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A method of encoding a hidden image in high frequency spatial frequencies of a line pattern of a host image. A set of host image spatial frequencies is generated based on a predefined mapping of a domain of a set of representative scalar values of the hidden image and a domain of the host image spat

A method of encoding a hidden image in high frequency spatial frequencies of a line pattern of a host image. A set of host image spatial frequencies is generated based on a predefined mapping of a domain of a set of representative scalar values of the hidden image and a domain of the host image spatial frequencies. The line pattern of the host image is generated based on the set of host image spatial frequencies. The host image may be composed of tiles containing parallel line segments, with each tile encoding a corresponding one of the scalar values. The host image may be composed of a stochastic line pattern generated from a white noise image convolved with a space variable kernel based on the predefined domain mapping. The hidden image may be decoded algorithmically or optically in a single step.

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1. A method of making a secure document including a host image encoding a hidden image, the method comprising: inputting the hidden image;determining a set of representative scalar values based on the hidden image;generating a set of host image spatial frequencies corresponding to the set of represe

1. A method of making a secure document including a host image encoding a hidden image, the method comprising: inputting the hidden image;determining a set of representative scalar values based on the hidden image;generating a set of host image spatial frequencies corresponding to the set of representative scalar values, wherein each host image spatial frequency is generated based on the corresponding representative scalar value and a predefined mapping of a domain of the set of representative scalar values and a domain of the host image spatial frequencies;generating the host image based on the set of host image spatial frequencies, the host image comprising a line pattern characterized by the set of host image spatial frequencies; andincorporating the host image in the secure document,wherein determining the set of representative scalar values comprises: resolving the hidden image into a set of hidden image tiles corresponding to the set of representative scalar values, each hidden image tile containing a corresponding subset of the hidden image; andfor each hidden image tile, determining the corresponding representative scalar value based on the corresponding subset of the hidden image contained in the hidden image tile;generating the host image comprises: generating a set of host image tiles corresponding to the set of representative scalar values, each host image tile containing a corresponding subset of the line pattern characterized by the host image spatial frequency corresponding to the representative scalar value corresponding to the host image tile; andassembling the host image tiles according to a predefined arrangement. 2. The method according to claim 1, wherein the hidden image is a greyscale image, and wherein, for each hidden image tile, determining the corresponding representative scalar value based on the corresponding subset of the hidden image contained in the hidden image tile comprises determining a representative greyscale value of the subset of the greyscale image contained in the hidden image tile. 3. The method according to claim 1, wherein the set of host image tiles comprises a plurality of circles or a plurality of edge-sharing polygons. 4. The method according to claim 1, wherein, for each host image tile, the subset of the line pattern contained in the host image tile comprises a set of spaced parallel line segments, wherein a spatial frequency of the set of line segments is characterized by the corresponding host image spatial frequency. 5. The method according to claim 1, wherein the line pattern comprises a plurality of line segments, the method further comprising: incorporating a visible image into the host image, wherein a thickness of each of selected ones of the line segments is selectively increased or decreased. 6. The method according to claim 1, wherein: determining the set of representative scalar values comprises determining each representative scalar value at a corresponding point in the hidden image;generating the host image comprises: generating a white noise image, wherein, for each of a plurality of points in the white noise image, a value of the white noise image is generated at least in part based on a probabilistic variable;generating an intermediate image based on a convolution of the white noise image with a space variable kernel, wherein, for each specified point in a plane of the intermediate image, a value of the space variable kernel is based on:a decay function characterized in that a value of the decay function decreases with distance from the specified point; anda periodic function characterized in that a value of the periodic function varies periodically with distance from the specified point and is dependent upon the host image spatial frequency corresponding to the representative scalar value determined for a corresponding point in the hidden image; andbinarizing the intermediate function according to a predefined threshold value, thereby generating the host image. 7. The method according to claim 6, wherein the hidden image is a greyscale image, and wherein each representative scalar value is determined based on a greyscale value of the greyscale image at the corresponding point in the greyscale image. 