Scalar data processing method and apparatus

Claim 2

A scalar data processing method for compressing two-dimensional scalar data defined on a two-dimensional surface having a horizontal direction and a vertical direction and for reconstructing said two-dimensional scalar data based on said compressed data, comprising the steps of: (a) detecting edge lines of said two-dimensional scalar data, said edge lines being detected when a change in value of said two-dimensional scalar data between adjacent points on said two-dimensional surface is larger than a predetermined threshold value; (b) cutting a domain on a horizontal line intersecting said edge lines and between said edge lines; (c) determining a function as an approximation of a Laplacian of said two-dimensional scalar data at each point in said domain; (d) compressing said two-dimensional scalar data by replacing aid two-dimensional scalar data at every point with scalar data at said edge lines, scalar data for providing gradients of said two-dimensional scalar data on said edge lines, and said function, to produce replaced data; and (e) reconstructing said two-dimensional scalar data by interpolating said two-dimensional scalar data based on said scalar data at said edge lines, scalar data for providing gradients of said two-dimensional scalar data on said edge lines, and said function obtained in said compressing step.

Claim 3

A scalar data processing method as claimed in claim 1, wherein said detecting edge lines in step (a) comprises a step (a) for detecting data of said edge lines.

Claim 4

A scalar data processing method as claimed in claim 2, wherein said cutting in step (b) comprises a step for cutting said domain based on said data of said edge lines.

Claim 5

A scalar data processing method as claimed in claim 1, wherein said step (c) for determining the function, the function is zero.

Claim 6

A scalar data processing method as claimed in claim 1, wherein said step (c) for determining the function, the function is a constant value.

Claim 7

A scalar data processing method as claimed in claim 1, wherein said step (c) for determining the function, the function is a linear function with respect to a coordinate of the horizontal line.

Claim 8

A scalar data processing method as claimed in claim 1, wherein said step (c) for determining the function, the function is a secondary order function with respect to a coordinate of the horizontal line.

Claim 9

A scalar data processing method as claimed in claim 1, wherein said step (c) for determining the function, the function is a third order function with respect to a coordinate of the horizontal line.

Claim 10

A scalar data processing method as claimed in claim 1, wherein said step (c) for determining the function, the function is determined by the method of least-square approximation with respect to the function and the Laplacian of said two-dimensional scalar data at each point on said two-dimensional surface.

Claim 11

A scalar data processing method as claimed in claim 1, wherein in said step (d) for compressing said two-dimensional scalar data, said replaced data is transmitted from a transmitting side to a receiving side when said two-dimensional scalar data is to be transmitted.

Claim 12

A scalar data processing method as claimed in claim 1, wherein in said step (d) for compressing said two-dimensional scalar data, said replaced data is transmitted from a transmitting side to a receiving side, and wherein in said step (e) the interpolation is carried out in said receiving said.

Claim 13

A scalar data processing method as claimed in claim 1, wherein said step (d) for compressing said two-dimensional scalar data, said replaced data is stored for reconstructing the two-dimensional scalar data in its original form by said interpolation step.

Claim 14

A scalar data processing method as claimed in claim 1, wherein said step (e) for reconstructing said two-dimensional scalar data, said interpolation is carried out by successive approximation which includes a first approximation in which the approximated two-dimensional data is determined based on said edge lines and the gradients of the two-dimensional scalar data, and then a difference between said function and a value of a Laplacian of approximated two-dimensional scalar data at each point falls within a predetermined threshold value.

Claim 15

A scalar data processing method as claimed in claim 13, wherein in said step (e) for reconstructing said two-dimensional scalar data, said value of the Laplacian of approximated two-dimensional scalar data at each point is expressed as Δφk(i,j)=φk(i+1,j)+φk(i,j+1)+φk(i-1,j)+φk(i,j-1)-4φk(i,j), where i is an x coordinate, j is a y coordinate, and k is a number of successive approximations.

Claim 16

A scalar data processing method as claimed in claim 13, wherein said step (e) for reconstructing said two-dimensional scalar data, said value of the Laplacian of approximated two-dimensional scalar data at each point is expressed as Δφk(i,j)=2φk(i,j)-2φk(i-1,j)+φk(i-2,j)-2φk(i,j-1)+φk(i,j-2), where i is an x coordinate, j is a y coordinate, and k is a number of successive approximations.

Claim 17

A scalar data processing apparatus for compressing two-dimensional scalar data defined on a two-dimensional surface having a horizontal direction and a vertical direction and for reconstructing said two-dimensional scalar data based on said compressed data, comprising: edge line detecting means for detecting edge lines of said two-dimensional scalar data, said edge lines being detected when the change value of said two-dimensional scalar data between adjacent points on said two-dimensional surface is larger than a predetermined threshold value; domain cutting means for cutting a domain on a horizontal line intersecting with said edge lines and between said edge lines; function determining means for determining a function as an approximation of a Laplacian of said two-dimensional scalar data at each point in said domain; compressing means for compressing said two-dimensional scalar data by replacing said two-dimensional scalar data at every point with scalar data at said edge lines, scalar data for providing gradients of said two-dimensional scalar data on said edge lines, and said function; and reconstructing means for reconstructing said two-dimensional scalar data by interpolating said two-dimensional scalar data based on said scalar data at said edge lines, scalar data for providing gradients of said two-dimensional scalar data on said edge lines, and said function.

Claim 18

A scalar data processing apparatus for compressing two-dimensional scalar data defined on a two-dimensional surface having a horizontal direction and a vertical direction and for reconstructing said two-dimensional scalar data based on said compressed data, comprising: edge line detecting means for detecting edge lines of said two-dimensional scalar data, said edge lines being detected when the change value of said two-dimensional scalar data between adjacent points on said two-dimensional surface is larger than a predetermined threshold value; domain cutting means for cutting a domain on a horizontal line intersecting with said edge lines and between said edge lines; function determining means for determining a function as an approximation of a Laplacian of said two-dimensional scalar data at each point in said domain; compressing means for compressing said two-dimensional scalar data by replacing said two-dimensional scalar data at every point with scalar data at said edge lines, scalar data for providing gradients of said two-dimensional scalar data on said edge lines, and said function; and reconstructing means for reconstructing said two-dimensional scalar data by interpolating said two-dimensional scalar data based on said scalar data at said edge lines, scalar data for providing gradients of said two-dimensional scalar data on said edge lines, and said function.