Image processing apparatus

Abstract

An image processing apparatus generates a sub-self-similar set F, which is a subset of a self-similar set A with respect to contraction maps f1, . . . , fn and forms an image expressing the sub-self-similar set F. The apparatus includes a base-address-set designating section, a generation-rule acquiring section and a sub-self-similar set generating section. The base-address-set designating section selects m addresses each of which formed of infinite sequence of {1, . . . , n} and generates a base address set M including the selected addresses. The generation-rule acquiring section acquires a rule of generating a hypothetical sub-self-similar set G, which is a subset of a hypothetical self-similar set B with respect to n hypothetical contraction maps g1, . . . , gn, by using the generated base address set M. The sub-self-similar set generating section generates a sub-self-similar set F, which is a subset of the self-similar set A.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a flow chart for explaining a processing flow in an image processing system according to an exemplary embodiment of the invention;

FIG. 2 is a diagram for explaining the functional configuration of the image processing system according to the exemplary embodiment;

FIG. 3 is a view for explaining an arcwise connected self-similar set in the exemplary embodiment;

FIG. 4 is a view for explaining a self-similar set as a first example of the exemplary embodiment;

FIG. 5 is a view for explaining a sub-self-similar set in the first example of the exemplary embodiment;

FIG. 6 is a view for explaining a self-similar set as a second example of the exemplary embodiment;

FIG. 7 is a view for explaining a sub-self-similar set (1) in the second example of the exemplary embodiment;

FIG. 8 is a view for explaining a sub-self-similar set (2) in the second example of the exemplary embodiment;

FIG. 9 is a view for explaining a sub-self-similar set (3) in the second example of the exemplary embodiment;

FIG. 10 is a view for explaining a sub-self-similar set (4) in the second example of the exemplary embodiment;

FIG. 11 is a view for explaining a sub-self-similar set (5) in the second example of the exemplary embodiment;

FIG. 12 is a view for explaining a sub-self-similar set (6) in the second example of the exemplary embodiment;

FIG. 13 is a view for explaining a sub-self-similar set (7) in the second example of the exemplary embodiment;

FIG. 14 is a view for typically explaining the first and second examples of the exemplary embodiment;

FIG. 15 is a view for typically explaining the first and second examples of the exemplary embodiment;

FIG. 16 is a view for typically explaining a third example of the exemplary embodiment;

FIG. 17 is a view (the same as FIG. 15) for typically explaining the third example of the exemplary embodiment

Claims

1. An image processing apparatus for generating a sub-self-similar set F, which is a subset of a self-similar set A with respect to a plurality of contraction maps f1, . . . , fn where n is a natural number and larger than 1, and for forming an image expressing the sub-self-similar set F, the apparatus comprising: a base-address-set designating section that selects m addresses each of which formed of infinite sequence of {1, . . . , n} and generates a base address set M including the selected addresses;a generation-rule acquiring section that acquires a rule of generating a hypothetical sub-self-similar set G, which is a subset of a hypothetical self-similar set B with respect to n hypothetical contraction maps g1, . . . , gn, by using the generated base address set M; anda sub-self-similar set generating section that generates a sub-self-similar set F, which is a subset of the self-similar set A, by applying the acquired generation rule to the contraction maps f1, . . . , fn.

2. The apparatus according to claim 1, further comprising: a self-similar set designating section that allows a user to input the plurality of contraction maps f1, . . . , fn and generates the self-similar set A with respect to the input contraction maps f1, . . . , fn.

3. The apparatus according to claim 2, wherein: the self-similar set designating section allows the user to select p points from an overlap portion of at least two of f1(A), . . . , fn(A), andthe m addresses with p<m selected by the base-address-set designating section correspond to the p points selected by the user.

4. The apparatus according to claim 2, wherein: the self-similar set designating section allows the user to select m addresses, andthe m addresses selected by the base-address-set designating section correspond to the m addresses selected by the user.

5. The apparatus according to claim 1, further comprising: an image drawing section that forms the image based on the sub-self-similar set F.

6. The apparatus according to claim 1, wherein the generation-rule acquiring section selects the hypothetical contraction maps g1, . . . , gn so that entire addresses of an overlap portion of g1(B), . . . , gn(B) coincide with the base address set M.

7. The apparatus according to claim 1, wherein the generation-rule acquiring section determine a generation address set P which is the projection of the whole of backward shift of the base address set M onto the hypothetical self-similar set B, to hypothetically determine the sub-self-similar set G as the smallest sub-continuum of the self-similar set B which include a generation address set P.

8. The apparatus according to claim 1, wherein: the generation-rule acquiring section determines a sofic system to hypothetically determine the sub-self-similar set G as a sum of finite number of subsets Gi.

9. The apparatus according to claim 1, wherein the self-similar set A with respect to the n contraction maps f1, . . . , fn is arcwise connected.

10. The apparatus according to claim 9, wherein: the self-similar set designating section that allows a user to select p points from an overlap portion of the self-similar set A, andthe base-address-set designating section adopts whole pseudo addresses of the selected points as the base address set M.

11. The apparatus according to claim 1, wherein the base-address-set designating section selects the base address set M so that the sub-self-similar set G does not contain any closed curve.

12. The apparatus according to claim 1, wherein the sub-self-similar set generating section maps the sub-self-similar set F predetermined number of times by the respective contraction maps f1, . . . , fn to form a new sub-self-similar set.

13. An image processing method for generating a sub-self-similar set F, which is a subset of a self-similar set A with respect to a plurality of contraction maps f1, . . . , fn where n is a natural number and larger than 1, and for forming an image expressing the sub-self-similar set F, the method comprising: selecting m addresses each of which formed of infinite sequence of {1, . . . , n} and generates a base address set M including the selected addresses;acquiring a rule of generating a hypothetical sub-self-similar set G, which is a subset of a hypothetical self-similar set B with respect to n hypothetical contraction maps g1, . . . , gn, by using the generated base address set M; andgenerating a sub-self-similar set F, which is a subset of the self-similar set A, by applying the acquired generation rule to the contraction maps f1, . . . , fn.

14. A computer readable medium storing a program causing a computer to execute a process for generating a sub-self-similar set F, which is a subset of a self-similar set A with respect to a plurality of contraction maps f1, . . . , fn where n is a natural number and larger than 1, and for forming an image expressing the sub-self-similar set F, the process comprising: selecting m addresses each of which formed of infinite sequence of {1, . . . , n} and generates abase address set M including the selected addresses;acquiring a rule of generating a hypothetical sub-self-similar set G, which is a subset of a hypothetical self-similar set B with respect to n hypothetical contraction maps g1, . . . , gn, by using the generated base address set; andgenerating a sub-self-similar set F, which is a subset of the self-similar set A, by applying the acquired generation rule to the contraction maps f1, . . . , fn.

15. A computer data signal embodied in a carrier wave for enabling a computer to perform a process for generating a sub-self-similar set F, which is a subset of a self-similar set A with respect to a plurality of contraction maps f1, . . . , fn where n is a natural number and larger than 1, and for forming an image expressing the sub-self-similar set F, the process comprising: selecting m addresses each of which formed of infinite sequence of {1, . . . , n} and generates a base address set M including the selected addresses;acquiring a rule of generating a hypothetical sub-self-similar set G, which is a subset of a hypothetical self-similar set B with respect to n hypothetical contraction maps g1, . . . , gn, by using the generated base address set M; andgenerating a sub-self-similar set F, which is a subset of the self-similar set A, by applying the acquired generation rule to the contraction maps f1, . . . , fn.