Abstract: The invention relates to a method of designing a refractive transparent or partially transparent light-redirecting surface, or a reflective light-redirecting surface, of a caustic layer comprising providing a discrete representation of an input target image, calculating a generalized power diagram for a set of image pixels pi of the target image and computing a piecewise light-redirecting surface of the caustic layer based on a calculated optimal set of weights minimizing a cost function associated with the set of image pixels pi. The invention also relates to an optical security element, a marked object, a method of visually authenticating an object and use of the optical security element for authenticating or securing against counterfeiting.

Abstract: A method of authenticating a product by taking an image of the product and comparing the image with a reference image of a genuine product taken previously to determine if the products in the two images are the same. The two images are captured under substantially similar conditions so that the two images are as similar as possible prior to the comparison. The two images are processed in order to calculate for each of them a list of significant points. The significant points are compared to determine a degree of correspondence between the significant points. An answer is output indicating the authenticity of the product based on the degree of correspondence. Some of the matching significant points may be used to define a common coordinate system for the two images. The two lists of significant points may be compared in this common coordinate system.

Abstract: A method of authenticating a product by taking an image of the product and comparing the image with a reference image of a genuine product taken previously to determine if the products in the two images are the same. The two images are captured under substantially similar conditions so that the two images are as similar as possible prior to the comparison. The two images are processed in order to calculate for each of them a list of significant points. The significant points are compared to determine a degree of correspondence between the significant points. An answer is output indicating the authenticity of the product based on the degree of correspondence. Some of the matching significant points may be used to define a common coordinate system for the two images. The two lists of significant points may be compared in this common coordinate system.