Signal processors and methods for estimating geometric transformations of images for digital data extraction

A non-transitory computer readable medium, on which is stored instructions, which when executed by a processor, perform a method of determining a geometric transform of a reference signal in an image for extracting digital data, the method comprising:

• the following acts:
• for plural reference signal components of a reference signal, transforming coordinates of a reference signal component according to a candidate geometric transform;
• measuring correlation between the transformed reference signal component and the image, the measured correlation comprising a combination of complex components of a frequency domain transform of the image at neighboring integer coordinates around the coordinates of the transformed reference signal component, wherein the complex combination combines complex components according to a phase relationship at the neighboring integer coordinates, wherein the phase relationship comprises weighting neighboring integer coordinates according to a point spread function;
• updating, based on the measured correlation that is below a threshold, the coordinates of the reference signal component to a location within a neighborhood around the coordinates of the transformed reference signal component;
• determining a new geometric transform that transforms the reference signal components to the updated coordinates;
• and
• applying the new geometric transform to extract encoded digital data from the image.

An apparatus for determining a geometric transform of a reference signal in an image for extracting digital data, the apparatus comprising:

• means for transforming coordinates of a reference signal component according to a candidate geometric transform, for plural reference signal components of a reference signal;
• means for measuring correlation between the transformed reference signal component and the image, the measured correlation comprising a combination of complex components of the frequency domain transform of the image at neighboring integer coordinates around the coordinates of the transformed reference signal component, wherein the complex combination combines complex components according to a phase relationship at the neighboring integer coordinates, wherein the phase relationship comprises weighting neighboring integer coordinates according to a point spread function;
• means for updating, based on the measured correlation that is below a threshold, the coordinates of the reference signal component to a location within a neighborhood around the coordinates of the transformed reference signal component;
• determining a new geometric transform that transforms the reference signal components to the updated coordinates;
• and
• means for applying the new geometric transform to extract encoded digital data from the image.