Apparatus and method for nonlinear normalization of image

An apparatus for nonlinear normalization of an image, which performs pre-processing for computing the correlation between an unknown character and a reference pattern, the unknown character being formed of lines and having a line pitch in the X direction and a line pitch in the Y direction, said apparatus comprising:

• means for obtaining a local spatial density function .rho.(X.sub.i, Y.sub.j) (i=1-I, j=1-J) from a two-dimensional pattern f(X.sub.i, Y.sub.j) which is obtained by sampling said unknown character at a sampling interval .gamma., said spatial density function .rho.(X.sub.i, Y.sub.j) being obtained as a correlate of both the line pitch in the X direction and the line pitch in the Y direction;
• means for computing an X-direction cumulative function hx(Xi) by successively adding said spatial density function .rho.(X.sub.i, Y.sub.j) while Y.sub.j is varied from Y.sub.1 to Y.sub.J and X.sub.i is fixed;
• means for computing a Y-direction cumulative function hy(Y.sub.j) by successively adding said spatial density function .rho.(X.sub.i, Y.sub.j) while Xi is varied from X.sub.1 to X.sub.I and Y.sub.j is fixed;
• means for extending said cumulative functions hx(X.sub.i) and hy(Y.sub.j) into continuous cumulative functions hx(X) and hy(Y), respectively;
• means for determining new sampling points (X.sub.i, Y.sub.j) at new sampling intervals (.delta.i, .epsilon.j) in the X and Y directions, the new sampling intervals satisfying the condition that the product of said cumulative function hx(X.sub.i) and .delta.i takes a first fixed value, and the product of said cumulative function hy(Y.sub.j) and .epsilon.j takes a second fixed value;
• and
• means for computing normalized sampled values at said new sampling points (X.sub.i, Y.sub.j) by resampling said unknown character or by performing a computation on said two-dimensional pattern f(X.sub.i, Y.sub.j),
• wherein said correlate of both the line pitch in the X direction and the line pitch in the Y direction is the sum of a term which includes the reciprocal of the line pitch in the X direction and a term which includes the reciprocal of the line pitch in the Y direction.

An apparatus for nonlinear normalization of an image, which performs pre-processing for computing the correlation between an unknown character and a reference pattern, the unknown character being formed of lines and having a line pitch in the X direction and a line pitch in the Y direction, said apparatus comprising:

• means for obtaining a local spatial density function .rho.(X.sub.i, Y.sub.j) (i=1-I, j=1-J) from a two-dimensional pattern f(X.sub.i, Y.sub.j) which is obtained by sampling said unknown character at a sampling interval .gamma., said spatial density function .rho.(X.sub.i, Y.sub.j) being obtained as a correlate of both the line pitch in the X direction and the line pitch in the Y direction;
• means for computing an X-direction cumulative function hx(Xi) by successively adding said spatial density function .rho.(X.sub.i, Y.sub.j) while Y.sub.j is varied from Y.sub.1 to Y.sub.J and X.sub.i is fixed;
• means for computing a Y-direction cumulative function hy(Y.sub.j) by successively adding said spatial density function .rho.(X.sub.i, Y.sub.j) while Xi is varied from X.sub.1 to X.sub.I and Y.sub.j is fixed;
• means for extending said cumulative functions hx(X.sub.i) and hy(Y.sub.j) into continuous cumulative functions hx(X) and hy(Y), respectively;
• means for determining new sampling points (X.sub.i, Y.sub.j) at new sampling intervals (.delta.i, .epsilon.j) in the X and Y directions, the new sampling intervals satisfying the condition that the product of said cumulative function hx(X.sub.i) and .delta.i takes a first fixed value, and the product of said cumulative function hy(Y.sub.j) and .epsilon.j takes a second fixed value;
• and
• means for computing normalized sampled values at said new sampling points (X.sub.i, Y.sub.j) by resampling said unknown character or by performing a computation on said two-dimensional pattern f(X.sub.i, Y.sub.j),
• wherein said correlate of both the line pitch in the X direction and the line pitch in the Y direction is the reciprocal of the sum of a term which includes the line pitch in the X direction and a term which includes the line pitch in the Y direction.