8. The method according to claim 6, wherein the space variable kernel is determined based on formula (1): h(x,y,u,v)=g(x,y)·sin(u·x+v·y) wherein (x, y) is the specified point in the plane of the intermediate image and the corresponding point in the hidden image, (u, v) are points in an angular frequency plane determined by the host image spatial frequency corresponding to the representative scalar value determined for the corresponding point (x, y) in the hidden image, h(x,y,u,v) is the space variable kernel, and g(x, y) is the decay function, wherein the decay function is a Gaussian function. 9. The method according to claim 6 further comprising: incorporating a visible image into the host image, wherein a thickness of selected graphical elements of the host image are selectively increased or decreased. 10. The method according to claim 1, wherein the hidden image is a first hidden image, the set of representative scalar values is a set of first representative scalar values, the set of host image spatial frequencies is a set of first host image spatial frequencies, and the predefined mapping is a first predefined mapping, the method further comprising: inputting a second hidden image;determining a set of second representative scalar values based on the second hidden image;generating a set of second host image spatial frequencies corresponding to the set of second representative scalar values, wherein each second host image spatial frequency is generated based on the corresponding second representative scalar value and a second predefined mapping of a domain of the set of second representative scalar values and a domain of the set of second host image spatial frequencies, wherein the domain of the set of first host image spatial frequencies and the domain of the set of second host image spatial frequencies are non-overlapping; andgenerating the host image based further on the set of second host image spatial frequencies. 11. The method according to claim 10, wherein: the host image comprises a first host image and a second host image, the first host image comprising a first subset of the line pattern, the second host image comprising a second subset of the line pattern;the first subset of the line pattern is characterized by the set of first host image spatial line frequencies;the second subset of the line pattern is characterized by the set of second host image spatial line frequencies; andincorporating the host image in the secure document comprises: printing the first host image on a substrate of the secure document using a first ink imageable under a first illumination spectrum, wherein the first ink is also imageable under a second illumination spectrum non-overlapping with the first illumination spectrum; andprinting the second host image on the substrate of the secure document using a second ink imageable under the second illumination spectrum, wherein the second ink is also imageable under a third illumination spectrum non-overlapping with the first and second illumination spectrums;wherein the first host image is imageable separately from the second host image under only the first illumination spectrum, and the second host image is imageable separately from the first host image under only the third illumination spectrum. 12. The method according to claim 1, wherein the hidden image is a first hidden image, the domain of the host image spatial frequencies comprises non-overlapping first and second sub-domains, and the predefined mapping maps the domain of the set of representative scalar values redundantly to the first and second sub-domains, the method further comprising: inputting a second hidden image;determining a set of representative binary values based on the second hidden image, the set of representative binary values corresponding to the set of representative scalar values;wherein each host image spatial frequency is generated based on the predefined mapping to only the first sub-domain or only the second sub-domain based on the corresponding representative binary value. 13. The method according to claim 12, wherein: a first sub-set of the line pattern is generated based on a first subset of the host image spatial frequencies based on the predefined mapping to the first sub-domain;a second sub-set of the line pattern is generated based on a second subset of the host image spatial frequencies based on the predefined mapping to the second sub-domain;each host image spatial frequency comprises a spatial frequency vector comprising a spatial frequency direction;the spatial frequency direction of each of the host image spatial frequencies based on the predefined mapping to the first sub-domain is within a first domain of spatial frequency directions;the spatial frequency direction of each of the host image spatial frequencies based on the predefined mapping to the second sub-domain is within a second domain of spatial frequency directions; andthe first domain of spatial frequency directions is non-overlapping with the second domain of spatial frequency directions. 14. The method according to claim 1, wherein: incorporating the host image in the secure document comprises printing the host image on a substrate of the secure document using a first ink imageable under a first illumination spectrum, wherein the first ink is also imageable under a second illumination spectrum non-overlapping with the first illumination spectrum;the method further comprising: printing a noise screen on the substrate of the secure document in overlapping relation to the host image using a second ink imageable under the second illumination spectrum;wherein the host image is imageable separately from the noise screen under the first illumination spectrum, and is imageable only in combination with the noise screen under the second illumination spectrum. 