Autocorrelation-based Fiducial Markers for Traceability

Classical approaches to the rectification of a single image of a product, without stereo correspondences, require spatial landmarks. These landmarks, constructed from high-contrast elementary shapes that can be detected with simple algorithms, are highly conspicuous. To rectify complex deformations, one can use chessboard patterns of markers with elements that break quadrilateral symmetry, such as the three eyes of a QR code. However, these marker boards are even more conspicuous than a single marker. In traceability applications, only one site of marking is used, limiting the complexity of the surface on which it can be read, and exposing the mark to deidentification attacks for diversion of the product to a grey market. We introduce a method for constructing stealth and robust fiducial markers that can be displayed across a surface, limiting exposure to marker tampering for product deidentification. These markers, which we refer to as self-rectifying textures, can be used to rectify complex deformations by solving an inverse problem rather than relying on pixel correspondences of conspicuous landmarks. These stealth textures place fiducial markers in the autocorrelation of the image. In this way, crops of the deformed texture can be rectified using only these spatially invariant statistical properties. Affine transformations of an image correspond to linear transformations of the autocorrelation, without phase component. Exploiting this fact, self-rectifying textures enable the local estimation of the differential of a planar deformation by identifying landmarks in the autocorrelation image, such as peaks, whose locations in the fronto-parallel view of the texture are known. The translation component can be recovered independently via phase correlation. A rectifying map, modulo translations, can also be fit directly to local observations of the differential of the deformation, without access to the rectified texture or need for phase correlation. Self-rectifying textures can be used for communication, watermarking, authentication, surface identification, calibration, and geometry processing.