An apparatus for nonlinear normalization of an image, which performs pre-processing for computing the correlation between an unknown character and a reference pattern, the unknown character being formed of lines and having a line pitch in the X direction and a line pitch in the Y direction, said apparatus comprising:

• means for obtaining a set of feature parameters from a two-dimensional pattern f(X.sub.i, Y.sub.j) (i=1-M, j=1-N) which is obtained by sampling said unknown character at a sampling interval .gamma.;
• means for computing a local spatial density function .rho.(X.sub.i, Y.sub.j) from said two-dimensional pattern f(X.sub.i, Y.sub.j), said spatial density function .rho.(X.sub.i, Y.sub.j) being obtained as a correlate of both the line ditch in the X direction and the line pitch in the Y direction;
• means for computing an X-direction cumulative function hx(X.sub.i) by successively adding said spatial density function .rho.(X.sub.i, Y.sub.j) while Y.sub.j is varied from Y.sub.1 to Y.sub.J and X.sub.i is fixed;
• means for computing a Y-direction cumulative function hy(Y.sub.j) by successively adding said spatial density function .rho.(X.sub.i, Y.sub.j) while Xi is varied from X.sub.1 to X.sub.I and Y.sub.j is fixed;
• means for extending said cumulative functions hx(X.sub.i) and hy(Y.sub.j) into continuous cumulative functions h.sub.x (X) and h.sub.y (Y), respectively;
• means for matching coordinates of said set of feature parameters and coordinates of said spatial density function .rho.(X.sub.i, Y.sub.j);
• and
• means for determining new sampling points (X.sub.i, Y.sub.j) of said set of feature parameters at new sampling intervals (.delta.i, .epsilon.j) in the X and Y directions, the new sampling intervals satisfying the condition that the product of said cumulative function hx(X.sub.i) and .delta.i takes a first fixed value, and the product of said cumulative function hy(y.sub.j) and .epsilon.j takes a second fixed value,
• wherein said correlate of both the line pitch in the X direction and the line pitch in the Y direction is a function of the product of the reciprocals of said line pitches in the X and Y directions.

An apparatus for nonlinear normalization of an image, which performs pre-processing for computing the correlation between an unknown character and a reference pattern, the unknown character being formed of lines and having a line pitch in the X direction and a line pitch in the Y direction, said apparatus comprising:

• means for obtaining a set of feature parameters from a two-dimensional pattern f(X.sub.i, Y.sub.j) (i=1-M, j=1-N) which is obtained by sampling said unknown character at a sampling interval .gamma.;
• means for computing a local spatial density function .rho.(X.sub.i, Y.sub.j) from said two-dimensional pattern f(X.sub.i, Y.sub.j), said spatial density function .rho.(X.sub.i, Y.sub.j) being obtained as a correlate of both the line pitch in the X direction and the line pitch in the Y direction;
• means for computing an X-direction cumulative function hx(X.sub.i) by successively adding said spatial density function .rho.(X.sub.i, Y.sub.j) while Y.sub.j is varied from Y.sub.1 to Y.sub.J and X.sub.i is fixed;
• means for computing a Y-direction cumulative function hy(Y.sub.j) by successively adding said spatial density function .rho.(X.sub.i, Y.sub.j) while Xi is varied from X.sub.1 to X.sub.I and Y.sub.j is fixed;
• means for extending said cumulative functions hx(X.sub.i) and hy(Y.sub.j) into continuous cumulative functions h.sub.x (X) and h.sub.y (Y), respectively;
• means for matching coordinates of said set of feature parameters and coordinates of said spatial density function .rho.(X.sub.i, Y.sub.j);
• and
• means for determining new sampling points (X.sub.i, Y.sub.j) of said set of feature parameters at new sampling intervals (.delta.i, .epsilon.j) in the X and Y directions, the new sampling intervals satisfying the condition that the product of said cumulative function hx(X.sub.i) and .delta.i takes a first fixed value, and the product of said cumulative function hy(Y.sub.j) and .epsilon.j takes a second fixed value,
• wherein said correlate of both the line pitch in the X direction and the line pitch in the Y direction is the sum of a term which includes the reciprocal of the line pitch in the X direction and a term which includes the reciprocal of the line pitch in the Y direction.

An apparatus for nonlinear normalization of an image, which performs pre-processing for computing the correlation between an unknown character and a reference pattern, the unknown character being formed of lines and having a line pitch in the X direction and a line pitch in the Y direction, said apparatus comprising:

