Abstract: On embedding electronic watermark data in point group data obtained from a three-dimensional measurement, an x-y plane region defining the point group data is divided into a plurality of small regions so that a point group is produced with respect to each of small regions. The coordinate values of each point group are offset with making a barycenter of the point group be an origin point. A discrete Fourier transform is carried out in order to produce a Fourier coefficient sequence, which is modified into a watermarked Fourier coefficient sequence. The inverse discrete Fourier transform is carried out on the watermarked coefficient sequence in order to produce a watermarked complex number sequence. An optimum watermark embedding strength is calculated. On the basis of the embedding strength, the Fourier coefficient sequence is modified to produce a watermarked Fourier coefficient sequence which is inversely offset into the watermarked point group data.

Abstract: On embedding electronic watermark data in point group data obtained from a three-dimensional measurement, an x-y plane region defining the point group data is divided into a plurality of small regions so that a point group is produced with respect to each of small regions. The coordinate values of each point group are offset with making a barycenter of the point group be an origin point. A discrete Fourier transform is carried out in order to produce a Fourier coefficient sequence, which is modified into a watermarked Fourier coefficient sequence. The inverse discrete Fourier transform is carried out on the watermarked coefficient sequence in order to produce a watermarked complex number sequence. An optimum watermark embedding strength is calculated. On the basis of the embedding strength, the Fourier coefficient sequence is modified to produce a watermarked Fourier coefficient sequence which is inversely offset into the watermarked point group data.

Abstract: On embedding electronic watermark data in point group data obtained from a three-dimensional measurement, an x-y plane region defining the point group data is divided into a plurality of small regions so that a point group is produced with respect to each of small regions. The coordinate values of each point group are offset with making a barycenter of the point group be an origin point. A discrete Fourier transform is carried out in order to produce a Fourier coefficient sequence, which is modified into a watermarked Fourier coefficient sequence. The inverse discrete Fourier transform is carried out on the watermarked coefficient sequence in order to produce a watermarked complex number sequence. An optimum watermark embedding strength is calculated. On the basis of the embedding strength, the Fourier coefficient sequence is modified to produce a watermarked Fourier coefficient sequence which is is inversely offset into the watermarked point group data.

Abstract: On embedding electronic watermark data in point group data which are obtained on the basis of a three-dimensional measurement, an x-y plane region defining the point group data is divided into a plurality of small regions in a predetermined number so that a point group is produced with respect to each of small regions. The x and y coordinate values of each point group are offset with making a barycenter of the point group be an origin point so that each point group is converted into an offset point group. The discrete Fourier transform is carried out with respect to each offset point group in order to produce the Fourier coefficient sequence, which is modified into a watermarked Fourier coefficient sequence in accordance with the electronic watermark data. The inverse discrete Fourier transform is carried out with respect to the watermarked Fourier coefficient sequence in order to produce a watermarked complex number sequence.