1. A method of applying a watermark to an image, the method comprising:
(a) providing image data that represents the image;
(b) providing a first message string that includes a first plurality of message bits and a second message string that includes a second plurality of message bits;
(c) arraying the message bits of the first message string at points of a four-dimensional lattice, the four-dimensional lattice being formed as a product of a two-dimensional position-domain lattice and a two-dimensional frequency-domain lattice;
(d) generating wavepacket data by convolving each of the message bits of the first message string with a respective watermark function in accordance with a position of the respective bit of the first message string in the four-dimensional lattice, thereby forming data corresponding to a respective wavepacket for each \u201c1\u201d bit of the first message string;
(e) modifying at least one of an intensity level and a phase of the respective wavepacket data for at least some of the \u201c1\u201d bits of the first message string to encode in the wavepacket data a message which corresponds to the second message string; and
(f) combining the modified wavepacket data generated at step (e) with the image data provided at step (a) to generate combined image data.
2. The method according to claim 1, further comprising:
(g) transforming pixel values of the combined image data.
3. The method according to claim 2, further comprising:
(h) printing an image using the transformed pixel values resulting from step (g).
4. The method according to claim 3, wherein the image is printed as part of a postage meter indicium.
5. The method according to claim 1, wherein phases of the wavepacket data are not modified in step (e).
6. The method according to claim 5, wherein two bits of the second message string are encoded in the wavepacket data for each \u201c1\u201d bit of the first message string.
7. The method according to claim 1, wherein the second message string represents an encrypted message.
8. A method of determining whether a printed-image-under-examination (PIUE) is authentic, the PIUE including a watermark formed of a plurality of wavepackets, the method comprising:
(a) scanning the PIUE to generate scanned image data comprising pixel data, the pixel data comprising gray scale values and representing the PIUE as a set of scanning pixels;
(b) forming a plurality of data blocks from the scanned image data, each data block consisting of pixel data which corresponds to a respective region of the PIUE;
(c) transforming the pixel data in at least some of the data blocks to obtain transform domain data;
(d) applying a watermark detecting operation to the transform domain data for respective ones of the data blocks to detect at least one of (i) variations in intensity among the wavepackets, and (ii) variations in phase among the wavepackets; and
(e) analyzing the detected variations in intensity andor variations in phase to detect a message encoded with said variations in intensity andor variations in phase.
9. The method according to claim 8, wherein step (c) includes applying at least one of a Fourier transform, a fast Fourier transform, a discrete cosine transform (DCT) and a wavelet transform to the pixel data in the at least some of the data blocks to obtain the transform domain data.
10. The method according to claim 8, wherein the PIUE is part of a postal indicium.
11. The method according to claim 8, wherein the regions of the PIUE to which the data blocks correspond are at least partially overlapping with each other.
12. The method according to claim 8, wherein step (d) includes detecting variations in phase among the wavepackets;
and further comprising:
presenting the detected variations in phase in the form of a color map comprising a plurality of colors each of which represents a respective phase.
The claims below are in addition to those above.
All refrences to claim(s) which appear below refer to the numbering after this setence.
1. A fuel cell stack comprising a cell stack in which a plurality of fuel battery single cells are stacked, a pair of end plates which sandwich the cell stack from respective sides in a stack direction, and a system component which is mounted on one end plate, and in which there is formed a manifold that extends in and through the cell stack in the stack direction and for supplying and discharging a fuel gas or an oxidizing agent gas for each of the fuel battery single cells, wherein
the one end plate has a stack-facing surface which faces the cell stack and a system component mounting surface on a side opposite of the stack facing surface, and a system component mounting portion for mounting the system component being formed in a projected manner on the system component mounting surface, and
the system component mounting portion has a trapezoidal side surface with a tip surface of the system component mounting portion having an inclination angle with respect to the stack-facing surface so that, when the fuel cell stack is placed such that the manifold has a downward inclination toward the one end plate, the surface of the system component mounting portion is oriented along a vertical direction,
wherein the system component includes at least a pump and a pipe.
2. The fuel cell stack according to claim 1, wherein
the one end plate is composed of a flat plate section having a constant thickness on a surface of which the system component mounting portion is formed in a projected manner.
3. The fuel cell stack according to claim 1, wherein
a lower side corner of the other end plate of the pair of end plates is removed.
4. The fuel cell stack according to claim 1, wherein
an upper side corner of the other end plate of the pair of end plates is removed.