• means for obtaining a set of feature parameters from a two-dimensional pattern f(X.sub.i, Y.sub.j) (i=1-M, j=1-N) which is obtained by sampling said unknown character at a sampling interval .gamma.;
• means for computing a local spatial density function .rho.(X.sub.i, Y.sub.j) from said two-dimensional pattern f(X.sub.i, Y.sub.j), said spatial density function .rho.(X.sub.i, Y.sub.j) being obtained as a correlate of both the line pitch in the X direction and the line pitch in the Y direction;
• means for computing an X-direction cumulative function hx(X.sub.i) by successively adding said spatial density function .rho.(X.sub.i, Y.sub.j) while Y.sub.j is varied from Y.sub.1 to Y.sub.J and X.sub.i is fixed;
• means for computing a Y-direction cumulative function hy(Y.sub.j) by successively adding said spatial density function .rho.(X.sub.i, Y.sub.j) while Xi is varied from X.sub.1 to X.sub.I and Y.sub.j is fixed;
• means for extending said cumulative functions hx(X.sub.i) and hy(Y.sub.j) into continuous cumulative functions h.sub.x (X) and h.sub.y (Y), respectively;
• means for matching coordinates of said set of feature parameters and coordinates of said spatial density function .rho.(X.sub.i, Y.sub.j);
• and
• means for determining new sampling points (X.sub.i, Y.sub.j) of said set of feature parameters at new sampling intervals (.delta.i, .epsilon.j) in the X and Y directions, the new sampling intervals satisfying the condition that the product of said cumulative function hx(X.sub.i) and .delta.i takes a first fixed value, and the product of said cumulative function hy(Y.sub.j) and .epsilon.j takes a second fixed value,
• wherein said correlate of both the line pitch in the X direction and the line pitch in the Y direction is the reciprocal of the sum of a term which includes the line pitch in the X direction and a term which includes the line pitch in the Y direction.

A method for nonlinear normalization of an image, which performs pre-processing for computing the correlation between an unknown character and a reference pattern, the unknown character being formed of lines and having a line pitch in the X direction and a line pitch in the Y direction, said method comprising the steps of:

• obtaining a local spatial density function .rho.(X.sub.i, Y.sub.j) (i=1-I, j=1-J) from a two-dimensional pattern f(X.sub.i, Y.sub.j) which is obtained by sampling said unknown character at a sampling interval .gamma., said spatial density function .rho.(X.sub.i, Y.sub.j) being obtained as a correlate of both the line pitch in the X direction and the line pitch in the Y direction;
• computing an X-direction cumulative function hx(X.sub.i) by successively adding said spatial density function .rho.(X.sub.i, Y.sub.j) while Y.sub.j is varied from Y.sub.1 to Y.sub.J and X.sub.i is fixed;
• computing a Y-direction cumulative function hy(Y.sub.j) by successively adding said spatial density function .rho.(X.sub.i, Y.sub.j) while X.sub.i is varied from X.sub.1 to X.sub.I and Y.sub.j is fixed;
• extending said cumulative functions hx(X.sub.i) and hy(Y.sub.j) into continuous cumulative functions hx(X) and hy(Y), respectively;
• determining new sampling points (X.sub.i, Y.sub.j) at new sampling intervals (.delta.i, .epsilon.j) in the X and Y directions, the new sampling intervals satisfying the condition that the product of said cumulative function hx(X.sub.i) and .delta.i takes a first fixed value, and the product of said cumulative function hy(Y.sub.j) and .epsilon.j takes a second fixed value;
• and
• computing normalized sampled values at said new sampling points (X.sub.i, Y.sub.j) by resampling said unknown character or by performing a computation on said two-dimensional pattern f(X.sub.i, Y.sub.j),
• wherein said correlate of both the line pitch in the X direction and the line pitch in the Y direction is a function of the product of the reciprocals of said line pitches in the X and Y directions.

A method for nonlinear normalization of an image, which performs pre-processing for computing the correlation between an unknown character and a reference pattern, the unknown character being formed of lines and having a line pitch in the X direction and a line pitch in the Y direction, said method comprising the steps of:

• obtaining a local spatial density function .rho.(X.sub.i, Y.sub.j) (i=1-I, j=1-J) from a two-dimensional pattern f(X.sub.i, Y.sub.j) which is obtained by sampling said unknown character at a sampling interval .gamma., said spatial density function .rho.(X.sub.i, Y.sub.j) being obtained as a correlate of both the line pitch in the X direction and the line pitch in the Y direction;
• computing an X-direction cumulative function hx(X.sub.i) by successively adding said spatial density function .rho.(X.sub.i, Y.sub.j) while Y.sub.j is varied from Y.sub.1 to Y.sub.J and X.sub.i is fixed;
• computing a Y-direction cumulative function hy(Y.sub.j) by successively adding said spatial density function .rho.(X.sub.i, Y.sub.j) while X.sub.i is varied from X.sub.1 to X.sub.I and Y.sub.j is fixed;
• extending said cumulative functions hx(X.sub.i) and hy(Y.sub.j) into continuous cumulative functions hx(X) and hy(Y), respectively;
• determining new sampling points (X.sub.i, Y.sub.j) at new sampling intervals (.delta.i, .epsilon.j) in the X and Y directions, the new sampling intervals satisfying the condition that the product of said cumulative function hx(X.sub.i) and .delta.i takes a first fixed value, and the product of said cumulative function hy(Y.sub.j) and .epsilon.j takes a second fixed value;
• and
• computing normalized sampled values at said new sampling points (X.sub.i, Y.sub.j) by resampling said unknown character or by performing a computation on said two-dimensional pattern f(X.sub.i, Y.sub.j),
• wherein said correlate of both the line pitch in the X direction and the line pitch in the Y direction is the sum of a term which includes the reciprocal of the line pitch in the X direction and a term which includes the reciprocal of the line pitch in the Y direction.

