Method and system for recovering a code image including blurring

1. An image processing system characterized by comprising:

a hardware including a processor;

an error-function determining unit, implemented by the processor, for making use of a blur function serving as a function representing the degree of blurring of a blurred input image and a geometrical-deformation matrix serving as a matrix for restricting an operation to lay out a 2-dimensional code shown by the input image on cells each serving as a configuration unit, implemented by the processor, of the 2-dimensional code in order to determine an error function serving as a function satisfying a relation that, the smaller the error between the input image and an image obtained by adding geometrical deformations and blurs to a recovered image obtained from a recovering process, the more the approach to a result determined in advance;

a pixel-value restricting unit, implemented by the processor, for determining pixel-value restriction information prescribing a restriction condition for a restriction imposed on a predetermined pixel value obtained from discretization of pixel values of the 2-dimensional code to be recovered;

an objective-function determining unit, implemented by the processor, for making use of the error function and the pixel-value restriction information as a basis for determining an objective function serving as a function satisfying a relation that, the closer the recovered image to the true image, the more the approach to a result determined in advance; and

an objective-function optimizing unit, implemented by the processor, for determining a recovered image which optimizes the objective function.

2. The image processing system according to claim 1 wherein:

the error-function determining unit determines an error function having an error-function value varying in such a way that, the smaller the error between the input image and an image obtained by adding geometrical deformations and blurs to the recovered image, the smaller the error-function value;

as a restriction condition, the pixel-value restricting unit, implemented by the processor, determines pixel-value restriction information taking a pixel-value restricting function serving as a function showing that, the closer the pixel values of pixels included in an image to any one of discretized pixel values, the more appropriate the image;

on the basis of the error function and the pixel-value restriction information, the objective-function determining unit, implemented by the processor, determines an objective function having an objective-function value varying in such a way that, the closer the recovered image to the true image, the smaller the objective-function value; and

the objective-function optimizing unit determines a recovered image which minimizes the objective function.

3. The image processing system according to claim 1 wherein:

the error-function determining unit determines an error function having an error-function value varying in such a way that, the smaller the error between the input image and an image obtained by adding geometrical deformations and blurs to the recovered image, the smaller the error-function value;

as pixel-value restriction information, the pixel-value restricting unit determines a restriction condition requiring that pixel values possible for the recovered image be discrete values the number of which is determined in advance;

the objective-function determining unit determines an objective function having objective-function values which are any ones of the discrete values determined as a restriction condition of the pixel-value restriction information; and

the objective-function optimizing unit determines a recovered image which minimizes the objective function.

4. The image processing system according to claim 1 , the system further having a pixel-value discretizing unit, implemented by the processor, for discretizing pixel values of a recovered image determined by the objective-function optimizing unit by making use of a threshold value determined in advance in order to generate a recovered image.

5. The image processing system according to claim 1 , the system further having:

a marker detecting unit, implemented by the processor, for detecting markers of a 2-dimensional code;

a cell-layout inferring unit, implemented by the processor, for inferring a cell layout of the 2-dimensional code from the markers detected by the marker detecting unit;

a blur-function determining unit, implemented by the processor, for determining a blur function for an input image;

a geometrical-deformation inferring unit, implemented by the processor, for inferring a geometrical-deformation matrix from the inferred cell layout of the 2-dimensional code; and

an optimized-area specifying unit, implemented by the processor, for specifying an area of the input image to be recovered,

wherein the error-function determining unit determines an error function on the basis of the input image, the blur function determined by the blur-function determining unit and the geometrical-deformation matrix inferred by the geometrical-deformation inferring unit.

6. The image processing system according to claim 5 , the system further having:

a plural-marker detecting unit, implemented by the processor, for detecting all markers existing in an image as markers having a plurality of types;

a code-type identifying unit, implemented by the processor, for identifying the type of a code of each detected marker; and

a blur-removal determining unit, implemented by the processor, for determining whether or not blur removal has been carried out for all codes in a recovered image determined by the objective-function optimizing unit,

wherein the cell-layout inferring unit infers a cell layout of a 2-dimensional code from markers detected by the plural-marker detecting unit.

7. The image processing system according to claim 1 , the system further having a simultaneously-optimized-variable specifying unit, implemented by the processor, for specifying elements among elements composing the objective function as variables to be simultaneously optimized by the objective-function optimizing unit,

wherein the objective-function optimizing unit determines a recovered image optimizing the objective function and determines the elements specified by the simultaneously-optimized-variable specifying unit.

8. The image processing system according to claim 1 , the system further having:

a cell-layout inputting unit, implemented by the processor, for receiving a cell layout of a 2-dimensional code;

a geometrical-deformation inputting unit, implemented by the processor, for receiving a geometrical-deformation matrix; and

a blur-function inputting unit, implemented by the processor, for receiving a blur function, wherein:

the error-function determining unit determines an error function by making use of the geometrical-deformation matrix received by the geometrical-deformation inputting unit and the blur function received by the blur-function inputting unit; and

the pixel-value restricting unit determines pixel-value restriction information on the basis of a cell layout received by the cell-layout inputting unit as the cell layout of a 2-dimensional code.

9. An image processing method characterized in that the method is carried out by:

determining an error function by making use of a blur function serving as a function representing the degree of blurring of a blurred input image and a geometrical-deformation matrix serving as a matrix for restricting an operation to lay out a 2-dimensional code shown by the input image on cells each serving as a configuration unit of the 2-dimensional code wherein the error function is a function satisfying a relation that, the smaller the error between the input image and an image obtained by adding geometrical deformations and blurs to a recovered image obtained from a recovering process, the more the approach to a result determined in advance;

determining pixel-value restriction information prescribing a restriction condition for a restriction imposed on a predetermined pixel value obtained from discretization of pixel values of the 2-dimensional code to be recovered;

determining an objective function on the basis of the error function and the pixel-value restriction information wherein the objective function is a function satisfying a relation that, the closer the recovered image to the true image, the more the approach to a result determined in advance; and

determining a recovered image which optimizes the objective function.

10. A non-transitory computer readable information recording medium storing an image processing program that, when executed by a processor, performs a method for:

determining an error function by making use of a blur function serving as a function representing the degree of blurring of a blurred input image and a geometrical-deformation matrix serving as a matrix for restricting an operation to lay out a 2-dimensional code shown by the input image on cells each serving as a configuration unit of the 2-dimensional code wherein the error function is a function satisfying a relation that, the smaller the error between the input image and an image obtained by adding geometrical deformations and blurs to a recovered image obtained from a recovering process, the more the approach to a result determined in advance;

determining pixel-value restriction information prescribing a restriction condition for a restriction imposed on a predetermined pixel value obtained from discretization of pixel values of the 2-dimensional code to be recovered;

determining an objective function on the basis of the error function and the pixel-value restriction information wherein the objective function is a function satisfying a relation that, the closer the recovered image to the true image, the more the approach to a result determined in advance; and

determining a recovered image which optimizes the objective function.