Circular coding with interleaving phase

A general two-dimensional coding method is presented that allows recovery of data based on only a cropped portion of the code, and without knowledge of the carrier image. A description of both an encoding and recovery system is provided. Our solution involves repeating a payload with a fixed number of bits, assigning one bit to every symbol in the image - whether that symbol is data carrying or non-data carrying - with the goal of guaranteeing recovery of all the bits in the payload. Because the technique is applied to images, for aesthetic reasons we do not use fiducials, and do not employ any end-of-payload symbols. The beginning of the payload is determined by a phase code that is interleaved between groups of payload rows. The recovery system finds the phase row by evaluating candidate rows, and ranks confidence based on the sample variance. The target application is data-bearing clustered-dot halftones, so special consideration is given to the resulting checkerboard subsampling. This particular application is examined via exhaustive simulations to quantify the likelihood of unrecoverable bits and bit redundancy as a function of offset, crop window size, and phase code spacing.