program further comprises a step of calculating Δ

x by right-shifting said calculated Δ

x′

by n digits.

27. A record medium in which the program is stored recited in claim 25 or claim 26, in making an information processing apparatus apply transformation processing to coordinates (x,y,z)^t to create coordinates (x′

,y′

,z′

)^t by means of an affine transformation representative of $\left(\begin{array}{c}{x}^{\mathrm{\prime <br><br>}}\\ y^{\mathrm{\prime <br><br>}}\\ z^{\mathrm{\prime <br><br>}}\end{array}\right)=A<br><br>\left(\begin{array}{c}x\\ y\\ z\end{array}\right)+\left(\begin{array}{c}{t}_1\\ t_2\\ t_3\end{array}\right),$

wherein coordinate values are limited to integers, characterized in that the program comprises steps of;

in transforming the coordinates (x,y,z)^t of the shape data into the coordinates (x′

,y′

,z′

)^t by means of an affine transformation of a matrix A and a matrix (t₁,t₂,t₃)^t, reading a parameter A′

$A^{\mathrm{\prime <br><br>}}=\left(\begin{array}{ccc}{a}_{11}^{\mathrm{\prime <br><br>}}& a_{12}^{\mathrm{\prime <br><br>}}& a_{13}^{\mathrm{\prime <br><br>}}\\ a_{21}^{\mathrm{\prime <br><br>}}& a_{22}^{\mathrm{\prime <br><br>}}& a_{23}^{\mathrm{\prime <br><br>}}\\ a_{31}^{\mathrm{\prime <br><br>}}& a_{32}^{\mathrm{\prime <br><br>}}& a_{33}^{\mathrm{\prime <br><br>}}\end{array}\right)=\mathrm{\lambda <br><br>}<br><br><br><br>A=\left(\begin{array}{ccc}\mathrm{\lambda <br><br>}<br><br><br><br>a_{11}& \mathrm{\lambda <br><br>}<br><br><br><br>a_{12}& \mathrm{\lambda <br><br>}<br><br><br><br>a_{13}\\ \mathrm{\lambda <br><br>}<br><br><br><br>a_{21}& \mathrm{\lambda <br><br>}<br><br><br><br>a_{22}& \mathrm{\lambda <br><br>}<br><br><br><br>a_{23}\\ \mathrm{\lambda <br><br>}<br><br><br><br>a_{31}& \mathrm{\lambda <br><br>}<br><br><br><br>a_{32}& \mathrm{\lambda <br><br>}<br><br><br><br>a_{33}\end{array}\right)$

that is obtained by multiplying the matrix A by λ

(≠

0), and the matrix (t₁,t₂,t₃)^t, which are stored in a memory; and

based on said read matrix A′ and

matrix (t₁,t₂,t₃)^t, calculating

x′

=(a′

₁₁*x+a′

₁₂*y+a′

₁₃*z)/λ

+t₁;

y′

=(a′

₂₁*x+a′

₂₂*y+a′

₂₃*z)/λ

+t₂;

z′

=(a′

₃₁*x+a′

₃₂*y+a′

₃₃*z)/λ

+t₃;

to calculate the coordinates (x′

,y′

,z′

)^t.

28. A record medium in which the program is stored recited in claim 27, characterized in that, in case that said λ

is limited to 2ⁿ(n≧

1),

said calculating step in said program is a step of, in the information processing apparatus, calculating division of

x′

=(a′

₁₁*x+a′

₁₂*y+a′

₁₃*z)/λ

+t₁;

y′

=(a′

₂₁*x+a′

₂₂*y+a′

₂₃*z)/λ

+t₂;

z′

=(a′

₃₁*x+a′

₃₂*y+a′

₃₃*z)/λ

+t₃;

by conducting right-shifting by n digits to calculate the coordinates (x′

,y′

,z′

)^t.

29. A record medium in which the program is stored recited in claim 28, characterized in that, in the information processing apparatus, said program further comprises a step of adding a constant λ

/2 to each number to be divided before conducting said right-shifting by n digits.

30. A record medium in which the program is stored recited in claim 27, characterized in that, in the information processing apparatus, said program further comprises a step of synthesizing two or more parameters that are multiplied by λ

(≠

0) in advance.

31. A record medium in which the program is stored recited in claim 28, characterized in that, in the information processing apparatus, said program further comprises a step of synthesizing two or more parameters that are multiplied by λ

(≠

0) in advance.

32. A record medium in which the program is stored recited in claim 29, characterized in that, in the information processing apparatus, said program further comprises a step of synthesizing two or more parameters that are multiplied by λ

(≠

0) in advance.