  This paper offers a new authentication algorithm based on image matching of
nano-resolution visual identifiers with tree-shaped patterns. The algorithm
includes image-to-tree conversion by greedy extraction of the fractal pattern
skeleton along with a custom-built graph matching algorithm that is robust
against imaging artifacts such as scaling, rotation, scratch, and illumination
change. The proposed algorithm is applicable to a variety of tree-structured
image matching, but our focus is on dendrites, recently-developed visual
identifiers. Dendrites are entropy rich and unclonable with existing 2D and 3D
printers due to their natural randomness, nano-resolution granularity, and 3D
facets, making them an appropriate choice for security applications such as
supply chain trace and tracking. The proposed algorithm improves upon graph
matching with standard image descriptors. For instance, image inconsistency due
to the camera sensor noise may cause unexpected feature extraction leading to
inaccurate tree conversion and authentication failure. Also, previous tree
extraction algorithms are prohibitively slow hindering their scalability to
large systems. In this paper, we fix the current issues of [1] and accelerate
the key points extraction up to 10-times faster by implementing a new skeleton
extraction method, a new key points searching algorithm, as well as an
optimized key point matching algorithm. Using minimum enclosing circle and
center points, make the algorithm robust to the choice of pattern shape. In
contrast to [1] our algorithm handles general graphs with loop connections,
therefore is applicable to a wider range of applications such as transportation
map analysis, fingerprints, and retina vessel imaging.