A method for nonlinear normalization of an image, which performs pre-processing for computing the correlation between an unknown character and a reference pattern, the unknown character being formed of lines and having a line pitch in the X direction and a line pitch in the Y direction, said method comprising the steps of:

• obtaining a local spatial density function .rho.(X.sub.i, Y.sub.j) (i=1-I, j=1-J) from a two-dimensional pattern f(X.sub.i, Y.sub.j) which is obtained by sampling said unknown character at a sampling interval .gamma., said spatial density function .rho.(X.sub.i, Y.sub.j) being obtained as a correlate of both the line pitch in the X direction and the line pitch in the Y direction;
• computing an X-direction cumulative function hx(X.sub.i) by successively adding said spatial density function .rho.(X.sub.i, Y.sub.j) while Y.sub.j is varied from Y.sub.1 to Y.sub.J and X.sub.i is fixed;
• computing a Y-direction cumulative function hy(Y.sub.j) by successively adding said spatial density function .rho.(X.sub.i, Y.sub.j) while X.sub.i is varied from X.sub.i to X.sub.I and Y.sub.j is fixed;
• extending said cumulative functions hx(X.sub.i) and hy(Y.sub.j) into continuous cumulative functions hx(X) and hy(Y), respectively;
• determining new sampling points (X.sub.i, Y.sub.j) at new sampling intervals (.delta.i, .epsilon.j) in the X and Y directions, the new sampling intervals satisfying the condition that the product of said cumulative function hx(X.sub.i) and .delta.i takes a first fixed value, and the product of said cumulative function hy(Y.sub.j) and .epsilon.j takes a second fixed value;
• and
• computing normalized sampled values at said new sampling points (X.sub.i, Y.sub.j) by resampling said unknown character or by performing a computation on said two-dimensional pattern f(X.sub.i, Y.sub.j),
• wherein said correlate of both the line pitch in the X direction and the line pitch in the Y direction is the reciprocal of the sum of a term which includes the line pitch in the X direction and a term which includes the line pitch in the Y direction.

A method for nonlinear normalization of an image, which performs pre-processing for computing the correlation between an unknown character and a reference pattern, the unknown character being formed of lines and having a line pitch in the X direction and a line pitch in the Y direction, said method comprising the steps of:

• obtaining a set of feature parameters from a two-dimensional pattern f(X.sub.i, Y.sub.j) (i=1-M, j=1-N) which is obtained by sampling said unknown character at a sampling interval .gamma.;
• computing a local spatial density function .rho.(X.sub.i, Y.sub.j) from said two-dimensional pattern f(X.sub.i, Y.sub.j), said spatial density function .rho.(X.sub.i, Y.sub.j) being obtained as a correlate of both the line pitch in the X direction and the line pitch in the Y direction;
• computing an X-direction cumulative function hx(X.sub.i) by successively adding said spatial density function .rho.(X.sub.i, Y.sub.j) while Y.sub.j is varied from Y.sub.1 to Y.sub.J and X.sub.i is fixed;
• computing a Y-direction cumulative function hy(Y.sub.j) by successively adding said spatial density function .rho.(X.sub.i, Y.sub.j) while X.sub.i is varied from X.sub.1 to X.sub.I and Y.sub.j is fixed;
• extending said cumulative functions hx(X.sub.i) and hy(Y.sub.j) into continuous cumulative functions hx(X) and hy(Y). respectively;
• matching coordinates of said set of feature parameters and coordinates of said spatial density function .rho.(X.sub.i, Y.sub.j);
• and
• determining new sampling points (X.sub.i, Y.sub.j) of said set of feature parameters at new sampling intervals (.delta.i, .epsilon.j) in the X and Y directions, the new sampling intervals satisfying the condition that the product of said cumulative function hx(X.sub.i) and .delta.i takes a first fixed value, and the product of said cumulative function hy(Y.sub.j) and .epsilon.j takes a second fixed value,
• wherein said correlate of both the line pitch in the X direction and the line pitch in the Y direction is a function of the product of the reciprocals of said line pitches in the X and Y directions.