15. The method according to claim 14, wherein graphical elements of the noise screen are characterized by spatial frequencies falling within the domain of the host image spatial frequencies. 16. The method according to claim 1, wherein: the line pattern comprises a plurality of line segments including a first set of line segments and a second set of line segments; andincorporating the host image in the secure document comprises: printing the first set of line segments on a substrate of the secure document using a first ink imageable under a first illumination spectrum, wherein the first ink is also imageable under a second illumination spectrum non-overlapping with the first illumination spectrum; andprinting the second set of line segments on the substrate of the secure document using a second ink, wherein the second ink is imageable under only the second illumination spectrum, or wherein the second ink is imageable under only the second illumination spectrum and a third illumination spectrum non-overlapping with the first and second illumination spectrums;whereby the first and second sets of line segments of the line pattern of the host image are imageable together under only the second illumination spectrum. 17. The method according to claim 16, wherein the first set of line segments are interleaved with the second set of line segments. 18. An apparatus for making a secure document including a host image encoding a hidden image, the apparatus comprising processing circuitry and a memory configured to perform the method according to claim 1. 19. A method of generating a decoded image from a host image comprising a periodic line pattern encoding a hidden image, the method comprising: inputting the host image;generating a frequency domain representation of a decoding filter, wherein a value of the decoding filter at any specified point in the frequency domain is based on a predefined mapping of a domain of a set of representative scalar values of the decoded image and a domain of host image spatial frequencies of the host image;generating a frequency domain representation of the host image,generating the set of representative scalar values based on the host image spatial frequencies of the host image and the decoding filter;generating the decoded image based on the set of representative scalar values; andoutputting the decoded image,wherein generating the set of representative scalar values comprises:generating a filtered image based on an entrywise product of the frequency domain representation of the host image and the frequency domain representation of the decoding filter; andgenerating a spatial domain representation of the filtered image, the spatial domain representation comprising the set of representative scalar values. 20. The method according to claim 19, wherein: the frequency domain representation of the host image comprises a Fourier transform of the host image; andthe spatial domain representation of the filtered image comprises an inverse Fourier transform of the filtered image. 21. The method according to claim 19 further comprising: displaying the decoded image. 22. A method of generating a decoded image from a host image comprising a periodic line pattern encoding a hidden image, the method comprising: inputting the host image;generating a frequency domain representation of a decoding filter, wherein a value of the decoding filter at any specified point in the frequency domain is based on a predefined mapping of a domain of a set of representative scalar values of the decoded image and a domain of host image spatial frequencies of the host image;generating a spatial domain representation of the decoding filter corresponding to the frequency domain representation of the decoding filter,generating the set of representative scalar values based on the host image spatial frequencies of the host image and the decoding filter;generating the decoded image based on the set of representative scalar values; andoutputting the decoded image, and and wherein generating the set of representative scalar values comprises:generating a filtered image based on a convolution of a spatial domain representation of the host image and the spatial domain representation of the decoding filter;wherein the filtered image comprises the set of representative scalar values. 23. An apparatus for generating a decoded image from a host image comprising a periodic line pattern encoding a hidden image, the apparatus comprising processing circuitry and a memory configured to perform the method according to claim 20. 24. The apparatus according to claim 23 further comprising an imager for capturing the host image from a secure document. 25. The apparatus according to claim 23 further comprising a display for displaying the decoded image. 26. A method of generating a decoded image from a host image comprising a periodic line pattern encoding a hidden image, the method comprising: providing the host image on a transparent medium, wherein the periodic line pattern produces a transparency modulation in the transparent medium;illuminating the transparent medium with collimated monochromatic coherent light at normal incidence so as to transfer linearly the transparency modulation onto a light field amplitude of the light, thereby producing a modified light field;passing the modified light field through a lens system comprising an aperture based on a frequency domain representation of a decoding kernel based on a predefined mapping of a domain of representative scalar values of the hidden image and a domain of host image spatial frequencies, thereby producing a further modified light field;illuminating an image plane with the further modified light field, thereby generating the decoded image. 27. The method according to claim 26 using an optical 4f correlator comprising the lens system, the image plane, and a source of the collimated monochromatic coherent light.