A method for nonlinear normalization of an image, which performs pre-processing for computing the correlation between an unknown character and a reference pattern, the unknown character being formed of lines and having a line pitch in the X direction and a line pitch in the Y direction, said method comprising the steps of:

• obtaining a set of feature parameters from a two-dimensional pattern f(X.sub.i, Y.sub.j) (i=1-M, j=1-N) which is obtained by sampling said unknown character at a sampling interval .gamma.;
• computing a local spatial density function .rho.(X.sub.i, Y.sub.j) from said two-dimensional pattern f(X.sub.i, Y.sub.j), said spatial density function .rho.(X.sub.i, Y.sub.j) being obtained as a correlate of both the line pitch in the X direction and the line pitch in the Y direction;
• computing an X-direction cumulative function hx(X.sub.i) by successively adding said spatial density function .rho.(X.sub.i, Y.sub.j) while Y.sub.j is varied from Y.sub.1 to Y.sub.J and X.sub.i is fixed;
• computing a Y-direction cumulative function hy(Y.sub.j) by successively adding said spatial density function .rho.(X.sub.i, Y.sub.j) while X.sub.i is varied from X.sub.1 to X.sub.I and Y.sub.j is fixed;
• extending said cumulative functions hx(X.sub.i) and hy(Y.sub.j) into continuous cumulative functions hx(X) and hy(Y), respectively;
• matching coordinates of said set of feature parameters and coordinates of said spatial density function .rho.(X.sub.i, Y.sub.j);
• and
• determining new sampling points (X.sub.i, Y.sub.j) of said set of feature parameters at new sampling intervals (.delta.i, .epsilon.j) in the X and Y directions, the new sampling intervals satisfying the condition that the product of said cumulative function hx(X.sub.i) and .delta.i takes a first fixed value, and the product of said cumulative function hy(Y.sub.j) and .epsilon.j takes a second fixed value,
• wherein said correlate of both the line pitch in the X direction and the line pitch in the Y direction is the sum of a term which includes the reciprocal of the line pitch in the X direction and a term which includes the reciprocal of the line pitch in the Y direction.

A method for nonlinear normalization of an image, which performs pre-processing for computing the correlation between an unknown character and a reference pattern, the unknown character being formed of lines and having a line pitch in the X direction and a line pitch in the Y direction, said method comprising the steps of:

• obtaining a set of feature parameters from a two-dimensional pattern f(X.sub.i, Y.sub.j) (i=1-M, j=1-N) which is obtained by sampling said unknown character at a sampling interval .gamma.;
• computing a local spatial density function .rho.(X.sub.i, Y.sub.j) from said two-dimensional pattern f(X.sub.i, Y.sub.j), said spatial density function .rho.(X.sub.i, Y.sub.j) being obtained as a correlate of both the line pitch in the X direction and the line pitch in the Y direction;
• computing an X-direction cumulative function hx(X.sub.i) by successively adding said spatial density function .rho.(X.sub.i, Y.sub.j) while Y.sub.j is varied from Y.sub.1 to Y.sub.J and X.sub.i is fixed;
• computing a Y-direction cumulative function hy(Y.sub.j) by successively adding said spatial density function .rho.(X.sub.i, Y.sub.j) while X.sub.i is varied from X.sub.1 to X.sub.I and Y.sub.j is fixed;
• extending said cumulative functions hx(X.sub.i) and hy(Y.sub.j) into continuous cumulative functions hx(X) and hy(Y), respectively;
• matching coordinates of said set of feature parameters and coordinates of said spatial density function .rho.(X.sub.i, Y.sub.j);
• and
• determining new sampling points (X.sub.i, Y.sub.j) of said set of feature parameters at new sampling intervals (.delta.i, .epsilon.j) in the X and Y directions, the new sampling intervals satisfying the condition that the product of said cumulative function hx(X.sub.i) and .delta.i takes a first fixed value, and the product of said cumulative function hy(Y.sub.j) and .epsilon.j takes a second fixed value,
• wherein said correlate of both the line pitch in the X direction and the line pitch in the Y direction is the reciprocal of the sum a term which includes the line pitch in the X direction and a term which includes the line pitch in the Y direction.